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数理人口学・数理生物学セミナー
過去の記録 ～04/17｜次回の予定｜今後の予定 04/18～
過去の記録
2023年03月24日(金)
10:00-11:00 オンライン開催
難波利幸 氏 (大阪公立大学)
ギルド内捕食系における予期せぬ共存と絶滅 (Japanese)
難波利幸 氏 (大阪公立大学)
ギルド内捕食系における予期せぬ共存と絶滅 (Japanese)
[ 講演概要 ]
３種以上の個体群からなる生物群集の動態には間接効果が大きな役割を果たす。３種の個体群からなる生物群集のモジュールでは，１捕食者－２被食者系と３栄養段階の食物連鎖ではカオスが，３種競争系ではヘテロクリニックサイクルが現れることなどが知られている。３種系の中でも，共通の資源を利用する２種の消費者の間に捕食－被食関係が生じるギルド内捕食系では，今なお，不明なことが多い。ギルド内捕食の基本モデルは，系の生産性が低いとき，高いときにはそれぞれ捕食者と中間の消費者が絶滅し，生産性が中間の時にのみ両者が共存することを予測するが，実証研究は高生産性環境での消費者の絶滅を支持しない。また，消費者は捕食者に食われるので，資源利用競争においては消費者が有利であることが共存の必要条件とされるが，本当にそうなのだろうか？ 本講演では，捕食者にとっての資源と消費者の餌としての好適度を鍵に，これらの謎の解明に挑む。
３種以上の個体群からなる生物群集の動態には間接効果が大きな役割を果たす。３種の個体群からなる生物群集のモジュールでは，１捕食者－２被食者系と３栄養段階の食物連鎖ではカオスが，３種競争系ではヘテロクリニックサイクルが現れることなどが知られている。３種系の中でも，共通の資源を利用する２種の消費者の間に捕食－被食関係が生じるギルド内捕食系では，今なお，不明なことが多い。ギルド内捕食の基本モデルは，系の生産性が低いとき，高いときにはそれぞれ捕食者と中間の消費者が絶滅し，生産性が中間の時にのみ両者が共存することを予測するが，実証研究は高生産性環境での消費者の絶滅を支持しない。また，消費者は捕食者に食われるので，資源利用競争においては消費者が有利であることが共存の必要条件とされるが，本当にそうなのだろうか？ 本講演では，捕食者にとっての資源と消費者の餌としての好適度を鍵に，これらの謎の解明に挑む。
2022年01月19日(水)
15:00-16:00 オンライン開催
梶原 毅 氏 (岡山大学名誉教授)
時間遅れ, 免疫, 吸収効果による不安定化
(Japanese)
オンラインですので，参加希望のかたは稲葉(inaba@ms.u-tokyo.ac.jp)へご連絡ください．
梶原 毅 氏 (岡山大学名誉教授)
時間遅れ, 免疫, 吸収効果による不安定化
(Japanese)
[ 講演概要 ]
生物集団, 特に病原体と細胞の係わるダイナミクスにおいて振動が起こる時,
しばしば時間遅れ, 宿主の免疫反応などが関係していることが多いが,
思いもかけない現象として, 病原体が宿主細胞に感染するときに１個, ある
いは数個減少する効果が振動に関係することもある。
本講演においては, ある場合において, これらの３つの効果の中で２つでは
振動が発生せず, ３つ揃うと振動が発生しうる状況について, 報告する。
また, 以前にさかのぼり, さまざまな場合における安定性の議論について
も振り返る。
[ 参考URL ]生物集団, 特に病原体と細胞の係わるダイナミクスにおいて振動が起こる時,
しばしば時間遅れ, 宿主の免疫反応などが関係していることが多いが,
思いもかけない現象として, 病原体が宿主細胞に感染するときに１個, ある
いは数個減少する効果が振動に関係することもある。
本講演においては, ある場合において, これらの３つの効果の中で２つでは
振動が発生せず, ３つ揃うと振動が発生しうる状況について, 報告する。
また, 以前にさかのぼり, さまざまな場合における安定性の議論について
も振り返る。
オンラインですので，参加希望のかたは稲葉(inaba@ms.u-tokyo.ac.jp)へご連絡ください．
2021年11月30日(火)
15:30-17:00 数理科学研究科棟(駒場) オンライン開催号室
小島健 氏 (福島大学経済経営学類)
リスク行動異質性のあるSIRモデルにおける内生的な波 (Japanese)
オンライン開催です．参加希望者は inaba@ms.u-tokyo.ac.jp までご連絡ください．
小島健 氏 (福島大学経済経営学類)
リスク行動異質性のあるSIRモデルにおける内生的な波 (Japanese)
[ 講演概要 ]
リスク行動異質性のあるSIRモデルを構築し、モデルにおいて内生的な感染の波が生じることを示す.
[ 参考URL ]リスク行動異質性のあるSIRモデルを構築し、モデルにおいて内生的な感染の波が生じることを示す.
オンライン開催です．参加希望者は inaba@ms.u-tokyo.ac.jp までご連絡ください．
2021年11月26日(金)
15:00-16:30 オンライン開催
中岡慎治 氏 (北海道大学大学院 先端生命科学研究院)
エネルギー地形に基づく構造化個体群モデルの構築
オンライン参加希望の方は，inaba@ms.u-tokyo.ac.jp までご連絡ください．
中岡慎治 氏 (北海道大学大学院 先端生命科学研究院)
エネルギー地形に基づく構造化個体群モデルの構築
[ 講演概要 ]
細胞分化 (目の網膜細胞や外敵侵入を防ぐ免疫細胞など、体の各組織を構成する細胞へと変化する過程)や疾患発症を説明する上で、エネルギー地形の概念は幅広く用いられている。エネルギー地形を構成する計算方法によって、データから細胞分化や疾患発症の経路を推定することはできるが、その妥当性を保証する数学理論の整備はこれからの課題である。本講演では、あるエネルギー状態から年齢構造個体群モデルを導出できることを示す。また、エネルギー地形の観点から、細胞分化・発症経路を記述した構造化個体群モデルを解釈する方法について紹介する。
[ 参考URL ]細胞分化 (目の網膜細胞や外敵侵入を防ぐ免疫細胞など、体の各組織を構成する細胞へと変化する過程)や疾患発症を説明する上で、エネルギー地形の概念は幅広く用いられている。エネルギー地形を構成する計算方法によって、データから細胞分化や疾患発症の経路を推定することはできるが、その妥当性を保証する数学理論の整備はこれからの課題である。本講演では、あるエネルギー状態から年齢構造個体群モデルを導出できることを示す。また、エネルギー地形の観点から、細胞分化・発症経路を記述した構造化個体群モデルを解釈する方法について紹介する。
オンライン参加希望の方は，inaba@ms.u-tokyo.ac.jp までご連絡ください．
2021年10月07日(木)
15:00-16:30 オンライン開催
大森亮介 氏 (北海道大学 人獣共通感染症国際共同研究所)
感染症流行制御の実践の中での数理モデルの貢献 (Japanese)
大森亮介 氏 (北海道大学 人獣共通感染症国際共同研究所)
感染症流行制御の実践の中での数理モデルの貢献 (Japanese)
[ 講演概要 ]
数理生物学において、生命現象を数式を用いて表現した数理モデルを構築し、その数理モデルを解析することで生命現象を理解しようとする研究の流れはこれまでの研究でよく見られてきた。もしこの研究の流れが正しいと仮定すると、生命現象を理解するためには数理モデルが生命現象の特徴を十分にとらえている必要がある。特に昨今においては数理モデルによる生命現象の定量的な理解が求められており、モデルの模倣の正確性が問題となる場合がある様に見受けられる。感染症疫学においては、昨今の新型コロナウイルスの台頭により、数理モデルによる流行動態の把握と制御の定量的な理解が求められている。このニーズに対し、数理モデルがどの様に貢献できるかを発表者の発表してきた研究を例に議論したい。
数理生物学において、生命現象を数式を用いて表現した数理モデルを構築し、その数理モデルを解析することで生命現象を理解しようとする研究の流れはこれまでの研究でよく見られてきた。もしこの研究の流れが正しいと仮定すると、生命現象を理解するためには数理モデルが生命現象の特徴を十分にとらえている必要がある。特に昨今においては数理モデルによる生命現象の定量的な理解が求められており、モデルの模倣の正確性が問題となる場合がある様に見受けられる。感染症疫学においては、昨今の新型コロナウイルスの台頭により、数理モデルによる流行動態の把握と制御の定量的な理解が求められている。このニーズに対し、数理モデルがどの様に貢献できるかを発表者の発表してきた研究を例に議論したい。
2021年05月27日(木)
15:00-16:00 オンライン開催
ZOOMによる遠隔講演となります。参加希望の方は稲葉までご連絡ください。
南 就将 氏 (慶應義塾大学医学部)
感染性接触の点過程によるモデル化
(Japanese)
ZOOMによる遠隔講演となります。参加希望の方は稲葉までご連絡ください。
南 就将 氏 (慶應義塾大学医学部)
感染性接触の点過程によるモデル化
(Japanese)
[ 講演概要 ]
典型的な1個体と集団の他の成員とのランダムな接触時刻の系列がポアソン点過程をなすと仮定し、さらにこの個体が感染した時刻を起点として、他者への感染性と接触頻度が感染齢とともに変化するというモデルを構成する。このモデルに基づいて実効再生産数の意味を考えたい。また、感染者の増加が分枝過程に従うと仮定すると、流行初期における感染者数の指数関数的増大度と基本再生産数との関係がある確率分布のモーメント母関数を通じて与えられるというよく知られた公式が導かれる。
典型的な1個体と集団の他の成員とのランダムな接触時刻の系列がポアソン点過程をなすと仮定し、さらにこの個体が感染した時刻を起点として、他者への感染性と接触頻度が感染齢とともに変化するというモデルを構成する。このモデルに基づいて実効再生産数の意味を考えたい。また、感染者の増加が分枝過程に従うと仮定すると、流行初期における感染者数の指数関数的増大度と基本再生産数との関係がある確率分布のモーメント母関数を通じて与えられるというよく知られた公式が導かれる。
2021年01月14日(木)
15:00-16:00 数理科学研究科棟(駒場) 号室
ZOOMによるウエビナー（要事前申し込み）
浅井雄介 氏 (国立国際医療研究センター 国際感染症センター)
COVID-19 流行時におけるチャーター便派遣の効果推定
ZOOMによるウエビナー（要事前申し込み）
浅井雄介 氏 (国立国際医療研究センター 国際感染症センター)
COVID-19 流行時におけるチャーター便派遣の効果推定
[ 講演概要 ]
2019 年12 月に中国・武漢市において新型コロナウイルス（以下，SARS-CoV-2）による感染者が報告され，2020 年1 月にはSARS-CoV-2 感染者は武漢市だけでなく中国全土に広がり始めた．それを受け，日本政府は1 月末に武漢市へチャーター便を派遣，邦人566 名が帰国した．チャーター便による避難は有効だと考えられるが，感染症流行対策としての避難は日本においては今回が初めてであり，その効果に関してはいまだ議論がなされていない．
本研究では報告の遅れや行動変化といった感染症拡大に寄与する要因と，COVID-19 で特異的に現れるコンパートメントをSIR モデルに追加し，COVID-19 の流行を記述するモデルを構築した．さらに，湖北省における感染者数と武漢市における感染者数から，感染率，報告割合のパラメータを推定，チャーター便派遣以降の邦人感染者数をシミュレーションにより算出した．
2019 年12 月に中国・武漢市において新型コロナウイルス（以下，SARS-CoV-2）による感染者が報告され，2020 年1 月にはSARS-CoV-2 感染者は武漢市だけでなく中国全土に広がり始めた．それを受け，日本政府は1 月末に武漢市へチャーター便を派遣，邦人566 名が帰国した．チャーター便による避難は有効だと考えられるが，感染症流行対策としての避難は日本においては今回が初めてであり，その効果に関してはいまだ議論がなされていない．
本研究では報告の遅れや行動変化といった感染症拡大に寄与する要因と，COVID-19 で特異的に現れるコンパートメントをSIR モデルに追加し，COVID-19 の流行を記述するモデルを構築した．さらに，湖北省における感染者数と武漢市における感染者数から，感染率，報告割合のパラメータを推定，チャーター便派遣以降の邦人感染者数をシミュレーションにより算出した．
2020年11月26日(木)
15:00-16:00 数理科学研究科棟(駒場) 号室
zoomによる遠隔セミナーです。視聴希望者は稲葉までご連絡ください。
中田行彦 氏 (青山学院大学理工学部物理・数理学科)
いくつかの再感染数理モデルについて (Japanese)
zoomによる遠隔セミナーです。視聴希望者は稲葉までご連絡ください。
中田行彦 氏 (青山学院大学理工学部物理・数理学科)
いくつかの再感染数理モデルについて (Japanese)
[ 講演概要 ]
個体の再感染を含む感染症数理モデルでは、周期的流行を含む複雑な感染症流行ダイナミクスや感染症の一時的流行と定着に関する閾値条件（Reinfection threshold）、感受性の不均一性が引き起こす時間遅れの流行現象（Nakata and Omori (2018,2019)）などSIR型の感染症数理モデルでは見られない現象がこれまでに報告されている。感染個体が獲得する免疫の不均一性や減衰をはじめとする変容、また病原体の変化による免疫防御機能の相対的な変化、が引き起こす感染症流行ダイナミクスの理解に向けて、個体の再感染現象を記述する感染症数理モデルについて再検討する。簡単な数理モデルを用いて、個体の感染が複数回起こるような場合には、流行曲線の動態の理解には、時間と共に変動する人口レベルでの感受性変化の理解が重要であることを示す。またInaba (2017)によって一般的に定式化されたAron (1983)の数理モデルに関する最近の数理解析結果についても紹介する。
個体の再感染を含む感染症数理モデルでは、周期的流行を含む複雑な感染症流行ダイナミクスや感染症の一時的流行と定着に関する閾値条件（Reinfection threshold）、感受性の不均一性が引き起こす時間遅れの流行現象（Nakata and Omori (2018,2019)）などSIR型の感染症数理モデルでは見られない現象がこれまでに報告されている。感染個体が獲得する免疫の不均一性や減衰をはじめとする変容、また病原体の変化による免疫防御機能の相対的な変化、が引き起こす感染症流行ダイナミクスの理解に向けて、個体の再感染現象を記述する感染症数理モデルについて再検討する。簡単な数理モデルを用いて、個体の感染が複数回起こるような場合には、流行曲線の動態の理解には、時間と共に変動する人口レベルでの感受性変化の理解が重要であることを示す。またInaba (2017)によって一般的に定式化されたAron (1983)の数理モデルに関する最近の数理解析結果についても紹介する。
2020年10月07日(水)
16:00-17:00 数理科学研究科棟(駒場) 号室
zoomによるオンラインセミナーです．
並木正夫 氏 ( 元(株)東芝 取締役・代表執行役副社長)
実効SIQRモデルによる第3波予測の方法 (日本語)
zoomによるオンラインセミナーです．
並木正夫 氏 ( 元(株)東芝 取締役・代表執行役副社長)
実効SIQRモデルによる第3波予測の方法 (日本語)
[ 講演概要 ]
SIQRモデルに実効感染機会人口の概念を取り入れ，この実効感染機会人口は感染の拡大と共に変化して行くとし，これを実効SIQRモデル（Effective SIQR Model）とした．このモデルで計算すると，時間の経過と共に未感染人口Sが減少するが，それ以上に実効感染機会人口Nが増加すると，感染しきい値が1よりも大きくなり，第1波が収まったように見えた後でも，再び感染が拡大し始める．このモデルによる計算結果が第1波と第2波のデータに合うように実効感染機会人口変化の曲線を求め，次に，この曲線を使って第2波のデータでフィッティングを行って第3波の予測をする試みを行った．新型コロナウイルスの感染では，数理モデルの個々の係数を同定するデータ採集には種々制約があり真値は殆ど不明であるので，本論で論じるのは，あくまでも予測計算のためのデータ・フィッティングに関することで，真値に基づいたシミュレーションをしている訳ではない．しかし，感染者のデータは真値を反映したものであるから，データ・フィッティングの結果は感染者や隔離療養者，入院者および重症者の予測や，感染の定性的な理解に活用できる．
SIQRモデルに実効感染機会人口の概念を取り入れ，この実効感染機会人口は感染の拡大と共に変化して行くとし，これを実効SIQRモデル（Effective SIQR Model）とした．このモデルで計算すると，時間の経過と共に未感染人口Sが減少するが，それ以上に実効感染機会人口Nが増加すると，感染しきい値が1よりも大きくなり，第1波が収まったように見えた後でも，再び感染が拡大し始める．このモデルによる計算結果が第1波と第2波のデータに合うように実効感染機会人口変化の曲線を求め，次に，この曲線を使って第2波のデータでフィッティングを行って第3波の予測をする試みを行った．新型コロナウイルスの感染では，数理モデルの個々の係数を同定するデータ採集には種々制約があり真値は殆ど不明であるので，本論で論じるのは，あくまでも予測計算のためのデータ・フィッティングに関することで，真値に基づいたシミュレーションをしている訳ではない．しかし，感染者のデータは真値を反映したものであるから，データ・フィッティングの結果は感染者や隔離療養者，入院者および重症者の予測や，感染の定性的な理解に活用できる．
2019年10月17日(木)
14:00-16:00 数理科学研究科棟(駒場) 052号室
Merlin C. Koehnke 氏 (Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrueck University) 14:00-15:00
Complex spatiotemporal dynamics in a simple predator-prey model (ENGLISH)
Functional response of competing populations to environmental variability (ENGLISH)
Merlin C. Koehnke 氏 (Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrueck University) 14:00-15:00
Complex spatiotemporal dynamics in a simple predator-prey model (ENGLISH)
[ 講演概要 ]
A simple reaction-diffusion predator-prey model with Holling type IV functional response
and logistic growth in the prey is considered. The functional response can be interpreted as
a group defense mechanism, i.e., the predation rate decreases with resource density when the
prey density is high enough [1]. Such a mechanism has been described in diverse biological
interactions [2,3]. For instance, high densities of filamentous algae can decrease filtering
rates of filter feeders [4].
The model will be described and linked to plankton dynamics. Nonspatial considerations reveal that the zooplankton may go extinct or coexistence (stationary or oscillatory) between
zoo- and phytoplankton may emerge depending on the choice of parameters. However,
including space, the dynamics are more complex. In particular, spatiotemporal irregular
oscillations can rescue the predator from extinction. These oscillations can be characterized
as spatiotemporal chaos. The results provide a simple mechanism not only for the emergence
of inhomogeneous plankton distributions [5] but also for the occurrence of chaos in plankton communities [6]. Possible underlying mechanisms for this phenomenon will be discussed.
References
[1] Freedman, H. I., Wolkowicz, G. S. (1986). Predator-prey systems with group defence: the
paradox of enrichment revisited. Bulletin of Mathematical Biology, 48(5-6), 493–508.
[2] Tener, J. S.. Muskoxen in Canada: a biological and taxonomic review. Vol. 2. Dept. of Northern
Affairs and National Resources, Canadian Wildlife Service, 1965.
[3] Holmes, J. C. (1972). Modification of intermediate host behaviour by parasites. Behavioural
aspects of parasite transmission.
[4] Davidowicz, P., Gliwicz, Z. M., Gulati, R. D. (1988). Can Daphnia prevent a blue-green algal
bloom in hypertrophic lakes? A laboratory test. Limnologica. Jena, 19(1), 21–26.
[5] Abbott, M., 1993. Phytoplankton patchiness: ecological implicationsand observation methods.
In: Levin, S.A., Powell, T.M., Steele, J.H.(Eds.), Patch Dynamics. Lecture Notes in Biomathematics, vol. 96. Springer-Verlag, Berlin, pp. 37–49.
[6] Beninc`a, E. et al. (2008). Chaos in a long-term experiment with a plankton community. Nature,
451(7180), 822.
Horst Malchow 氏 (Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrueck University) 15:00-16:00A simple reaction-diffusion predator-prey model with Holling type IV functional response
and logistic growth in the prey is considered. The functional response can be interpreted as
a group defense mechanism, i.e., the predation rate decreases with resource density when the
prey density is high enough [1]. Such a mechanism has been described in diverse biological
interactions [2,3]. For instance, high densities of filamentous algae can decrease filtering
rates of filter feeders [4].
The model will be described and linked to plankton dynamics. Nonspatial considerations reveal that the zooplankton may go extinct or coexistence (stationary or oscillatory) between
zoo- and phytoplankton may emerge depending on the choice of parameters. However,
including space, the dynamics are more complex. In particular, spatiotemporal irregular
oscillations can rescue the predator from extinction. These oscillations can be characterized
as spatiotemporal chaos. The results provide a simple mechanism not only for the emergence
of inhomogeneous plankton distributions [5] but also for the occurrence of chaos in plankton communities [6]. Possible underlying mechanisms for this phenomenon will be discussed.
References
[1] Freedman, H. I., Wolkowicz, G. S. (1986). Predator-prey systems with group defence: the
paradox of enrichment revisited. Bulletin of Mathematical Biology, 48(5-6), 493–508.
[2] Tener, J. S.. Muskoxen in Canada: a biological and taxonomic review. Vol. 2. Dept. of Northern
Affairs and National Resources, Canadian Wildlife Service, 1965.
[3] Holmes, J. C. (1972). Modification of intermediate host behaviour by parasites. Behavioural
aspects of parasite transmission.
[4] Davidowicz, P., Gliwicz, Z. M., Gulati, R. D. (1988). Can Daphnia prevent a blue-green algal
bloom in hypertrophic lakes? A laboratory test. Limnologica. Jena, 19(1), 21–26.
[5] Abbott, M., 1993. Phytoplankton patchiness: ecological implicationsand observation methods.
In: Levin, S.A., Powell, T.M., Steele, J.H.(Eds.), Patch Dynamics. Lecture Notes in Biomathematics, vol. 96. Springer-Verlag, Berlin, pp. 37–49.
[6] Beninc`a, E. et al. (2008). Chaos in a long-term experiment with a plankton community. Nature,
451(7180), 822.
Functional response of competing populations to environmental variability (ENGLISH)
[ 講演概要 ]
The possible control of competitive invasion by infection of the invader and multiplicative
noise is studied. The basic model is the Lotka-Volterra competition system with emergent
carrying capacities. Several stationary solutions of the non-infected and infected system are
identi ed as well as parameter ranges of bistability. The latter are used for the numerical
study of di usive invasion phenomena. The Fickian di usivities, the infection but in particular the white and colored multiplicative noise are the control parameters. It is shown
that not only competition, possible infection and mobilities are important drivers of the
invasive dynamics but also the noise and especially its color and the functional response of
populations to the emergence of noise.
The variability of the environment can additionally be modelled by applying Fokker-Planck
instead of Fickian di usion. An interesting feature of Fokker-Planck di usion is that for spatially varying di usion coecients the stationary solution is not a homogeneous distribution.
Instead, the densities accumulate in regions of low di usivity and tend to lower levels for
areas of high di usivity. Thus, the stationary distribution of the Fokker-Planck di usion can
be interpreted as a re
ection of di erent levels of habitat quality [1-5]. The latter recalls the
seminal papers on environmental density, cf. [6-7]. Appropriate examples will be presented.
References
[1] Bengfort, M., Malchow, H., Hilker, F.M. (2016). The Fokker-Planck law of diffusion and
pattern formation in heterogeneous media. Journal of Mathematical Biology 73(3), 683-704.
[2] Siekmann, I., Malchow, H. (2016). Fighting enemies and noise: Competition of residents
and invaders in a stochastically fluctuating environment. Mathematical Modelling of Natural
Phenomena 11(5), 120-140.
[3] Siekmann, I., Bengfort, M., Malchow, H. (2017). Coexistence of competitors mediated by
nonlinear noise. European Physical Journal Special Topics 226(9), 2157-2170.
[4] Kohnke, M.C., Malchow, H. (2017). Impact of parameter variability and environmental noise
on the Klausmeier model of vegetation pattern formation. Mathematics 5, 69 (19 pages).
[5] Bengfort, M., Siekmann, I., Malchow, H. (2018). Invasive competition with Fokker-Planck
di usion and noise. Ecological Complexity 34, 134-13.
[6] Morisita, M. (1971). Measuring of habitat value by the \environmental density" method. In:
Spatial patterns and statistical distributions (Patil, C.D., Pielou, E.C., Waters, W.E., eds.),
Statistical Ecology, vol. 1, pp. 379-401. Pennsylvania State University Press, University Park.
[7] N. Shigesada, N., Kawasaki, K., Teramoto, E. (1979). Spatial segregation of interacting species.
Journal of Theoretical Biology 79, 83-99.
The possible control of competitive invasion by infection of the invader and multiplicative
noise is studied. The basic model is the Lotka-Volterra competition system with emergent
carrying capacities. Several stationary solutions of the non-infected and infected system are
identi ed as well as parameter ranges of bistability. The latter are used for the numerical
study of di usive invasion phenomena. The Fickian di usivities, the infection but in particular the white and colored multiplicative noise are the control parameters. It is shown
that not only competition, possible infection and mobilities are important drivers of the
invasive dynamics but also the noise and especially its color and the functional response of
populations to the emergence of noise.
The variability of the environment can additionally be modelled by applying Fokker-Planck
instead of Fickian di usion. An interesting feature of Fokker-Planck di usion is that for spatially varying di usion coecients the stationary solution is not a homogeneous distribution.
Instead, the densities accumulate in regions of low di usivity and tend to lower levels for
areas of high di usivity. Thus, the stationary distribution of the Fokker-Planck di usion can
be interpreted as a re
ection of di erent levels of habitat quality [1-5]. The latter recalls the
seminal papers on environmental density, cf. [6-7]. Appropriate examples will be presented.
References
[1] Bengfort, M., Malchow, H., Hilker, F.M. (2016). The Fokker-Planck law of diffusion and
pattern formation in heterogeneous media. Journal of Mathematical Biology 73(3), 683-704.
[2] Siekmann, I., Malchow, H. (2016). Fighting enemies and noise: Competition of residents
and invaders in a stochastically fluctuating environment. Mathematical Modelling of Natural
Phenomena 11(5), 120-140.
[3] Siekmann, I., Bengfort, M., Malchow, H. (2017). Coexistence of competitors mediated by
nonlinear noise. European Physical Journal Special Topics 226(9), 2157-2170.
[4] Kohnke, M.C., Malchow, H. (2017). Impact of parameter variability and environmental noise
on the Klausmeier model of vegetation pattern formation. Mathematics 5, 69 (19 pages).
[5] Bengfort, M., Siekmann, I., Malchow, H. (2018). Invasive competition with Fokker-Planck
di usion and noise. Ecological Complexity 34, 134-13.
[6] Morisita, M. (1971). Measuring of habitat value by the \environmental density" method. In:
Spatial patterns and statistical distributions (Patil, C.D., Pielou, E.C., Waters, W.E., eds.),
Statistical Ecology, vol. 1, pp. 379-401. Pennsylvania State University Press, University Park.
[7] N. Shigesada, N., Kawasaki, K., Teramoto, E. (1979). Spatial segregation of interacting species.
Journal of Theoretical Biology 79, 83-99.
2019年08月01日(木)
15:00-16:00 数理科学研究科棟(駒場) 118号室
Yueping Dong 氏 (Central China Normal University)
Mathematical study of the inhibitory role of regulatory T cells in tumor immune response
Yueping Dong 氏 (Central China Normal University)
Mathematical study of the inhibitory role of regulatory T cells in tumor immune response
[ 講演概要 ]
The immune system against tumor is a complex dynamical process showing a dual role. On the one hand, the immune system can activate some immune cells to kill tumor cells, such as cytotoxic T lymphocytes (CTLs) and natural killer cells (NKs), but on the other hand, more evidence shows that some immune cells can help tumor escape, such as regulatory T cells (Tregs). In this talk, we propose a tumor immune interaction model based on Tregs mediated tumor immune escape mechanism. When HTCs stimulation rate by the presence of identified tumor antigens below the critical value, the interior equilibrium P* is always stable in the region of existence. When HTCs stimulation rate higher than the critical value, the Inhibition rate of ECs by Tregs can destabilize P* and cause Hopf bifurcations and produce limit cycle. This model shows that Tregs might play a crucial role in triggering the immune escape of tumor cells. Furthermore, we introduce the adoptive cellular immunotherapy (ACI) and monoclonal immunotherapy as the treatment to boost the immune system to fight against tumors. The numerical results show that ACI can control more tumor cells, while monoclonal immunotherapy can delay the inhibitory effect of Tregs on effector cells (ECs). The results also show that the combination immunotherapy can control tumor cells and reduce the inhibitory effect of Tregs better than single immunotherapy.
The immune system against tumor is a complex dynamical process showing a dual role. On the one hand, the immune system can activate some immune cells to kill tumor cells, such as cytotoxic T lymphocytes (CTLs) and natural killer cells (NKs), but on the other hand, more evidence shows that some immune cells can help tumor escape, such as regulatory T cells (Tregs). In this talk, we propose a tumor immune interaction model based on Tregs mediated tumor immune escape mechanism. When HTCs stimulation rate by the presence of identified tumor antigens below the critical value, the interior equilibrium P* is always stable in the region of existence. When HTCs stimulation rate higher than the critical value, the Inhibition rate of ECs by Tregs can destabilize P* and cause Hopf bifurcations and produce limit cycle. This model shows that Tregs might play a crucial role in triggering the immune escape of tumor cells. Furthermore, we introduce the adoptive cellular immunotherapy (ACI) and monoclonal immunotherapy as the treatment to boost the immune system to fight against tumors. The numerical results show that ACI can control more tumor cells, while monoclonal immunotherapy can delay the inhibitory effect of Tregs on effector cells (ECs). The results also show that the combination immunotherapy can control tumor cells and reduce the inhibitory effect of Tregs better than single immunotherapy.
2019年07月11日(木)
15:00-16:00 数理科学研究科棟(駒場) 056号室
Dipo Aldila 氏 (Universitas Indonesia)
Understanding The Seasonality of Dengue Disease Incidences From Empirical Data (ENGLISH)
Dipo Aldila 氏 (Universitas Indonesia)
Understanding The Seasonality of Dengue Disease Incidences From Empirical Data (ENGLISH)
[ 講演概要 ]
Investigating the seasonality of dengue incidences is very important in dengue surveillance in regions with periodical climatic patterns. In lieu of the paradigm about dengue incidences varying seasonally in line with meteorology, this talk seeks to determine how well standard epidemic mo-dels (SIRUV) can capture such seasonality for better forecasts and optimal futuristic interventions. Once incidence data are assimilated by a periodic model, asymptotic analysis in relation to the long-term behavior of the dengue occurrences will be performed. For a test case, we employed an SIRUV model (later become IR model with QSSA method) to assimilate weekly dengue incidence data from the city of Jakarta, Indonesia, which we present in their raw and moving-average-filtered versions. To estimate a periodic parameter toward performing the asymptotic analysis, some optimization schemes were assigned returning magnitudes of the parameter that vary insignificantly across schemes. Furthermore, the computation results combined with the analytical results indicate that if the disease surveillance in the city does not improve, then the incidence will raise to a certain positive orbit and remain cyclical.
Investigating the seasonality of dengue incidences is very important in dengue surveillance in regions with periodical climatic patterns. In lieu of the paradigm about dengue incidences varying seasonally in line with meteorology, this talk seeks to determine how well standard epidemic mo-dels (SIRUV) can capture such seasonality for better forecasts and optimal futuristic interventions. Once incidence data are assimilated by a periodic model, asymptotic analysis in relation to the long-term behavior of the dengue occurrences will be performed. For a test case, we employed an SIRUV model (later become IR model with QSSA method) to assimilate weekly dengue incidence data from the city of Jakarta, Indonesia, which we present in their raw and moving-average-filtered versions. To estimate a periodic parameter toward performing the asymptotic analysis, some optimization schemes were assigned returning magnitudes of the parameter that vary insignificantly across schemes. Furthermore, the computation results combined with the analytical results indicate that if the disease surveillance in the city does not improve, then the incidence will raise to a certain positive orbit and remain cyclical.
2019年07月01日(月)
11:00-12:00 数理科学研究科棟(駒場) 123号室
Joel E. Cohen 氏 (The Rockefeller University and Columbia University)
Taylor's Law of Fluctuation Scaling
https://www.rockefeller.edu/our-scientists/heads-of-laboratories/940-joel-e-cohen/
Joel E. Cohen 氏 (The Rockefeller University and Columbia University)
Taylor's Law of Fluctuation Scaling
[ 講演概要 ]
A family of nonnegative random variables is said to obey Taylor's law when the variance is proportional to some power b of the mean. For example, in the family of exponential distributions, if the mean is m, then the variance is m^2, so the family of exponential distributions obeys Taylor's law exactly with b=2. Many stochastic processes and the prime numbers obey Taylor's law (exactly or asymptotically). Thousands of empirical illustrations of Taylor's law have been published in many different fields including ecology, demography, finance (stock and currency trading), cancer biology, genetics, fisheries, forestry, meteorology, agriculture, physics, cell biology, computer network engineering, and number theory. This survey talk will review some empirical and theoretical results and open problems about Taylor's law, including recently proved versions of Taylor's law for nonnegative stable laws with infinite mean.
[ 参考URL ]A family of nonnegative random variables is said to obey Taylor's law when the variance is proportional to some power b of the mean. For example, in the family of exponential distributions, if the mean is m, then the variance is m^2, so the family of exponential distributions obeys Taylor's law exactly with b=2. Many stochastic processes and the prime numbers obey Taylor's law (exactly or asymptotically). Thousands of empirical illustrations of Taylor's law have been published in many different fields including ecology, demography, finance (stock and currency trading), cancer biology, genetics, fisheries, forestry, meteorology, agriculture, physics, cell biology, computer network engineering, and number theory. This survey talk will review some empirical and theoretical results and open problems about Taylor's law, including recently proved versions of Taylor's law for nonnegative stable laws with infinite mean.
https://www.rockefeller.edu/our-scientists/heads-of-laboratories/940-joel-e-cohen/
2019年06月20日(木)
16:00-17:00 数理科学研究科棟(駒場) 056号室
Eric Foxall 氏 (University of Alberta)
Diffusion limit for the partner model at the critical value (ENGLISH)
Eric Foxall 氏 (University of Alberta)
Diffusion limit for the partner model at the critical value (ENGLISH)
[ 講演概要 ]
The partner model is a stochastic SIS model of infection spread over a dynamic network of monogamous partnerships. In previous work, Edwards, Foxall and van den Driessche identify a threshold in parameter space for spread of the infection and show the time to extinction of the infection is of order log(N) below the threshold, where N is population size, and grows exponentially in N above the
threshold. Later, Foxall shows the time to extinction at threshold is of order sqrt(N). Here we go further and derive a single-variable diffusion limit for the number of infectious individuals rescaled by sqrt(N) in both population and time, and show convergence in distribution of the rescaled extinction time. Since the model has effectively four variables and two relevant time scales, the proof features a succession of probability estimates to control trajectories, as well as an averaging result to contend with the fast partnership dynamics.
The partner model is a stochastic SIS model of infection spread over a dynamic network of monogamous partnerships. In previous work, Edwards, Foxall and van den Driessche identify a threshold in parameter space for spread of the infection and show the time to extinction of the infection is of order log(N) below the threshold, where N is population size, and grows exponentially in N above the
threshold. Later, Foxall shows the time to extinction at threshold is of order sqrt(N). Here we go further and derive a single-variable diffusion limit for the number of infectious individuals rescaled by sqrt(N) in both population and time, and show convergence in distribution of the rescaled extinction time. Since the model has effectively four variables and two relevant time scales, the proof features a succession of probability estimates to control trajectories, as well as an averaging result to contend with the fast partnership dynamics.
2018年10月04日(木)
15:00-16:00 数理科学研究科棟(駒場) 056号室
Robin Thompson 氏 (University of Oxford, UK)
Modelling the beginnings, middles and ends of infectious disease outbreaks
(ENGLISH)
http://www.robin-thompson.co.uk/
Robin Thompson 氏 (University of Oxford, UK)
Modelling the beginnings, middles and ends of infectious disease outbreaks
(ENGLISH)
[ 講演概要 ]
There have been a number of high profile infectious disease epidemics recently. For example, the 2013-16 Ebola epidemic in West Africa led to more than 11,000 deaths, putting it at the centre of the news agenda. However, when a pathogen enters a host population, it is not necessarily the case that a major epidemic follows. The Ebola virus survives in animal populations, and enters human populations every few years. Typically, a small number of individuals are infected in an Ebola outbreak, with the 2013-16 epidemic being anomalous. During this talk, using Ebola as a case study, I will discuss how stochastic epidemiological models can be used at different stages of infectious disease outbreaks. At the beginning of an outbreak, key questions include: how can surveillance be performed effectively, and will the outbreak develop into a major epidemic? When a major epidemic is ongoing, modelling can be used to predict the final size and to plan control interventions. And at the apparent end of an epidemic, an important question is whether the epidemic is really over once there are no new symptomatic cases. If time permits, I will also discuss several current projects that I am working on. One of these - in collaboration with Professor Hiroshi Nishiura at Hokkaido University - involves appropriately modelling disease detection during epidemics, and investigating the impact of the sensitivity of surveillance on the outcome of control interventions.
Relevant references:
Thompson RN, Hart WS, Effect of confusing symptoms and infectiousness on forecasting and control of Ebola outbreaks, Clin. Inf. Dis., In Press, 2018.
Thompson RN, Gilligan CA and Cunniffe NJ, Control fast or control Smart: when should invading pathogens be controlled?, PLoS Comp. Biol., 14(2):e1006014, 2018.
Thompson RN, Gilligan CA and Cunniffe NJ, Detecting presymptomatic infection is necessary to forecast major epidemics in the earliest stages of infectious disease outbreaks, PLoS Comp. Biol., 12(4):e1004836, 2016.
Thompson RN, Cobb RC, Gilligan CA and Cunniffe NJ, Management of invading pathogens should be informed by epidemiology rather than administrative boundaries, Ecol. Model., 324:28-32, 2016.
[ 参考URL ]There have been a number of high profile infectious disease epidemics recently. For example, the 2013-16 Ebola epidemic in West Africa led to more than 11,000 deaths, putting it at the centre of the news agenda. However, when a pathogen enters a host population, it is not necessarily the case that a major epidemic follows. The Ebola virus survives in animal populations, and enters human populations every few years. Typically, a small number of individuals are infected in an Ebola outbreak, with the 2013-16 epidemic being anomalous. During this talk, using Ebola as a case study, I will discuss how stochastic epidemiological models can be used at different stages of infectious disease outbreaks. At the beginning of an outbreak, key questions include: how can surveillance be performed effectively, and will the outbreak develop into a major epidemic? When a major epidemic is ongoing, modelling can be used to predict the final size and to plan control interventions. And at the apparent end of an epidemic, an important question is whether the epidemic is really over once there are no new symptomatic cases. If time permits, I will also discuss several current projects that I am working on. One of these - in collaboration with Professor Hiroshi Nishiura at Hokkaido University - involves appropriately modelling disease detection during epidemics, and investigating the impact of the sensitivity of surveillance on the outcome of control interventions.
Relevant references:
Thompson RN, Hart WS, Effect of confusing symptoms and infectiousness on forecasting and control of Ebola outbreaks, Clin. Inf. Dis., In Press, 2018.
Thompson RN, Gilligan CA and Cunniffe NJ, Control fast or control Smart: when should invading pathogens be controlled?, PLoS Comp. Biol., 14(2):e1006014, 2018.
Thompson RN, Gilligan CA and Cunniffe NJ, Detecting presymptomatic infection is necessary to forecast major epidemics in the earliest stages of infectious disease outbreaks, PLoS Comp. Biol., 12(4):e1004836, 2016.
Thompson RN, Cobb RC, Gilligan CA and Cunniffe NJ, Management of invading pathogens should be informed by epidemiology rather than administrative boundaries, Ecol. Model., 324:28-32, 2016.
http://www.robin-thompson.co.uk/
2018年07月27日(金)
15:00-16:00 数理科学研究科棟(駒場) 118号室
Somdatta Sinha 氏 (Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali INDIA)
Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches
Somdatta Sinha 氏 (Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali INDIA)
Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches
[ 講演概要 ]
Malaria has existed in India since antiquity. Different periods of
elimination and control policies have been adopted by the government for
tackling the disease. Malaria parasite was dissevered in India by Sir
Ronald Ross who also developed the simplest mathematical model in early
1900. Malaria modelling has since come through many variations that
incorporated various intrinsic and extrinsic/environmental factors to
describe the disease progression in population. Collection of disease
incidence and prevalence data, however, has been quite variable with both
governmental and non-governmental agencies independently collecting data at
different space and time scales. In this talk I will describe our work on
modelling malaria prevalence using three different approaches. For monthly
prevalence data, I will discuss (i) a regression-based statistical model
based on a specific data-set, and (ii) a general mathematical model that
fits the same data. For more coarse-grained temporal (yearly) data, I will
show graphical analysis that uncovers some useful information from the mass
of data tables. This presentation aims to highlight the suitability of
multiple modelling methods for disease prevalence from variable quality data.
Malaria has existed in India since antiquity. Different periods of
elimination and control policies have been adopted by the government for
tackling the disease. Malaria parasite was dissevered in India by Sir
Ronald Ross who also developed the simplest mathematical model in early
1900. Malaria modelling has since come through many variations that
incorporated various intrinsic and extrinsic/environmental factors to
describe the disease progression in population. Collection of disease
incidence and prevalence data, however, has been quite variable with both
governmental and non-governmental agencies independently collecting data at
different space and time scales. In this talk I will describe our work on
modelling malaria prevalence using three different approaches. For monthly
prevalence data, I will discuss (i) a regression-based statistical model
based on a specific data-set, and (ii) a general mathematical model that
fits the same data. For more coarse-grained temporal (yearly) data, I will
show graphical analysis that uncovers some useful information from the mass
of data tables. This presentation aims to highlight the suitability of
multiple modelling methods for disease prevalence from variable quality data.
2018年07月18日(水)
15:00-16:00 数理科学研究科棟(駒場) 118号室
Malay Banerjee 氏 (Department of Mathematics & Statistics, IIT Kanpur)
Effect of demographic stochasticity on large amplitude oscillation
Malay Banerjee 氏 (Department of Mathematics & Statistics, IIT Kanpur)
Effect of demographic stochasticity on large amplitude oscillation
[ 講演概要 ]
Classical Rosenzweig-MacArthur model exhibits two types of stable coexistence, steady-state and oscillatory coexistence. The oscillatory coexistence is the result of super-critical Hopf-bifurcation and the Hopf-bifurcating limit cycle remains stable for parameter values beyond the bifurcation threshold. The size of the limit cycle grows with the increase in carrying capacity of prey and finally both the populations show high amplitude oscillations. Time evolution of prey and predator population densities exhibit large amplitude peaks separated by low density lengthy valleys. Persistence of both the populations at low population density over a longer time period is more prominent in case of fast growth of prey and comparatively slow growth of predator species due to slow-fast dynamics. In this situation, small amount of demographic stochasticity can cause the extinction of one or both the species. Main aim of this talk is to explain the effect of demographic stochasticity on the high amplitude oscillations produced by two and higher dimensional interacting population models.
Classical Rosenzweig-MacArthur model exhibits two types of stable coexistence, steady-state and oscillatory coexistence. The oscillatory coexistence is the result of super-critical Hopf-bifurcation and the Hopf-bifurcating limit cycle remains stable for parameter values beyond the bifurcation threshold. The size of the limit cycle grows with the increase in carrying capacity of prey and finally both the populations show high amplitude oscillations. Time evolution of prey and predator population densities exhibit large amplitude peaks separated by low density lengthy valleys. Persistence of both the populations at low population density over a longer time period is more prominent in case of fast growth of prey and comparatively slow growth of predator species due to slow-fast dynamics. In this situation, small amount of demographic stochasticity can cause the extinction of one or both the species. Main aim of this talk is to explain the effect of demographic stochasticity on the high amplitude oscillations produced by two and higher dimensional interacting population models.
2018年05月28日(月)
15:30-16:30 数理科学研究科棟(駒場) 122号室
Sourav Kumar Sasmal 氏 (Department of Physics and Mathematics, Aoyama Gakuin University)
T-cell mediated adaptive immunity in primary dengue infections
https://www.sciencedirect.com/science/article/pii/S0022519317303211
Sourav Kumar Sasmal 氏 (Department of Physics and Mathematics, Aoyama Gakuin University)
T-cell mediated adaptive immunity in primary dengue infections
[ 講演概要 ]
Currently, dengue virus (DENV) is the most common mosquito-borne viral disease in the world, which is endemic across tropical Asia, Latin America, and Africa. The global DENV incidence is increasing day by day due to climate changing. According to a report, DENV cases increase almost five times since 1980, than the previous 30 years. Mathematical modeling is a common tool for understanding, studying and analyzing the mechanisms that govern the dynamics of infectious disease. In addition, models can be used to study different mitigation measures to control outbreaks. Here, we present a mathematical model of DENV dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T -cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment effect for DENV in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects.
[ 参考URL ]Currently, dengue virus (DENV) is the most common mosquito-borne viral disease in the world, which is endemic across tropical Asia, Latin America, and Africa. The global DENV incidence is increasing day by day due to climate changing. According to a report, DENV cases increase almost five times since 1980, than the previous 30 years. Mathematical modeling is a common tool for understanding, studying and analyzing the mechanisms that govern the dynamics of infectious disease. In addition, models can be used to study different mitigation measures to control outbreaks. Here, we present a mathematical model of DENV dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T -cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment effect for DENV in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects.
https://www.sciencedirect.com/science/article/pii/S0022519317303211
2018年03月19日(月)
17:00-18:00 数理科学研究科棟(駒場) 509号室
杉山 友規 氏 (東京大学生産技術研究所)
Age構造付き増殖過程の大偏差原理を用いた解析
杉山 友規 氏 (東京大学生産技術研究所)
Age構造付き増殖過程の大偏差原理を用いた解析
[ 講演概要 ]
細胞集団の“集団”としての増殖率（集団増殖率）を制御することは様々な分野で現れるユビキタスな問題である。例えば医学的分野においては、我々はがん細胞や病原性細胞の集団サイズを抗がん剤や抗生物質などを用いて抑制することを考える。一方進化生物学の文脈では、細胞集団は変動する環境の中を生き残るため、集団増殖率を最大化する。近年の実験装置の発展により、我々は細胞集団が増殖していく様を表す非常に大きな系譜（家系図）データを取ることが出来るようになった。本講演では、この系譜データを用いて集団増殖の振る舞いを解析する方法について紹介する。特にここでは、系譜上に定義される大偏差原理を用いた統計物理学的な構造が重要な役割を果たす。結果としては、集団増殖率が、細胞タイプの確率的変化を表すsemi-Markov過程上の大偏差関数のLegendre変換で評価されることが明らかになる。またこの構造を用いることにより、我々は環境変動に対する集団増殖率の応答を時間遡及的に系譜を辿ったときに得られる統計量を用いて知ることが出来る。
細胞集団の“集団”としての増殖率（集団増殖率）を制御することは様々な分野で現れるユビキタスな問題である。例えば医学的分野においては、我々はがん細胞や病原性細胞の集団サイズを抗がん剤や抗生物質などを用いて抑制することを考える。一方進化生物学の文脈では、細胞集団は変動する環境の中を生き残るため、集団増殖率を最大化する。近年の実験装置の発展により、我々は細胞集団が増殖していく様を表す非常に大きな系譜（家系図）データを取ることが出来るようになった。本講演では、この系譜データを用いて集団増殖の振る舞いを解析する方法について紹介する。特にここでは、系譜上に定義される大偏差原理を用いた統計物理学的な構造が重要な役割を果たす。結果としては、集団増殖率が、細胞タイプの確率的変化を表すsemi-Markov過程上の大偏差関数のLegendre変換で評価されることが明らかになる。またこの構造を用いることにより、我々は環境変動に対する集団増殖率の応答を時間遡及的に系譜を辿ったときに得られる統計量を用いて知ることが出来る。
2017年12月21日(木)
16:30-18:00 数理科学研究科棟(駒場) 056号室
山道真人 氏 (東京大学大学院総合文化研究科)
生態-進化フィードバックを理解するための理論的アプローチ
山道真人 氏 (東京大学大学院総合文化研究科)
生態-進化フィードバックを理解するための理論的アプローチ
[ 講演概要 ]
近年になって、短期間で起こる適応的な進化（遺伝子頻度の変化）が、生態学的プロセスに大きな影響を与えることが明らかになってきた。一方、生態学的プロセスは適応進化を駆動するため、生態と進化の間には複雑なフィードバックが生じることになる。このような動態を理解するために、プランクトンの培養実験系と数理モデルを組み合わせてさかんに研究が進められている。本発表では、この分野での研究の展開について紹介するとともに、最近取り組んでいる共進化モデルと進化的救助モデルについての結果を紹介し、今後の展開を議論したい。
近年になって、短期間で起こる適応的な進化（遺伝子頻度の変化）が、生態学的プロセスに大きな影響を与えることが明らかになってきた。一方、生態学的プロセスは適応進化を駆動するため、生態と進化の間には複雑なフィードバックが生じることになる。このような動態を理解するために、プランクトンの培養実験系と数理モデルを組み合わせてさかんに研究が進められている。本発表では、この分野での研究の展開について紹介するとともに、最近取り組んでいる共進化モデルと進化的救助モデルについての結果を紹介し、今後の展開を議論したい。
2017年12月14日(木)
13:00-16:40 数理科学研究科棟(駒場) 126号室
江夏洋一 氏 (東京理科大学) 13:00-13:30
On a mosquito-borne disease transmission by Wolbachia infection (JAPANESE)
Delayed feedback controls in an Escherichia coli and Tetrahymena system (ENGLISH)
構造人口モデルにおける固有関数と生活史進化 (JAPANESE)
Reinfection epidemic models in a heterogeneous host population (JAPANESE)
Time evolution of Tajima's D of a pathogen during its outbreak (JAPANESE)
Mathematical analysis for HBV model and HBV-HDV coinfection model (ENGLISH)
江夏洋一 氏 (東京理科大学) 13:00-13:30
On a mosquito-borne disease transmission by Wolbachia infection (JAPANESE)
[ 講演概要 ]
Symbiotic bacteria called Wolbachia pipientis inside mosquitoes are experimentally observed to prevent transmission of Zika virus. Wolbachia-infected mosquitoes have been widely released and it is reported that they reduce vector competence for Zika virus.
In order to study dynamical behavior of the population of the mosquitoes, Xue et al. (2017) formulated a system of ODEs and investigated stability of three equilibria; a disease-free
equilibrium, a complete infection equilibrium and an endemic equilibrium. In this presentation, we propose a system of DDEs to investigate the effect of a time lag from the egg stage to the aquatic stage. Out talk is based on a collaborated work with Professor Emiko Ishiwata and Mr. Masatoshi Kanamori.
Don Yueping 氏 (青山学院大学) 13:30-14:00Symbiotic bacteria called Wolbachia pipientis inside mosquitoes are experimentally observed to prevent transmission of Zika virus. Wolbachia-infected mosquitoes have been widely released and it is reported that they reduce vector competence for Zika virus.
In order to study dynamical behavior of the population of the mosquitoes, Xue et al. (2017) formulated a system of ODEs and investigated stability of three equilibria; a disease-free
equilibrium, a complete infection equilibrium and an endemic equilibrium. In this presentation, we propose a system of DDEs to investigate the effect of a time lag from the egg stage to the aquatic stage. Out talk is based on a collaborated work with Professor Emiko Ishiwata and Mr. Masatoshi Kanamori.
Delayed feedback controls in an Escherichia coli and Tetrahymena system (ENGLISH)
[ 講演概要 ]
In this talk, we develop a novel mathematical model to investigate the interaction between Shiga-toxin producing Escherichia coli and Tetrahymena with delayed feedback controls by Shiga-toxin and neutrophils in a community. By applying the quasi steady state approximation, the proposed model can be reduced to a Lotka-Volterra predator-prey type system with two discrete delays. By investigating the distributions of the roots of the characteristic equation, the local stability as well as Hopf bifurcation are well studied when two delays are present. Numerical simulations are carried out to verify the analytical results. Our findings reveal that the instability regions of coexistence equilibrium in two delays plane always enlarge as the increase of negative feedback control coefficients, and especially the controls on Tetrahymena population play a dominant role in the destabilization of coexistence equilibrium. Besides, we observe some interesting phenomena such as quasi-periodic behaviors and chaotic behaviours.
大泉嶺 氏 (国立社会保障・人口問題研究所) 14:00-14:30In this talk, we develop a novel mathematical model to investigate the interaction between Shiga-toxin producing Escherichia coli and Tetrahymena with delayed feedback controls by Shiga-toxin and neutrophils in a community. By applying the quasi steady state approximation, the proposed model can be reduced to a Lotka-Volterra predator-prey type system with two discrete delays. By investigating the distributions of the roots of the characteristic equation, the local stability as well as Hopf bifurcation are well studied when two delays are present. Numerical simulations are carried out to verify the analytical results. Our findings reveal that the instability regions of coexistence equilibrium in two delays plane always enlarge as the increase of negative feedback control coefficients, and especially the controls on Tetrahymena population play a dominant role in the destabilization of coexistence equilibrium. Besides, we observe some interesting phenomena such as quasi-periodic behaviors and chaotic behaviours.
構造人口モデルにおける固有関数と生活史進化 (JAPANESE)
[ 講演概要 ]
年齢構造モデルの基本であるMacKendrick方程式は, 支配的な特性根に対する左右固
有関数がそれぞれ繁殖価と定常年齢構造に対応することはよく知られた事実である．
本研究では，年齢構造のに加え，拡散過程を含む状態構造を持つ構造人口モデルに対
して左右固有関数による展開を試みた．結果として，これら固有関数は繁殖価と定常
年齢構造を状態構造を含むものに拡張できる事を示した．本講演では繁殖価を与える
固有関数が満たす条件から，状態の成長に関する生活史の進化を解析する制御方程式
を導出するとともに，密度効果や環境変動下での生活史進化への応用について報告し
たい．
中田行彦 氏 (島根大学) 14:40-15:10年齢構造モデルの基本であるMacKendrick方程式は, 支配的な特性根に対する左右固
有関数がそれぞれ繁殖価と定常年齢構造に対応することはよく知られた事実である．
本研究では，年齢構造のに加え，拡散過程を含む状態構造を持つ構造人口モデルに対
して左右固有関数による展開を試みた．結果として，これら固有関数は繁殖価と定常
年齢構造を状態構造を含むものに拡張できる事を示した．本講演では繁殖価を与える
固有関数が満たす条件から，状態の成長に関する生活史の進化を解析する制御方程式
を導出するとともに，密度効果や環境変動下での生活史進化への応用について報告し
たい．
Reinfection epidemic models in a heterogeneous host population (JAPANESE)
[ 講演概要 ]
In our recent studies, interplay of heterogeneous susceptible
population and reinfection indicates fragility of the threshold
phenomena, which is frequently observed in epidemic models, with
respect to the basic reproduction number. To elaborate this aspect, we
formulate a mathematical model by a system of ODEs and analyze its
equilibrium structure. If time permits, we analyze the transient
solution in detail for a special case and discuss the complexity in
the epidemic dynamics induced by the heterogeneous susceptibility.
大森亮介 氏 (北海道大学) 15:10-15:40In our recent studies, interplay of heterogeneous susceptible
population and reinfection indicates fragility of the threshold
phenomena, which is frequently observed in epidemic models, with
respect to the basic reproduction number. To elaborate this aspect, we
formulate a mathematical model by a system of ODEs and analyze its
equilibrium structure. If time permits, we analyze the transient
solution in detail for a special case and discuss the complexity in
the epidemic dynamics induced by the heterogeneous susceptibility.
Time evolution of Tajima's D of a pathogen during its outbreak (JAPANESE)
[ 講演概要 ]
Tajima’s D measures the selection pressure by calculating the difference between two estimates of genetic diversity in a given sample set of nucleic acid sequences, however, it is believed that Tajima’s D is biased by the population dynamics. To analyze the impact of population dynamics of infectious disease pathogen, which described by the standard SIR model on Tajima’s D, we developed an inductive algorithm for calculating the site-specific nucleotide frequencies from a standard multi-strain susceptible-infective-removed model (both deterministic and stochastic). We show that these frequencies are fully determined by the mutation rate and the initial condition of the frequencies. We prove that the sign of Tajima’s D is independent of the disease population dynamics in the deterministic model. We also show that the stochasticity in the transmission and evolution dynamics induces the dependency of Tajima’s D on the population dynamics of pathogens.
Xu Yaya 氏 (東京大学大学院数理科学研究科) 15:40-16:10Tajima’s D measures the selection pressure by calculating the difference between two estimates of genetic diversity in a given sample set of nucleic acid sequences, however, it is believed that Tajima’s D is biased by the population dynamics. To analyze the impact of population dynamics of infectious disease pathogen, which described by the standard SIR model on Tajima’s D, we developed an inductive algorithm for calculating the site-specific nucleotide frequencies from a standard multi-strain susceptible-infective-removed model (both deterministic and stochastic). We show that these frequencies are fully determined by the mutation rate and the initial condition of the frequencies. We prove that the sign of Tajima’s D is independent of the disease population dynamics in the deterministic model. We also show that the stochasticity in the transmission and evolution dynamics induces the dependency of Tajima’s D on the population dynamics of pathogens.
Mathematical analysis for HBV model and HBV-HDV coinfection model (ENGLISH)
[ 講演概要 ]
The hepatitis beta virus (HBV) and hepatitis delta viurs (HDV)
are two common forms of viral hepatitis. However HDV is dependent
on coinfection with HBV since replication of HDV requires the hepati-
tis B surface antigen (HBsAg) which can only been produced by HBV.
Here we start with analyzing HBV only model, the dynamics between
healthy cells, HBV infected cells and free HBV.We show that a postive
equilbrium exsits and it's globally asmptotically stable for R0 > 1, an
infection free equilibrium is globally asymptotically stable for R0 < 1.
Then we introduce HDV to form a coinfection model which contains
three more variables, HDV infected cells, coinfected cells and free HDV.
Additionally, we investigate two coinfection models, one without and
one with treatment by oral drugs which are valid for HBV only. We
consider several durgs with variable eciencies. As a result, compari-
son of model simulations indicate that treatment is necessary to taking
contiously for choric infection.
The hepatitis beta virus (HBV) and hepatitis delta viurs (HDV)
are two common forms of viral hepatitis. However HDV is dependent
on coinfection with HBV since replication of HDV requires the hepati-
tis B surface antigen (HBsAg) which can only been produced by HBV.
Here we start with analyzing HBV only model, the dynamics between
healthy cells, HBV infected cells and free HBV.We show that a postive
equilbrium exsits and it's globally asmptotically stable for R0 > 1, an
infection free equilibrium is globally asymptotically stable for R0 < 1.
Then we introduce HDV to form a coinfection model which contains
three more variables, HDV infected cells, coinfected cells and free HDV.
Additionally, we investigate two coinfection models, one without and
one with treatment by oral drugs which are valid for HBV only. We
consider several durgs with variable eciencies. As a result, compari-
son of model simulations indicate that treatment is necessary to taking
contiously for choric infection.
2017年11月16日(木)
16:30-18:00 数理科学研究科棟(駒場) 123号室
中林潤 氏 (横浜市立大学 先端医科学研究センター )
Human Immunodeficiency Virus (HIV) の細胞内複製ダイナミクスと感染個体内における進化 (JAPANESE)
中林潤 氏 (横浜市立大学 先端医科学研究センター )
Human Immunodeficiency Virus (HIV) の細胞内複製ダイナミクスと感染個体内における進化 (JAPANESE)
[ 講演概要 ]
今回のセミナーではHuman Immunodeficiency Virus (HIV) の細胞内複製ダイナミクスと感染個体内における進化を取り扱った研究を紹介する。
HIVは+鎖RNAをゲノムとして持つレンチウイルス属に属するレトロウイルスである。RNAを鋳型として逆転写酵素によって産生されたウイルスDNAが、ホストのゲノムにintegrateされ、そこからウイルス遺伝子産物が産生され、最終的にウイルス粒子が複製される。HAART (Highly Active Antiretroviral Therapy) によってHIV感染患者の予後は劇的に改善されたが、いったんintegrateされたprovirusが休眠状態で残存し、何らかのきっかけで再びウイルスを産生することがあり、これがHIV治療の大きな妨げとなっている。Integration siteの決定機構を解明することは、HIVの治療戦略を検討するのに重要である。
HIVのintegration siteはホストのゲノム中に一様ではなく偏って分布していることが知られている。HIV細胞内複製を記述する数理モデルと、これを用いた進化シミュレーションを使って、HIV integration siteの選好性がどのように決定されるか検討した。またデータベースに登録されたHIV integration siteの情報と、ホストのepigenomeデータを統合して網羅的な解析を行い、integration site特異的な塩基配列について検討したので、これらの結果について紹介したい。
今回のセミナーではHuman Immunodeficiency Virus (HIV) の細胞内複製ダイナミクスと感染個体内における進化を取り扱った研究を紹介する。
HIVは+鎖RNAをゲノムとして持つレンチウイルス属に属するレトロウイルスである。RNAを鋳型として逆転写酵素によって産生されたウイルスDNAが、ホストのゲノムにintegrateされ、そこからウイルス遺伝子産物が産生され、最終的にウイルス粒子が複製される。HAART (Highly Active Antiretroviral Therapy) によってHIV感染患者の予後は劇的に改善されたが、いったんintegrateされたprovirusが休眠状態で残存し、何らかのきっかけで再びウイルスを産生することがあり、これがHIV治療の大きな妨げとなっている。Integration siteの決定機構を解明することは、HIVの治療戦略を検討するのに重要である。
HIVのintegration siteはホストのゲノム中に一様ではなく偏って分布していることが知られている。HIV細胞内複製を記述する数理モデルと、これを用いた進化シミュレーションを使って、HIV integration siteの選好性がどのように決定されるか検討した。またデータベースに登録されたHIV integration siteの情報と、ホストのepigenomeデータを統合して網羅的な解析を行い、integration site特異的な塩基配列について検討したので、これらの結果について紹介したい。
2017年06月28日(水)
14:55-15:45 数理科学研究科棟(駒場) 122号室
Malay Banerjee 氏 (Department of Mathematics & Statistics，IIT Kanpur)
Stabilizing role of maturation delay on prey-predator dynamics (ENGLISH)
Malay Banerjee 氏 (Department of Mathematics & Statistics，IIT Kanpur)
Stabilizing role of maturation delay on prey-predator dynamics (ENGLISH)
[ 講演概要 ]
Discrete and continuous time delays are often introduced into mathematical models of interacting populations to take into account stage-structuring of one or more species. There are other aspects for the incorporation of time delays. In prey-predator models, maturation time delay is introduced to the growth equation of predators to implicitly model the stage-structure of predators. Most of the prey-predator models with maturation delay are known to exhibit regular and rregular, even chaotic, oscillations due to destabilization of coexistence steady-state when maturation time period is significantly large. However, such kind of instability can results in due to the introduction of maturation delay into predator’s growth equation with lack of ecological justification and inappropriate choice of the length of time delay. Recently we have worked on a class of delayed prey-predator models, where discrete time delay represents the maturation time for specialist predator implicitly, with ratio-dependent functional response [1] and Michaelis-Menten type
functional response [2]. We have established (i) the stabilizing role of maturation delay, (ii)extinction of predator for significantly long maturation period and (iii) suppression of Hopf bifurcation for large time delay, when the delayed model is constructed with appropriate biological rationale. Main objective of this talk is to discuss analytical results for the stable coexistence of both the species for a class of delayed prey-predator models with maturation delay for specialist predator. Analytical results will be illustrated with the help of numerical simulation results and appropriate bifurcation diagrams with time delay as bifurcation parameter. Main content of this talk is based upon the recent work with Prof. Y. Takeuchi [2].
References:
[1] M. Sen, M. Banerjee, A. Morozov. (2014). Stage-structured ratio-dependent predatorprey models revisited: When should the maturation lag result in systems destabilization?, Ecological Complexity, 19(2), 23–34.
[2] M. Banerjee, Y. Takeuchi. (2017). Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models, Journal of Theoretical Biology, 412, 154–171.
Discrete and continuous time delays are often introduced into mathematical models of interacting populations to take into account stage-structuring of one or more species. There are other aspects for the incorporation of time delays. In prey-predator models, maturation time delay is introduced to the growth equation of predators to implicitly model the stage-structure of predators. Most of the prey-predator models with maturation delay are known to exhibit regular and rregular, even chaotic, oscillations due to destabilization of coexistence steady-state when maturation time period is significantly large. However, such kind of instability can results in due to the introduction of maturation delay into predator’s growth equation with lack of ecological justification and inappropriate choice of the length of time delay. Recently we have worked on a class of delayed prey-predator models, where discrete time delay represents the maturation time for specialist predator implicitly, with ratio-dependent functional response [1] and Michaelis-Menten type
functional response [2]. We have established (i) the stabilizing role of maturation delay, (ii)extinction of predator for significantly long maturation period and (iii) suppression of Hopf bifurcation for large time delay, when the delayed model is constructed with appropriate biological rationale. Main objective of this talk is to discuss analytical results for the stable coexistence of both the species for a class of delayed prey-predator models with maturation delay for specialist predator. Analytical results will be illustrated with the help of numerical simulation results and appropriate bifurcation diagrams with time delay as bifurcation parameter. Main content of this talk is based upon the recent work with Prof. Y. Takeuchi [2].
References:
[1] M. Sen, M. Banerjee, A. Morozov. (2014). Stage-structured ratio-dependent predatorprey models revisited: When should the maturation lag result in systems destabilization?, Ecological Complexity, 19(2), 23–34.
[2] M. Banerjee, Y. Takeuchi. (2017). Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models, Journal of Theoretical Biology, 412, 154–171.
2017年06月28日(水)
15:50-16:40 数理科学研究科棟(駒場) 122号室
Moitri Sen 氏 (Department. of Mathematics, National Institute of Technology Patna)
Allee effect induced rich dynamics of a two prey one predator model where the predator is
generalist (ENGLISH)
Moitri Sen 氏 (Department. of Mathematics, National Institute of Technology Patna)
Allee effect induced rich dynamics of a two prey one predator model where the predator is
generalist (ENGLISH)
[ 講演概要 ]
One of the important ecological challenges is to capture the chaotic dynamics and understand the underlying regulating factors. Allee effect is one of the important factors in ecology and taking it into account can cause signi cant changes to the system dynamics. In this work we propose a two prey-one predator model where the growth of both the prey population is governed by Allee effect, and the predator is generalist and hence survived on both the prey populations. We analyze the role of Allee e ect on the chaotic dynamics of the system. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee e ect enriches the dynamics of the system. Specially after a certain threshold of the Allee e ect, it has a very signi cant e ect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurca-tions such as namely the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively.
One of the important ecological challenges is to capture the chaotic dynamics and understand the underlying regulating factors. Allee effect is one of the important factors in ecology and taking it into account can cause signi cant changes to the system dynamics. In this work we propose a two prey-one predator model where the growth of both the prey population is governed by Allee effect, and the predator is generalist and hence survived on both the prey populations. We analyze the role of Allee e ect on the chaotic dynamics of the system. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee e ect enriches the dynamics of the system. Specially after a certain threshold of the Allee e ect, it has a very signi cant e ect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurca-tions such as namely the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively.
2017年05月11日(木)
16:30-17:30 数理科学研究科棟(駒場) 126号室
大泉嶺 氏 (国立社会保障・人口問題研究所)
環境変動と個体差の構造人口模型～2重のランダムネスにおける最適戦略の進化～ (JAPANESE)
大泉嶺 氏 (国立社会保障・人口問題研究所)
環境変動と個体差の構造人口模型～2重のランダムネスにおける最適戦略の進化～ (JAPANESE)
[ 講演概要 ]
環境変動に対する生物の可塑性や，ロバストネス，個体の多様性の適応は最適戦
略として進化してきたと考えられている．その論拠の中に，Markov過程を基礎に
置くモデルにおいて，環境変動が適応度を減衰させることや，集団の絶滅を引き
起こすことが挙げられる．その中でも特にランダム推移行列モデルを基礎とした
研究は，生活史と観測データを両方ともに扱えることから理論研究のみならず実
証研究に多くの影響を及ぼしきた．例えば，環境変動（外的不確実性）による適
応度の減少を個々の種がどのような生活史戦略をもって適応しているかといった
議論である．これらの議論の根底にあるのものは，ランダム推移行列の固有値に
関する摂動展開がその平均行列の固有値と左右固有ベクトルによって表現できる
事から，生活史パラメータと環境変動リスクの因果関係が評価できることにある．
一方，個体の多様性には遺伝子疾患や性的優位などの異質性は環境変動とは別
の（内的）不確実性がある，この中で最適生活史スケジュールを考えるには確率
論を含む制御理論が必要である．推移行列モデルと制御理論を統一して生活史進
化と個体群動態を議論する為には，推移行列モデルに対応する偏微分方程式モデ
ルを見つける必要がある．本研究ではまず著者が研究してきた個体の多様性を表
現する偏微分方程式モデルと，確率制御理論による最適生活史スケジュール問題
を統一した研究を紹介する．さらに、前述の摂動展開理論の連続バージョンへの
拡張とそれを用いた具体的なモデルによる環境変動における個体の多様性の進化
を議論したい．
環境変動に対する生物の可塑性や，ロバストネス，個体の多様性の適応は最適戦
略として進化してきたと考えられている．その論拠の中に，Markov過程を基礎に
置くモデルにおいて，環境変動が適応度を減衰させることや，集団の絶滅を引き
起こすことが挙げられる．その中でも特にランダム推移行列モデルを基礎とした
研究は，生活史と観測データを両方ともに扱えることから理論研究のみならず実
証研究に多くの影響を及ぼしきた．例えば，環境変動（外的不確実性）による適
応度の減少を個々の種がどのような生活史戦略をもって適応しているかといった
議論である．これらの議論の根底にあるのものは，ランダム推移行列の固有値に
関する摂動展開がその平均行列の固有値と左右固有ベクトルによって表現できる
事から，生活史パラメータと環境変動リスクの因果関係が評価できることにある．
一方，個体の多様性には遺伝子疾患や性的優位などの異質性は環境変動とは別
の（内的）不確実性がある，この中で最適生活史スケジュールを考えるには確率
論を含む制御理論が必要である．推移行列モデルと制御理論を統一して生活史進
化と個体群動態を議論する為には，推移行列モデルに対応する偏微分方程式モデ
ルを見つける必要がある．本研究ではまず著者が研究してきた個体の多様性を表
現する偏微分方程式モデルと，確率制御理論による最適生活史スケジュール問題
を統一した研究を紹介する．さらに、前述の摂動展開理論の連続バージョンへの
拡張とそれを用いた具体的なモデルによる環境変動における個体の多様性の進化
を議論したい．
