過去の記録 ~02/18次回の予定今後の予定 02/19~



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
[ 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.
[ 講演参考URL ]


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
[ 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.


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
[ 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.


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
[ 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.

[ 講演参考URL ]


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)
[ 講演概要 ]


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)
[ 講演概要 ]


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)
[ 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) 13:30-14:00
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) 14:00-14:30
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
中田行彦 氏 (島根大学) 14:40-15:10
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) 15:10-15:40
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) 15:40-16:10
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.


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)
[ 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。


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)
[ 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].
[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.


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)
[ 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.


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)
[ 講演概要 ]


16:00-17:00   数理科学研究科棟(駒場) 126号室
中岡慎治 氏 (JST さきがけ・東京大学生産技術研究所)
既存種が存在する条件下での新規種の侵入・絶滅を表す指標に関する考察 (JAPANESE)
[ 講演概要 ]
腸に常在する細菌群集 (菌叢) は種数でいうと数百種類は存在するといわれている。健常な成人の菌叢の種構成や個体数は、短期的にみれば変動せず安定しているといわれるが、とりわけ乳児期の発達段階や離乳による食習慣の変化、もしくは成人であっても、抗菌剤投与による外的摂動によって種構成は大きく変動し得る。菌叢の種構成が個体によって異なることもしられているが、その理由や疾患発症との関連などは不明である。 本研究では、生誕もしくは抗菌剤投与で理想的には初期化された環境において、菌の定着の順序や相互作用が種構成にどういう影響を及ぼすかを調べるための数理解析手法について考察する。本発表では、いわゆる先住者効果を系統的に調べる上で役立つ数学的指標の定義や検証に関して進捗結果を報告する。既に他種が存在する条件の下、ある菌が環境に侵入できるかを表す再生産数 (侵入に関する基本再生産数) のようなを定義し、群集個体群モデルの線形安定性との関連性を議論する予定である


17:00-18:00   数理科学研究科棟(駒場) 126号室
五島祐樹 氏 (筑波大学医学群医学類)
数理的立場から見た造血幹細胞移植における急性GVHDの発症機序 (JAPANESE)
[ 講演概要 ]
血液系腫瘍に対する主な治療法は化学療法と造血幹細胞移植である。特に後者は化学療法に不応な患者にとっての最終手段とも言える。しかしここで問題がある。それは一部の患者では、ドナー(造血幹細胞の提供者)の血球がレシピエント(患者)の主に肝臓、消化管、皮膚を攻撃することで激烈な炎症が生じることである。これはGVHD(Graft Versus Host Disease)と呼ばれる。この反応に関与している細胞は主にCD8陽性細胞とされるが、詳細なことは不明であった。しかし近年、CD226というCD8陽性細胞等に発現する分子が細胞障害に関わるということが分かってきていて、GVHDのバイオマーカーとしても期待されている*[1]。そこで今回、臨床試験で得られた血液中のCD226の経時的な変化を数理モデル(微分方程式モデル)で説明することで、分子細胞レベルの反応について1つの仮説を提案したい。

[1] Soluble DNAM-1, as a Predictive Biomarker for Acute Graft-Versus-Host Disease.Kanaya et al/PLOS ONE 2016


13:30-14:30   数理科学研究科棟(駒場) 126号室
原 朱音 氏 (九州大学システム生命科学府)
When is the allergen immunotherapy effective? (JAPANESE)
[ 講演概要 ]
Allergen immunotherapy is a method to treat allergic symptoms, for example rhinitis and sneezing in Japanese cedar pollen allergy (JCPA). In the immunotherapy of JCPA, patients take in a small amount of pollen over several years, which suppress severe allergic symptoms when exposed to a large amount of environmental pollen after the therapy. We develop a simple mathematical model to identify the condition for successful therapy. We consider the dynamics of type 2 T helper cells (Th2) and regulatory T cells (Treg) and both of them are differentiated from naive T cells. We assume that Treg cells have a much longer lifespan than Th2 cells, which makes Treg cells accumulate over many years during the therapy.
We regard that the therapy is successful if (1) without therapy the patient develops allergic symptoms upon exposure to the environmental pollen, (2) the patient does not develop allergic symptoms caused by the therapy itself, and (3) with therapy the patient does not develop symptoms upon exposure. We find the conditions of each parameter for successful therapy. We also find that the therapy of linearly increasing dose is able to reduce the risk of allergic symptoms caused by the therapy itself, rather than constant dose. We would like to consider application of this model to other kind of allergy, such as food allergy.


15:00-16:00   数理科学研究科棟(駒場) 128号室
Saki Takahashi 氏 (Princeton University)
The ecological dynamics of non-polio enteroviruses: Case studies from China and Japan (ENGLISH)
[ 講演概要 ]
As we approach global eradication of poliovirus (Enterovirus C species), its relatives are rapidly emerging as public health threats. One of these viruses, Enterovirus A71 (EV-A71), has been implicated in large outbreaks of hand, foot, and mouth disease (HFMD), a childhood illness that has had a substantial burden throughout East and Southeast Asia over the past fifteen years. HFMD is typically a self-limiting disease, but a small proportion of EV-A71 infections lead to the development of neurological and systemic complications that can be fatal. EV-A71 also exhibits puzzling spatial characteristics: the virus circulates at low levels worldwide, but has so far been endemic and associated with severe disease exclusively in Asia. In this talk, I will present findings from a recent study that we did to characterize the transmission dynamics of HFMD in China, where over one million cases are reported each year. I will then describe recent efforts to explain the observed multi-annual cyclicity of EV-A71 incidence in Japan and to probe the contributions of other serotypes to the observed burden of HFMD. In closing, I will discuss plans for unifying data and modeling to study this heterogeneity in the endemicity of EV-A71, as well as to broadly better understand the spatial and viral dynamics of this group of infections.


15:00-16:00   数理科学研究科棟(駒場) 128演習室号室
Yu Min 氏 (青山学院大学理工学部)
腫瘍免疫系における時間遅れの二元的な役割 (ENGLISH)
[ 講演概要 ]
In this talk, a previous tumor immune interaction model is simplified by considering a relatively weak immune activation, which can still keep the essential dynamics properties. Since the immune activation process is not instantaneous, we incorporate one delay effect for the activation of the effector cells by helper T cells into the model. Furthermore, we investigate the stability and instability region of the tumor-presence equilibrium state of the delay-induced system with respect to two parameters, the activation rate of effector cells by helper T cells and the helper T cells stimulation rate by the presence of identified tumor antigens. We show the dual role of this delay that can induce stability switches exhibiting destabilization as well as stabilization of the tumor-presence equilibrium. Besides, our results show that the appropriate immune activation time plays a significant role in control of tumor growth.


16:30-17:30   数理科学研究科棟(駒場) 128演習室号室
蕭 冬遠 氏 (東京大学大学院数理科学研究科)
A variational problem associated with the minimal speed of traveling waves for the spatially
periodic KPP equation (ENGLISH)
[ 講演概要 ]
We consider a spatially periodic KPP equation of the form
This equation is motivated by a model in mathematical ecology describing the invasion of an alien species into spatially periodic habitat. We deal with the following variational problem:
$$\underset{b\in A_i}{\mbox{Maximize}}\ \ c^*(b),\ i=1,2,$$
where $c^*(b)$ denotes the minimal speed of the traveling wave of the above equation, and sets $A_1$, $A_2$ are defined by
$$A_1:=\{b\ |\ \int_0^Lb=\alpha L,||b||_{\infty}\le h \},$$
$$A_2:=\{b\ |\ \int_0^Lb^2=\beta L\},$$
with $h>\alpha>0$ and $\beta>0$ being arbitrarily given constants. It is known that $c^*(b)$ is given by the principal eigenvalue $k(\lambda,b)$ associated with the one-dimensional elliptic operator under the periodic boundary condition:
+\lambda^2)\psi\ \ (x\in\mathbb{R}/L\mathbb{Z}).$$
It is important to note that, in one-dimensional reaction-diffusion equations, the minimal speed $c^*(b)$ coincides with the so-called spreading speed. The notion of spreading speed was introduced in mathematical ecology to describe how fast the invading species expands its territory. In other words, our goal is to find an optimal coefficient $b(x)$ that gives the fastest spreading speed under certain given constraints and to study the properties of such $b(x)$.


15:00-16:00   数理科学研究科棟(駒場) 128演習室号室
Lev Idels 氏 (Vanvouver Island University)
Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)
[ 講演概要 ]
In general, delay differential equations provide a richer mathematical
framework (compared with ordinary differential equations) for the
analysis of biosystems dynamics. The inclusion of explicit time lags in
tumor growth models allows direct reference to experimentally measurable
and/or controllable cell growth characteristics. For three different
types of angiogenesis models with variable delays, we consider either
continuous or impulse therapy that eradicates tumor cells and suppresses
angiogenesis. It was shown that with the growth of delays, even
constant, the equilibrium can lose its stability, and sustainable
oscillation, as well as chaotic behavior, can be observed. The analysis
outlines the difficulties which occur in the case of unbounded growth
rates, such as classical Gompertz model, for small volumes of cancer
cells compared to available blood vessels. The Wheldon model (1975) of a
Chronic Myelogenous Leukemia (CML) dynamics is revisited in the light of
recent discovery that this model has a major drawback.
[ 講演参考URL ]


13:30-16:30   数理科学研究科棟(駒場) 128号室
中岡慎治 氏 (東京大学大学院医学系研究科) 15:10-15:50
HIV 感染リンパ器官ネットワークモデルの数理解析 (JAPANESE)
[ 講演概要 ]
バクテリアやウィルスからの感染を防御する働きを担う上で重要な T細胞は、通常リンパ節やリンパ器官に存在する。リンパ器官は免疫応答を活性化する場であると同時に、扁桃炎などウィルス感染の場になることもある。ヒト免疫不全ウィルス(HIV) は、T 細胞に感染するが、T 細胞が常駐するリンパ節に常駐している。リンパ節が HIV感染存続において重要であると示唆されているが、薬剤投与時でも HIV が消滅しない機構については、未だ明らかになっていない。
先行研究では、1000 以上あるヒト体内のリンパ器官ネットワークを計算機上で模したネットワーク数理モデルを構築し、HIV 感染伝播の数値計算を行った(Nakaoka, Satoh, Iwami, J. Math. Biol.2015)。ネットワーク数理モデルに対して定義される次世代行列から導出した基本再生産数をベースに数値解析を行い、リンパ節内で薬剤の効果が弱いことを示唆する臨床研究の理由付けを与えた。
先行研究では数値計算が主であり、ネットワーク数理モデル自体の数理解析はほとんど行ってこなかった。そこで本研究では、数理解析に主眼をおいた最近の進展について議論する。一般にN 個のリンパ器官が結合した状態において、基本再生産数をベースに感染平衡点の存在、また特殊な場合に Lyapunov関数を用いた大域的漸近安定性を示した。
解析中の課題として、基本再生産数が 1 より大きい場合に感染が定着する状況を示した一様パーシステンス (パーマネンス) 性、Inaba and Nishiura (Math. Biosci. 2008) によって定義された状態別再生産数の応用可能性と再生方程式を用いた定式化など、進行中の解析についても紹介する。本研究は、江夏洋一 (東京理科大)、國谷紀良 (神戸大)、中田行彦 (東京大)、竹内康博 (青山学院大学) 氏 (敬称略) らとの共同研究 (contributed equally) である。

佐野英樹 氏 (神戸大学大学院システム情報学研究科) 13:30-14:10
無限次元制御系に対する安定半径の近似について (JAPANESE)
[ 講演概要 ]
We discuss the problem of approximating stability radius appearing
in the design procedure of finite-dimensional stabilizing controllers
for an infinite-dimensional dynamical system. The calculation of
stability radius needs the value of the H-infinity norm of a transfer
function whose realization is described by infinite-dimensional
operators in a Hilbert space. From the practical point of view, we
need to prepare a family of approximate finite-dimensional operators
and then to calculate the H-infinity norm of their transfer functions.
However, it is not assured that they converge to the value of the
H-infinity norm of the original transfer function. The purpose of
this study is to justify the convergence. In a numerical example,
we treat parabolic distributed parameter systems with distributed
control and distributed/boundary observation.

國谷紀良 氏 (神戸大学大学院システム情報学研究科) 14:10-14:50
バックステッピング法に基づく感染人口の増減予測 (JAPANESE)
[ 講演概要 ]
Kermack and McKendrick (1927) から現在に至るまで長く研究されている。その
出するバックステッピング法は近年 Smyshlyaev and Krstic (2004) によって研
布野孝明 氏 (九州大学理学部生物学科) 15:50-16:30
[ 講演概要 ]


14:55-16:40   数理科学研究科棟(駒場) 128号室
八島健太 氏 (総合研究大学院大学)
[ 講演概要 ]

[ 講演参考URL ]


14:55-16:40   数理科学研究科棟(駒場) 128号室
高須夫悟 氏 (奈良女子大学理学部情報科学科)
Spatial population dynamics as a point pattern dynamics (JAPANESE)
[ 講演概要 ]
Spatial population dynamics has been conventionally described as
dynamical system where population size (or population density) changes
with time over space as a continuous "real-valued" variable; these are
often given as partial differential equations as reaction-diffusion
models. In this approach, we implicitly assume infinitely large
population thereby population size changes smoothly and
deterministically. In reality, however, a population is a collection of
a certain number of individuals each of which gives birth or dies with
some stochasticity in a space and the population size as the number of
individuals is "integer-valued". In this talk, I introduce an approach
to reconstruct conventional spatial population dynamics in terms of
point pattern dynamics as a stochastic process. I discuss how to
mathematically describe such spatial stochastic processes using the
moments of increasing order of dimension; densities of points, pairs,
and triplets, etc. are described by integro-differential equations.
Quantification of a point pattern is the key issue here. As examples, I
introduce spatial epidemic SIS and SIR models as point pattern dynamics;
each individual has a certain "mark" depending on its health status; a
snapshot of individuals’ distribution over space is represented by a
marked point pattern and this marked point pattern dynamically changes
with time.
[ 講演参考URL ]


14:55-16:40   数理科学研究科棟(駒場) 128演習室号室
大泉嶺 氏 (厚生労働省)
r/K選択説における確率制御理論の応用 (JAPANESE)
[ 講演概要 ]
r/K 選択説が提唱されてから半世紀になろうとしている.この仮説は生物の生活


14:55-16:40   数理科学研究科棟(駒場) 128演習室号室
大森亮介 氏 (北海道大学人獣共通感染症リサーチセンター バイオインフォマティクス部門)
The distribution of the duration of immunity determines the periodicity of Mycoplasma pneumoniae incidence. (JAPANESE)
[ 講演概要 ]
Estimating the periodicity of outbreaks is sometimes equivalent to the
prediction of future outbreaks. However, the periodicity may change
over time so understanding the mechanism of outbreak periodicity is
important. So far, mathematical modeling studies suggest several
drivers for outbreak periodicity including, 1) environmental factors
(e.g. temperature) and 2) host behavior (contact patterns between host
individuals). Among many diseases, multiple determinants can be
considered to cause the outbreak periodicity and it is difficult to
understand the periodicity quantitatively. Here we introduce our case
study of Mycoplasma pneumoniae (MP) which shows three to five year
periodic outbreaks, with multiple candidates for determinants for the
outbreak periodicity being narrowed down to the last one, the variance
of the length of the immunity duration. To our knowledge this is the
first study showing that the variance in the length of the immunity
duration is essential for the periodicity of the outbreaks.
[ 講演参考URL ]


14:55-16:40   数理科学研究科棟(駒場) 128演習室号室
柿添友輔 氏 (九州大学大学院システム生命科学)
ウイルス感染に伴う時間遅れと保存量の存在:ウイルスダイナミクスの立場から (JAPANESE)
[ 講演概要 ]


14:55-16:40   数理科学研究科棟(駒場) 128演習室号室
岩田繁英 氏 (東京海洋大学大学院海洋科学技術研究科)
[ 講演概要 ]

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