## 数理人口学・数理生物学セミナー

### 2018年03月19日(月)

17:00-18:00   数理科学研究科棟(駒場) 509号室

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 ]

### 2017年12月21日(木)

16:30-18:00   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

### 2017年12月14日(木)

13:00-16:40   数理科学研究科棟(駒場) 126号室

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.

[ 講演概要 ]

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

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.

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.
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 eciencies. 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

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 ]

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)
[ 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.

### 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)
[ 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.

### 2017年05月11日(木)

16:30-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

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

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

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

を議論したい．

### 2017年04月06日(木)

16:00-17:00   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

### 2017年04月06日(木)

17:00-18:00   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

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

### 2016年10月28日(金)

13:30-14:30   数理科学研究科棟(駒場) 126号室

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.

### 2016年07月27日(水)

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.

### 2016年07月13日(水)

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)

[ 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.

### 2016年06月01日(水)

16:30-17:30   数理科学研究科棟(駒場) 128演習室号室

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
$$u_t=u_{xx}+b(x)u(1-u).$$
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:
$$-L_{\lambda,b}\psi=-\frac{d^2}{dx^2}\psi-2\lambda\frac{d}{dx}\psi-(b(x) +\lambda^2)\psi\ \ (x\in\mathbb{R}/L\mathbb{Z}).$$
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 $b(x)$.

### 2016年04月26日(火)

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 ]
https://web.viu.ca/idelsl/

### 2016年01月27日(水)

13:30-16:30   数理科学研究科棟(駒場) 128号室

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。

[ 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.

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
モデルは数学的には1階偏微分方程式の境界値問題と見なすことができ、その境

の境界値問題に対し、自明平衡解の安定化のための境界フィードバック制御を導

ルエンザの報告データに対してこの予測法を適用すると、その精度は8割を超え
ることが確認された。本研究は佐野英樹教授（神戸大学大学院システム情報学研

[ 講演概要 ]
マラリアは蚊によって媒介される感染症であるため、その流行を考察するにあたってヒトと蚊と両方の動態を考えることが必要である。主な流行地域の一つである南アフリカでは一つ一つの村(人口密集地)間の間隔が広く、村から村へとマラリアの感染を伝播させているのは主に車などの移動手段によるヒトの移動・交流であると考えられる。本研究では村間のヒトの往来に焦点を当て、マラリア流行の古典的なモデルであるRossモデルを下敷きとした数理モデルを構築した。また実際の村間のネットワーク構造を用いて南アフリカにおける感染報告データと比較しながら、何がマラリア感染の伝播のリスク要因となっているのかを解析してゆくために、今回は基本的なモデル解析を行った結果を報告する。

### 2015年12月02日(水)

14:55-16:40   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]
ネットワーク上における感染症流行を阻止するために，中心性指標を用いた

れることから，我々は基本増殖率の感受性解析を用いた新たなネットワーク中心

ったところ，既存の中心性指標では見落とされてきた流行動態を明らかにできた．

また，侵入阻止（基本増殖率低下）のために注力すべき箇所と，侵入が起こった
さいに被害低減（最終規模低下）のために注力すべき箇所が必ずしも一致しない
ことが分かった．本講演では，提案したネットワーク中心性指標の紹介および上

[ 講演参考URL ]
http://www.soken.ac.jp/

### 2015年11月18日(水)

14:55-16:40   数理科学研究科棟(駒場) 128号室

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 ]
http://www.ics.nara-wu.ac.jp/jp/staff/takasu.html

### 2015年10月28日(水)

14:55-16:40   数理科学研究科棟(駒場) 128演習室号室

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

スティック方程式を構成するパラメータ、内的増加率rと環境収容力Kをもちいて

であると論じたものである．この説は発表当初から賛否両論を巻き起こしてきた．

が環境収容力を最大化するために少産少死長寿という特質を獲得するという主張
である．実証研究はこの主張をウミガメや樹木、サルの群れ構造などの例を用い
て反駁してきた．2000年代に入るまでに様々な理論モデルや実証研究結果が示さ
れたが、議論の盛り上がりは“飽和した人口の中で起こる生活史進化とは何か？”
という疑問を残したまま停滞している．そこで、本研究では非線形齢―状態構造
モデルと生活史戦略理論を確率制御理論によって統合したモデルを構築し、この

### 2015年10月21日(水)

14:55-16:40   数理科学研究科棟(駒場) 128演習室号室

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 ]
http://researchers.general.hokudai.ac.jp/profile/ja.e3OkdvtshzEabOVZ2w5OYw==.html

### 2015年06月17日(水)

14:55-16:40   数理科学研究科棟(駒場) 128演習室号室

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 ]

### 2015年06月03日(水)

14:55-16:40   数理科学研究科棟(駒場) 128演習室号室

[ 講演概要 ]

マ類、外洋性サメ類などが挙げられる．回遊により地域ごとに漁獲される水産資

ても未成魚を漁獲する地域と成魚を漁獲する地域が異なる場合が多い．しかし、

を考慮した個体群動態モデルを基本モデルとする．次にモデルから得られる個体

### 2015年04月15日(水)

14:55-16:40   数理科学研究科棟(駒場) 128演習室号室

(JAPANESE)
[ 講演概要 ]

が歴然としているのは、成熟年齢やサイズなど個体の持つ生活史の特性が、双方
とも異なる事に起因すると考えられている．しかし、それら個体の特性が個体群

ズ構造、両方を考慮した構造人口模型を考える．具体的には、人口規模の増大が

また、この種をあるサイズに達したときに繁殖する一回繁殖生物と仮定する．こ
れらの仮定から生成された構造人口模型の定常状態を環境収容力と考え、サイズ
の成長率の分散（個体差）が環境収容力とそこでの個体群構造への影響を解析し
たい．

### 2014年12月22日(月)

15:00-16:20   数理科学研究科棟(駒場) 122号室
Don Yueping 氏 (Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo)
Estimating the seroincidence of pertussis in Japan
[ 講演概要 ]
Despite relatively high vaccination coverage of pertussis for decades, the disease keeps circulating among both vaccinated and unvaccinated individuals and a periodic large epidemic is observed every 4 years. To understand the transmission dynamics, specific immunoglobulin G (IgG) antibodies against pertussis toxin (PT) have been routinely measured in Japan. Using the cross-sectional serological survey data with a known decay rate of antibody titres as a function of time since infection, we estimate the age-dependent seroincidence of pertussis. The estimated incidence of pertussis declined with age, the shape of which will be extremely useful for reconstructing the transmission dynamics and considering effective countermeasures.

### 2014年12月17日(水)

14:50-16:20   数理科学研究科棟(駒場) 122号室

(JAPANESE)
[ 講演概要 ]

ます。その動きはケラーシーゲル系と呼ばれる連立偏微分方程式系を用いて記述されます。本研究においては、標準的ブラウン運動によって駆動される確率過程を導入した確率微分方程式を用いることによって、ケラーシーゲル系の解に確率論的表記を与えることが目標です。また、モンテカルロ法を用いた近似解の構成方法について発表します。

### 2014年12月03日(水)

14:50-16:20   数理科学研究科棟(駒場) 122号室

(JAPANESE)
[ 講演概要 ]
Busenberg et al. (1991) では、非線形偏微分方程式系として記述されるある年