## Mathematical Biology Seminar

Seminar information archive ～06/14｜Next seminar｜Future seminars 06/15～

**Seminar information archive**

### 2017/04/06

16:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Shinji Nakaoka**(JAPANESE)

### 2017/04/06

17:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

### 2016/10/28

13:30-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)

When is the allergen immunotherapy effective? (JAPANESE)

**Akane Hara**(Graduate School of Systems Life Sciences, Kyushu University)When is the allergen immunotherapy effective? (JAPANESE)

[ Abstract ]

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.

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.

### 2016/07/27

15:00-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The ecological dynamics of non-polio enteroviruses: Case studies from China and Japan (ENGLISH)

**Saki Takahashi**(Princeton University)The ecological dynamics of non-polio enteroviruses: Case studies from China and Japan (ENGLISH)

[ Abstract ]

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.

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.

### 2016/07/13

15:00-16:00 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

Dual role of delay effect in a tumor immune system (ENGLISH)

**Yu Min**(College of Science and Engineering, Aoyama Gakuin University)Dual role of delay effect in a tumor immune system (ENGLISH)

[ Abstract ]

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.

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.

### 2016/06/01

16:30-17:30 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

A variational problem associated with the minimal speed of traveling waves for the spatially

periodic KPP equation (ENGLISH)

**Xiao Dongyuan**(Graduate School of Mathematical Sciences, The University of Tokyo)A variational problem associated with the minimal speed of traveling waves for the spatially

periodic KPP equation (ENGLISH)

[ Abstract ]

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 $b(x)$.

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 $b(x)$.

### 2016/04/26

15:00-16:00 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)

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

**Lev Idels**(Vanvouver Island University)Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)

[ Abstract ]

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.

[ Reference URL ]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.

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

### 2016/01/27

13:30-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Mathematical analysis for HIV infection dynamics in lymphoid tissue network (JAPANESE)

On approximation of stability radius for an infinite-dimensional closed-loop control system

(JAPANESE)

Prediction of the increase or decrease of infected population based on the backstepping method

(JAPANESE)

Mathematical model of malaria spread for a village network

**Shinji Nakaoka**(Graduate School of Medicine, The University of Tokyo) 15:10-15:50Mathematical analysis for HIV infection dynamics in lymphoid tissue network (JAPANESE)

**Hideki Sano**(Graduate School of System Informatics, Kobe University) 13:30-14:10On approximation of stability radius for an infinite-dimensional closed-loop control system

(JAPANESE)

[ Abstract ]

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.

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.

**Toshikazu Kiniya**(Graduate School of System Informatics, Kobe University) 14:10-14:50Prediction of the increase or decrease of infected population based on the backstepping method

(JAPANESE)

**Takaaki Funo**(Faculty of science, Kyushu University) 15:50-16:30Mathematical model of malaria spread for a village network

### 2015/12/02

14:55-16:40 Room #128 (Graduate School of Math. Sci. Bldg.)

Network centrality measure based on sensitivity analysis of the basic reproductive ratio

[ Reference URL ]

http://www.soken.ac.jp/

**Kenta Yajima**( The Graduate University for Advanced Studies (Sokendai), School of Advanced Sciences)Network centrality measure based on sensitivity analysis of the basic reproductive ratio

[ Reference URL ]

http://www.soken.ac.jp/

### 2015/11/18

14:55-16:40 Room #128 (Graduate School of Math. Sci. Bldg.)

Spatial population dynamics as a point pattern dynamics (JAPANESE)

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

**Fugo TAKASU**(Nara Women's University)Spatial population dynamics as a point pattern dynamics (JAPANESE)

[ Abstract ]

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.

[ Reference URL ]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.

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

### 2015/10/28

14:55-16:40 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

Application of stochastic control theory to r/K selection theory affiliation (JAPANESE)

**Ryo Oizumi**(Ministry of Health, Labour and Welfare)Application of stochastic control theory to r/K selection theory affiliation (JAPANESE)

### 2015/10/21

14:55-16:40 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

The distribution of the duration of immunity determines the periodicity of Mycoplasma pneumoniae incidence. (JAPANESE)

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

**Ryosuke Omori**(Research Center for Zoonosis Control, Hokkaido University, Japan)The distribution of the duration of immunity determines the periodicity of Mycoplasma pneumoniae incidence. (JAPANESE)

[ Abstract ]

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.

[ Reference URL ]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.

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

### 2015/06/17

14:55-16:40 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

A conservation law and time-delay for viral infection dynamics (JAPANESE)

**Yusuke Kakizoe**(Graduate school of systems life sciences, Kyushu University)A conservation law and time-delay for viral infection dynamics (JAPANESE)

### 2015/06/03

14:55-16:40 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

Population dynamics of fish stock with migration and its management strategy

**Shigehide Iwata**(The graduate school of marine science and technology, Tokyo University of Marine Science and Technology)Population dynamics of fish stock with migration and its management strategy

### 2015/04/15

14:55-16:40 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

Mathematical modeling of life history and population dynamics: Effects of individual difference on carrying capacity in semelparous species (JAPANESE)

**Ryo Oizumi**(Graduate School of Mathematical Sciences, University of Tokyo)Mathematical modeling of life history and population dynamics: Effects of individual difference on carrying capacity in semelparous species (JAPANESE)

### 2014/12/22

15:00-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)

Estimating the seroincidence of pertussis in Japan

**Don Yueping**(Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo)Estimating the seroincidence of pertussis in Japan

[ Abstract ]

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.

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.

### 2014/12/17

14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)

A probabilistic interpretation of an evolution model of slime bacteria

(JAPANESE)

**Yumi YAHAGI**(Tokyo City University)A probabilistic interpretation of an evolution model of slime bacteria

(JAPANESE)

### 2014/12/03

14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)

Global analysis of age-structured SIS epidemic models with spatial

heterogeneity (JAPANESE)

**Toshikazu Kuniya**(Graduate School of System Informatics, Kobe University)Global analysis of age-structured SIS epidemic models with spatial

heterogeneity (JAPANESE)

### 2014/11/19

14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)

Introduction of Adaptive Dynamics and its application to finite population (JAPANESE)

http://joefs.mind.meiji.ac.jp/~joe/

**Joe Yuichiro Wakano**(Department of Mathematical Sciences Based on Modeling and Analysis)Introduction of Adaptive Dynamics and its application to finite population (JAPANESE)

[ Abstract ]

本講演では、まず無限集団を仮定する通常のAdaptive Dynamicsを紹介し、

進化的安定性と収束安定性を解説する。また、対応する個体ベースシミュレーションを

紹介する。個体数が有限の場合に不可避的に現れる揺らぎ（遺伝的浮動）が、

進化動態に大きな影響を与えることを、まずはシミュレーション研究から示す。

揺らぎの影響を解析的に示すために、無限集団のAdaptive Dynamicsを

Replicator-Mutator方程式系（積分微分方程式系）によって定式化し、

そこから得られるモーメントの時間発展方程式（ODE）に揺らぎの項を

加えた確率微分方程式(SDE)モデルを導出し、個体数が進化的分岐に与える影響を

解析的に導出する。

[ Reference URL ]本講演では、まず無限集団を仮定する通常のAdaptive Dynamicsを紹介し、

進化的安定性と収束安定性を解説する。また、対応する個体ベースシミュレーションを

紹介する。個体数が有限の場合に不可避的に現れる揺らぎ（遺伝的浮動）が、

進化動態に大きな影響を与えることを、まずはシミュレーション研究から示す。

揺らぎの影響を解析的に示すために、無限集団のAdaptive Dynamicsを

Replicator-Mutator方程式系（積分微分方程式系）によって定式化し、

そこから得られるモーメントの時間発展方程式（ODE）に揺らぎの項を

加えた確率微分方程式(SDE)モデルを導出し、個体数が進化的分岐に与える影響を

解析的に導出する。

http://joefs.mind.meiji.ac.jp/~joe/

### 2014/11/05

14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)

Ecological conditions favoring budding in colonial organisms under environmental disturbance (JAPANESE)

[ Reference URL ]

https://sites.google.com/site/mayukonakamarulab/

**Mayuko Nakamaru**(Department of Value and Decision Science, Tokyo Institute of Technology)Ecological conditions favoring budding in colonial organisms under environmental disturbance (JAPANESE)

[ Reference URL ]

https://sites.google.com/site/mayukonakamarulab/

### 2014/10/22

14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)

Fast reaction limit of a system with different reaction terms (JAPANESE)

**Harunori Monobe**(Meiji Institute for Advanced Study of Mathematical Sciences)Fast reaction limit of a system with different reaction terms (JAPANESE)

### 2014/10/08

14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Qualitative analysis of disease transmission dynamics for renewal equations (JAPANESE)

**Yoichi Enatsu**(Graduate School of Math. Sci. Bldg.)Qualitative analysis of disease transmission dynamics for renewal equations (JAPANESE)

### 2014/08/06

14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)

The stochastic SIS epidemic model in a periodic environment (ENGLISH)

**Nicolas Bacaer**(Insitut de Recherche pour le Developpement (IRD))The stochastic SIS epidemic model in a periodic environment (ENGLISH)

[ Abstract ]

In the stochastic SIS epidemic model with a contact rate a,

a recovery rate bT is such that (log T)/N converges to c=b/a-1-log(b/a) as N grows to

infinity. We consider the more realistic case where the contact rate

a(t) is a periodic function whose average is bigger than b. Then (log

T)/N converges to a new limit C, which is linked to a time-periodic

Hamilton-Jacobi equation. When a(t) is a cosine function with small

amplitude or high (resp. low) frequency, approximate formulas for C

can be obtained analytically following the method used in [Assaf et

al. (2008) Population extinction in a time-modulated environment. Phys

Rev E 78, 041123]. These results are illustrated by numerical

simulations.

In the stochastic SIS epidemic model with a contact rate a,

a recovery rate bT is such that (log T)/N converges to c=b/a-1-log(b/a) as N grows to

infinity. We consider the more realistic case where the contact rate

a(t) is a periodic function whose average is bigger than b. Then (log

T)/N converges to a new limit C, which is linked to a time-periodic

Hamilton-Jacobi equation. When a(t) is a cosine function with small

amplitude or high (resp. low) frequency, approximate formulas for C

can be obtained analytically following the method used in [Assaf et

al. (2008) Population extinction in a time-modulated environment. Phys

Rev E 78, 041123]. These results are illustrated by numerical

simulations.

### 2014/07/23

14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Resting-state brain networks, their energy landscapes, and sleep (JAPANESE)

**Naoki Masuda**(University of Bristol, Department of Engineering Mathematics)Resting-state brain networks, their energy landscapes, and sleep (JAPANESE)

### 2014/06/25

14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Mathematical modeling and classification of tumor immunity in cell transfer therapy (JAPANESE)

**Shinnji Nakaoka**(理化学研究所統合生命医科学研究センター)Mathematical modeling and classification of tumor immunity in cell transfer therapy (JAPANESE)