## Mathematical Biology Seminar

Seminar information archive ～09/23｜Next seminar｜Future seminars 09/24～

**Seminar information archive**

### 2023/03/24

10:00-11:00 Online

Unexpected coexistence and extinction in an intraguild predation system (Japanese)

**Toshiyuki Namba**(Osaka Metropolitan University)Unexpected coexistence and extinction in an intraguild predation system (Japanese)

### 2022/01/19

15:00-16:00 Online

Destabilization induced by time delay, immunity and absorbing effect

(Japanese)

[ Reference URL ]

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．

**Tsuyoshi Kajiwara**(Professor Emeritus, Okayama University)Destabilization induced by time delay, immunity and absorbing effect

(Japanese)

[ Reference URL ]

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．

### 2021/11/30

15:30-17:00 Room #オンライン開催 (Graduate School of Math. Sci. Bldg.)

Endogenous Waves in a SIR Model with Risk Heterogeneity

(Japanese)

[ Reference URL ]

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．

**Takeshi OJIMA**(Fukushima University)Endogenous Waves in a SIR Model with Risk Heterogeneity

(Japanese)

[ Reference URL ]

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．

### 2021/11/26

15:00-16:30 Online

Derivation of structured population models of cellular proliferation on an

energy landscape

[ Reference URL ]

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．

**Shinji NAKAOKA**(Faculty of Advanced Life Science, Hokkaido University)Derivation of structured population models of cellular proliferation on an

energy landscape

[ Reference URL ]

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．

### 2021/10/07

15:00-16:30 Online

The role of mathematical model in the practice of infectious disease control (Japanese)

**Ryosuke Omori**(International Institute for Zoonosis Control, Hokkaido University)The role of mathematical model in the practice of infectious disease control (Japanese)

### 2021/05/27

15:00-16:00 Online

Modeling infective contact by point process (Japanese)

**Nariyuki Minami**(Keio University School of Medicine)Modeling infective contact by point process (Japanese)

### 2021/01/14

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

Estimation of the evacuation effect from Wuhan, China, during COVID-19 outbreak

**Yusuke Asai**(National Center for Global Health and Medicine)Estimation of the evacuation effect from Wuhan, China, during COVID-19 outbreak

### 2020/11/26

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

Some reinfection models (Japanese)

**Yukihiko Nakata**(Department of Physics and Mathematics, Aoyama Gakuin University)Some reinfection models (Japanese)

### 2020/10/07

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

The method of the third wave prediction of the infection by the Effective SIQR model (日本語)

**Masao Namiki**(Former Executive Vice President, Board of Directors and Representative Executive Officers)The method of the third wave prediction of the infection by the Effective SIQR model (日本語)

### 2019/10/17

14:00-16:00 Room #052 (Graduate School of Math. Sci. Bldg.)

Complex spatiotemporal dynamics in a simple predator-prey model (ENGLISH)

Functional response of competing populations to environmental variability (ENGLISH)

**Merlin C. Koehnke**(Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrueck University) 14:00-15:00Complex spatiotemporal dynamics in a simple predator-prey model (ENGLISH)

[ Abstract ]

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.

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**(Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrueck University) 15:00-16:00Functional response of competing populations to environmental variability (ENGLISH)

[ Abstract ]

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

identied as well as parameter ranges of bistability. The latter are used for the numerical

study of diusive invasion phenomena. The Fickian diusivities, 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 diusion. An interesting feature of Fokker-Planck diusion is that for spatially varying diusion coecients the stationary solution is not a homogeneous distribution.

Instead, the densities accumulate in regions of low diusivity and tend to lower levels for

areas of high diusivity. Thus, the stationary distribution of the Fokker-Planck diusion can

be interpreted as a re

ection of dierent 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

diusion 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

identied as well as parameter ranges of bistability. The latter are used for the numerical

study of diusive invasion phenomena. The Fickian diusivities, 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 diusion. An interesting feature of Fokker-Planck diusion is that for spatially varying diusion coecients the stationary solution is not a homogeneous distribution.

Instead, the densities accumulate in regions of low diusivity and tend to lower levels for

areas of high diusivity. Thus, the stationary distribution of the Fokker-Planck diusion can

be interpreted as a re

ection of dierent 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

diusion 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.

### 2019/08/01

15:00-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Mathematical study of the inhibitory role of regulatory T cells in tumor immune response

**Yueping Dong**(Central China Normal University)Mathematical study of the inhibitory role of regulatory T cells in tumor immune response

[ Abstract ]

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.

### 2019/07/11

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Understanding The Seasonality of Dengue Disease Incidences From Empirical Data (ENGLISH)

**Dipo Aldila**(Universitas Indonesia)Understanding The Seasonality of Dengue Disease Incidences From Empirical Data (ENGLISH)

[ Abstract ]

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.

### 2019/07/01

11:00-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Taylor's Law of Fluctuation Scaling

https://www.rockefeller.edu/our-scientists/heads-of-laboratories/940-joel-e-cohen/

**Joel E. Cohen**(The Rockefeller University and Columbia University)Taylor's Law of Fluctuation Scaling

[ Abstract ]

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.

[ Reference 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/

### 2019/06/20

16:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Diffusion limit for the partner model at the critical value (ENGLISH)

**Eric Foxall**(University of Alberta)Diffusion limit for the partner model at the critical value (ENGLISH)

[ Abstract ]

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.

### 2018/10/04

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Modelling the beginnings, middles and ends of infectious disease outbreaks

(ENGLISH)

http://www.robin-thompson.co.uk/

**Robin Thompson**(University of Oxford, UK)Modelling the beginnings, middles and ends of infectious disease outbreaks

(ENGLISH)

[ Abstract ]

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.

[ Reference 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/

### 2018/07/27

15:00-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches

**Somdatta Sinha**(Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali INDIA)Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches

[ Abstract ]

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.

### 2018/07/18

15:00-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Effect of demographic stochasticity on large amplitude oscillation

**Malay Banerjee**(Department of Mathematics & Statistics, IIT Kanpur)Effect of demographic stochasticity on large amplitude oscillation

[ Abstract ]

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.

### 2018/05/28

15:30-16:30 Room #122 (Graduate School of Math. Sci. Bldg.)

T-cell mediated adaptive immunity in primary dengue infections

https://www.sciencedirect.com/science/article/pii/S0022519317303211

**Sourav Kumar Sasmal**(Department of Physics and Mathematics, Aoyama Gakuin University)T-cell mediated adaptive immunity in primary dengue infections

[ Abstract ]

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.

[ Reference 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

### 2018/03/19

17:00-18:00 Room #509 (Graduate School of Math. Sci. Bldg.)

Large deviation theory for age-structured population dynamics

**Yuki Sugiyama**(Institute of Industrial Science, The University of Tokyo)Large deviation theory for age-structured population dynamics

[ Abstract ]

Control of population growth is ubiquitous problem in many fields. In the context of medical treatment, we attempt to diminish the growing speed of a cell population composed of cancer cells or pathogens by using antibiotics or some special therapies. In terms of evolutional biology, to survive in a fluctuating environment, cells maximize (optimize) their population growth by exploiting a risk hedge strategy for adaptation to the fluctuation. Recent development of experimental devices enables us to measure a big size lineage data that describes a growing cell population. In this study, by using these lineage data, we analyze a behavior of the population growth. Here, a structure of statistical mechanics using the large deviation theory plays an important role. As a results, we reveal that the population growth rate is given by the Legendre transform of the large deviation function for the semi-Markov process that describes a stochastic switch of cell types in the time evolution. Furthermore, by using this structure, we show that responses of the population growth rate with respect to an environmental change can be evaluated by statistics on a retrospective lineage path.

Control of population growth is ubiquitous problem in many fields. In the context of medical treatment, we attempt to diminish the growing speed of a cell population composed of cancer cells or pathogens by using antibiotics or some special therapies. In terms of evolutional biology, to survive in a fluctuating environment, cells maximize (optimize) their population growth by exploiting a risk hedge strategy for adaptation to the fluctuation. Recent development of experimental devices enables us to measure a big size lineage data that describes a growing cell population. In this study, by using these lineage data, we analyze a behavior of the population growth. Here, a structure of statistical mechanics using the large deviation theory plays an important role. As a results, we reveal that the population growth rate is given by the Legendre transform of the large deviation function for the semi-Markov process that describes a stochastic switch of cell types in the time evolution. Furthermore, by using this structure, we show that responses of the population growth rate with respect to an environmental change can be evaluated by statistics on a retrospective lineage path.

### 2017/12/21

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Theoretical approaches to understand eco-evolutionary feedbacks

**Masato Yamamichi**(Department of General Systems Studies, The University of Tokyo)Theoretical approaches to understand eco-evolutionary feedbacks

### 2017/12/14

13:00-16:40 Room #126 (Graduate School of Math. Sci. Bldg.)

Mathematical analysis for HBV model and HBV-HDV coinfection model (ENGLISH)

**Xu Yaya**15:40-16:10Mathematical analysis for HBV model and HBV-HDV coinfection model (ENGLISH)

[ Abstract ]

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.

### 2017/11/16

16:30-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Jun Nakabayashi**(Yokohama City University)(JAPANESE)

### 2017/06/28

14:55-15:45 Room #122 (Graduate School of Math. Sci. Bldg.)

Stabilizing role of maturation delay on prey-predator dynamics (ENGLISH)

**Malay Banerjee**(Department of Mathematics & Statistics，IIT Kanpur)Stabilizing role of maturation delay on prey-predator dynamics (ENGLISH)

[ Abstract ]

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.

### 2017/06/28

15:50-16:40 Room #122 (Graduate School of Math. Sci. Bldg.)

Allee effect induced rich dynamics of a two prey one predator model where the predator is

generalist (ENGLISH)

**Moitri Sen**(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)

[ Abstract ]

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 signicant 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 eect on the chaotic dynamics of the system. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee eect enriches the dynamics of the system. Specially after a certain threshold of the Allee eect, it has a very signicant eect 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 signicant 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 eect on the chaotic dynamics of the system. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee eect enriches the dynamics of the system. Specially after a certain threshold of the Allee eect, it has a very signicant eect 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.

### 2017/05/11

16:30-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Environmental stochasticity and Heterogeniety in structured

population models ~Optimal life schedule in twofold stochasticity (JAPANESE)

**Ryo Oizumi**Environmental stochasticity and Heterogeniety in structured

population models ~Optimal life schedule in twofold stochasticity (JAPANESE)