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2022 NCTS Summer Course on Mathematical Biology
 
9:00-16:00, August 1 - 5, 2022
Room 515, Cosmology Bldg., National Taiwan University (8/1~8/3 Onsite Course; 8/4~8/5 Cisco Webex+Online Course), Broadcasting in Lecture Room B, 4th Floor, The 3rd General Building , NTHU (8/1~8/3)

Speaker:
Feng-Bin Wang (Chang Gung University)
Chang-Yuan Cheng (National Pingtung University)
Chang-Hong Wu (National Yang Ming Chiao Tung University )
Naveen K. Vaidya (San Diego State University)
Yukihiko Nakata (Aoyama Gakuin University)


Organizers:
Feng-Bin Wang (Chang Gung University)
Chang-Yuan Cheng (National Pingtung University)
Chang-Hong Wu (National Yang Ming Chiao Tung University )


1. Background

It was known that mathematical modeling can play an important role in the understanding of mechanisms in epidemic systems. This summer course is intended to introduce autonomous models of ordinary differential equations (ODEs) with compartment structure, time-periodic compartmental ODEs models, reaction-diffusion epidemic models, and a class of time-delayed compartmental population models in a periodic environment. The theory and numerical computations of basic reproduction ratio will be included.
We will also give a brief survey of Lyapunov functionals to analyze the global stability of delay systems.
Then we will focus on mathematical models for COVID-19, and impacts of permanent immunity on disease transmission.

2. Course Outline

Topic 1.

Title: The theory of the basic reproduction ratio for the autonomous/time-periodic models in spatially homogeneous/heterogeneous environments

Speaker: Feng-Bin Wang (Chang Gung University)

Abstract:
The basic reproduction ratio R0 is an important index in population biology. In epidemiology,  is the expected number of secondary cases produced, in a completely susceptible population, by a typical infective individual. Usually,  defines the threshold behavior for classical epidemic models. It is a common case that a disease dies out if  is less than unity and the disease is established in the population if it is greater than unity. In this course, we shall introduce the theory of  for the autonomous models of ordinary differential equations (ODEs) with compartment structure, time-periodic compartmental ODEs models, reaction-diffusion epidemic models, and a large class of time-delayed compartmental population models in a periodic environment.

References:
[1] Van den Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29-48 (2002)
[2] W.Wang and X.-Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dynam. Differential Equations, 20, 699-717 (2008).
[3] W. Wang, X.-Q. Zhao : Basic reproduction numbers for reaction-diffusion epidemic models. SIAM J. Appl. Dyn. Syst. 11, 1652-1673 (2012)
[4] X.-Q. Zhao : Basic reproduction ratios for periodic compartmental models with time delay. J. Dyn. Differ. Equ. 29, 67-82 (2017)

 

Topic 2. 

Title: Numerical computations of basic reproduction numbers (ratios) in epidemiological models

Speaker: Chang-Yuan Cheng (National Pingtung University)

Abstract:
The basic reproduction number (ratio) is defined as the average number of secondary infection produced when one infected individual is introduced into a targeted population. In general, it can be used to determine the extinction or persistence of infection/epidemic, and even global convergence dynamics. In this short course, we will introduce its numerical computation in models in forms of non-autonomous ODE, autonomous PDE, and non-autonomous PDE.

References:
[1] Liang X, Zhang L, Zhao XQ (2019) Basic reproduction ratios for periodic abstract functional differential equations (with application to a spatial model for Lyme disease). J Dyn Differ Equ 31:1247–1278.

[2] Posny D,Wang J (2014) Computing the basic reproductive numbers for epidemiological models in nonhomogeneous environments. Appl Math Comput 242:473–490.

[3] Zhao XQ (2017) Basic reproduction ratios for periodic compartmental models with time delay. J Dyn Differ Equ 29:67–82.

 

Topic 3.

Title: Analysis for some delayed epidemic models

Speaker: Chang-Hong Wu (National Yang Ming Chiao Tung University)

Abstract:
This lecture will introduce some epidemic models with time delays based on the classical Kermack-McKendrick Model. We will also give a brief survey of Lyapunov functionals to analyze the global stability properties.

References:
[1] E. Beretta, Y. Takeuchi, Global stability of an SIR epidemic model with time delays, J. Math. Biol. 33 (1995) 250–260.
[2] K. L. Cooke, Stability analysis for a vector disease model, Rocky Mount. J. Math. 7 (1979) 253–263.
[3] C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal. RWA. 11 (2010) 1155–1159.

 

Topic 4.

Title: Mathematical Models for COVID-19

Speaker: Naveen K. Vaidya (San Diego State University, USA)

Abstract:
During the pandemic of new diseases, such as COVID-19, mathematical models offer valuable tools that help design control policies. In this lecture series, I will discuss various modeling techniques for COVID-19 pandemics. I will focus on using real-time data to formulate reproduction numbers and dynamical system models. I will also explore the basic analytical and simulation methods for developed models. Furthermore, I will present how suchdata-driven models can be helpful in the design of control strategies.

 

Topic 5.

Title: Disease transmission dynamics models with/out permanent immunity

Speaker: Yukihiko Nakata (Aoyama Gakuin University, Japan)

Abstract:
In the course, first, we study the formulation of the Kermack & McKendrick model and its property, namely the threshold phenomena and the final size relation with respect to R0. Then the following assumption is incorporated: the recovery individuals are not perfectly protected from the disease, thus they are reinfected. We study some epidemic models without permanent immunity assumption. The model studies suggest that the immune dynamics of individuals may drastically change the disease transmission dynamics in the population.

 

3. Registration

https://forms.gle/UVR5sE2pGNEmmeeZ8

 

Schedule

 

 August 1st   

 (Mon.)

 August 2nd 

 (Tue.)

 August 3rd

 (Wed.)

August 4th

 (Thu.)

August 5th

 (Fri.)

9:00-10:00

FBW

FBW

CHW

NKV

NKV

10:00-11:00

FBW

FBW

CHW

NKV

NKV

11:00-12:00

FBW

FBW

CHW

NKV

NKV

 

 

 

 

 

 

1:00-2:00

CYC

CYC

CHW

YN

YN

2:00-3:00

CYC

CYC

CHW

YN

YN

3:00-4:00

CYC

CYC

CHW

YN

YN

 

 

 

 

 

 

FBW: Feng-Bin Wang (Chang Gung University)
CYC: 
Chang-Yuan Cheng (National Pingtung University)
CHW: Chang-Hong Wu (National Yang Ming Chiao Tung University)
NKV: Naveen K. Vaidya (San Diego State University, USA)
YN: Yukihiko Nakata (Aoyama Gakuin University, Japan)



Contact: Murphy Yu

Poster: events_3_2542207054438160647.pdf


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