[00642] Traveling Waves in Mathematical Epidemiology
Session Time & Room : 1C (Aug.21, 13:20-15:00) @G601
Type : Proposal of Minisymposium
Abstract : Wave propagation in epidemic models is known as one of the interesting issues in the field of mathematical epidemiology. Mathematical theory of traveling wave solutions in epidemic models has been developed in recent years. In many cases, the basic reproduction number or a corresponding threshold value plays an important role in determining the existence of the traveling wave. The purpose of this minisymposium is to share and discuss recent developments and results on this topic among interested researchers.
[05106] Traveling wave solutions for an epidemic model with free boundary
Format : Talk at Waseda University
Author(s) :
Yoichi Enatsu (Tokyo University of Science)
Emiko Ishiwata (Tokyo University of Science)
Takeo Ushijima (Tokyo University of Science)
Abstract : Free boundary problems are recently used to model phenomena of biological invasion for species such as migration into a new habitat. In this talk, we consider a diffusive epidemic model with free boundary. We prove the existence and nonexistence of a traveling wave solution of the model. We numerically observe the traveling wave and the front motion of the model. This is a joint work with Takeo Ushijima and Emiko Ishiwata.
[01447] Traveling Wave Solutions for Discrete Diffusive SIR Epidemic Model
Format : Talk at Waseda University
Author(s) :
Ran Zhang (Heilongjiang University)
Jinliang Wang (Heilongjiang University)
Shengqiang Liu (Tiangong University)
Abstract : In this talk, we deal with the conditions of existence and nonexistence of traveling wave solutions for a class of discrete diffusive epidemic model. In addition, the boundary asymptotic behavior of traveling wave solutions is obtained by constructing a suitable Lyapunov functional and employing Lebesgue dominated convergence theorem. Our result could answer some unsolved problems in the previous studies on discrete diffusive epidemic model.
[04496] Traveling waves of a differential-difference diffusive Kermack-McKendrick epidemic model with age-structured protection phase
Format : Talk at Waseda University
Author(s) :
Mostafa Adimy (Inria and UCBL 1, Lyon)
Abdennasser Chekroun (University of Tlemcen)
Toshikazu Kuniya (Kobe University)
Abstract : We consider a general class of diffusive Kermack-McKendrick SIR epidemic models with an age-structured protection phase with limited duration, for example due to vaccination or drugs with temporary immunity. A saturated incidence rate is also considered which is more realistic than the bilinear rate. The characteristics method reduces the model to a coupled system of a reaction-diffusion equation and a continuous difference equation with a time-delay and a nonlocal spatial term caused by individuals moving during their protection phase. We study the existence and non-existence of non-trivial traveling wave solutions. We get almost complete information on the threshold and the minimal wave speed that describes the transition between the existence and non-existence of non-trivial traveling waves that indicate whether the epidemic can spread or not. We discuss how model parameters, such as protection rates, affect the minimal wave speed. The difficulty of our model is to combine a reaction-diffusion system with a continuous difference equation. We deal with our problem mainly by using Schauder’s fixed point theorem. More precisely, we reduce the problem of the existence of non-trivial traveling wave solutions to the existence of an admissible pair of upper and lower solutions.
