Analysis of a degenerate reaction-diffusion host-pathogen model with general incidence rate

2021 ◽  
pp. 125256
Author(s):  
Yinghui Shan ◽  
Xiaoqing Wu ◽  
Jianguo Gao
Keyword(s):  
Incidence Rate ◽  
Reaction Diffusion ◽  
General Incidence Rate ◽  
Host Pathogen

Dynamical analysis of a reaction–diffusion SEI epidemic model with nonlinear incidence rate

2021 ◽  
pp. 2150041
Author(s):  
Jianpeng Wang ◽  
Binxiang Dai
Keyword(s):  
Steady State ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Reaction Diffusion ◽  
Dynamical Analysis ◽  
Asymptotically Stable ◽  
Nonlinear Incidence Rate ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Positive Steady State

In this paper, a reaction–diffusion SEI epidemic model with nonlinear incidence rate is proposed. The well-posedness of solutions is studied, including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions. The basic reproduction numbers are given in both heterogeneous and homogeneous environments. For spatially heterogeneous environment, by the comparison principle of the diffusion system, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] if [Formula: see text], the system will be persistent and admit at least one positive steady state. For spatially homogenous environment, by constructing a Lyapunov function, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if [Formula: see text]. Finally, two examples are given via numerical simulations, and then some control strategies are also presented by the sensitive analysis.

scholarly journals A non-autonomous SEIRS model with general incidence rate

2014 ◽  
Vol 247 ◽  
pp. 169-189 ◽  
Author(s):  
Joaquim P. Mateus ◽  
César M. Silva
Keyword(s):  
Incidence Rate ◽  
General Incidence Rate
Sign in / Sign up

Export Citation Format

Share Document