scholarly journals Global behavior of a multi-group SEIR epidemic model with age structure and spatial diffusion

2020 ◽  
Vol 17 (6) ◽  
pp. 7248-7273
Author(s):  
Pengyan Liu ◽  
◽  
Hong-Xu Li
Keyword(s):  
Age Structure ◽  
Epidemic Model ◽  
Spatial Diffusion ◽  
Global Behavior

scholarly journals Global behavior of a multi-group SIS epidemic model with age structure

2005 ◽  
Vol 218 (2) ◽  
pp. 292-324 ◽  
Author(s):  
Zhilan Feng ◽  
Wenzhang Huang ◽  
Carlos Castillo-Chavez
Keyword(s):  
Age Structure ◽  
Epidemic Model ◽  
Global Behavior ◽  
Sis Epidemic Model ◽  
Sis Epidemic

scholarly journals The Global Behavior of a Periodic Epidemic Model with Travel between Patches

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Luosheng Wen ◽  
Bin Long ◽  
Xin Liang ◽  
Fengling Zeng
Keyword(s):  
Epidemic Model ◽  
Transmission Rate ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Periodic Transmission ◽  
Theoretical Results ◽  
Disease Free

We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratioR0and two theorems on the global behavior: ifR0< 1 the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then it is unstable; ifR0> 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.

scholarly journals Travelling Waves of a Diffusive Epidemic Model with Latency and Relapse

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Zhiping Wang ◽  
Rui Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Epidemic Model ◽  
Wave Solution ◽  
Local Stability ◽  
Travelling Waves ◽  
Upper And Lower Solutions ◽  
Travelling Wave ◽  
Spatial Diffusion ◽  
Travelling Wave Solution

An SEIR epidemic model with relapse and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of each of the feasible steady states to this model is discussed. The existence of a travelling wave solution is established by using the technique of upper and lower solutions and Schauder's fixed point theorem. Numerical simulations are carried out to illustrate the main results.

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