STABILITY AND TRAVELING WAVES OF AN EPIDEMIC MODEL WITH RELAPSE AND SPATIAL DIFFUSION

Zhiping Wang; Rui Xu

doi:10.11948/2014016

2014 Volume 4 Issue 3

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Zhiping Wang, Rui Xu. STABILITY AND TRAVELING WAVES OF AN EPIDEMIC MODEL WITH RELAPSE AND SPATIAL DIFFUSION[J]. Journal of Applied Analysis & Computation, 2014, 4(3): 307-322. doi: 10.11948/2014016

Citation:

Zhiping Wang, Rui Xu. STABILITY AND TRAVELING WAVES OF AN EPIDEMIC MODEL WITH RELAPSE AND SPATIAL DIFFUSION[J]. Journal of Applied Analysis & Computation, 2014, 4(3): 307-322. doi: 10.11948/2014016

STABILITY AND TRAVELING WAVES OF AN EPIDEMIC MODEL WITH RELAPSE AND SPATIAL DIFFUSION

Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

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Abstract

Abstract

An epidemic model with relapse and spatial diffusion is studied. Such a model is appropriate for tuberculosis, including bovine tuberculosis in cattle and wildlife, and for herpes. By using the linearized method, the local stability of each of feasible steady states to this model is investigated. It is proven that if the basic reproduction number is less than unity, the diseasefree steady state is locally asymptotically stable; and if the basic reproduction number is greater than unity, the endemic steady state is locally asymptotically stable. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder's fixed point theorem, the existence of a traveling wave solution which connects the two steady states is established. Furthermore, numerical simulations are carried out to complement the main results.
- Traveling waves /
- relapse /
- spatial diffusion /
- upper-lower solutions /
- time delay
MSC: 92B05;35C07

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References

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