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

Zhiping Wang | Zendy; Rui Xu | Zendy

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

Author(s) -

Zhiping Wang,

Rui Xu

Publication year - 2014

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2014016

Subject(s) - traveling wave , mathematics , steady state (chemistry) , epidemic model , stability theory , stability (learning theory) , basic reproduction number , complement (music) , diffusion , convergence (economics) , mathematical analysis , physics , computer science , demography , biology , economics , chemistry , quantum mechanics , population , machine learning , economic growth , sociology , biochemistry , nonlinear system , complementation , gene , phenotype

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 disease-free 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.

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