Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 12, Issue 1, Pages 52-68Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2010.05.035
Keywords
SIRS; Reaction diffusion; Travelling waves; Upper-lower solutions; Partial monotonicity
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Funding
- National Natural Science Foundation of China [10671209]
- Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
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This paper is concerned with the existence of travelling waves to an SIRS epidemic model with bilinear incidence rate, spatial diffusion and time delay. By analysing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this system under homogeneous Neumann boundary conditions is discussed. By using the cross iteration method and the Schauder's fixed point theorem, we reduce the existence of travelling waves to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a travelling wave solution connecting the disease-free steady state and the endemic steady state. Numerical simulations are carried out to illustrate the main results. (C) 2010 Elsevier Ltd. All rights reserved.
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