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Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion

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  • Jing Yang
  • Siyang Liang
  • Yi Zhang

Abstract

This paper is concerned with the existence of travlelling waves to a SIR epidemic model with nonlinear incidence rate, spatial diffusion and time delay. By analyzing 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 connecting the disease-free steady state and the endemic steady state. Numerical simulations are carried out to illustrate the main results.

Suggested Citation

  • Jing Yang & Siyang Liang & Yi Zhang, 2011. "Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion," PLOS ONE, Public Library of Science, vol. 6(6), pages 1-14, June.
    • Handle: RePEc:plo:pone00:0021128
    DOI: 10.1371/journal.pone.0021128
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    References listed on IDEAS

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    1. Fuentes, M.A. & Kuperman, M.N., 1999. "Cellular automata and epidemiological models with spatial dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 267(3), pages 471-486.
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    Cited by:

    1. Yi-Xiang Chen & Fang-Qian Xu, 2014. "Higher Dimensional Gaussian-Type Solitons of Nonlinear Schrödinger Equation with Cubic and Power-Law Nonlinearities in PT-Symmetric Potentials," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-12, December.

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