Geodesic
Traveling waves for a diffusive SIR model with delay and nonlinear incidence
Wang, Yanmei 1 ; Liu, Guirong 2 ; Zhao, Aimin 2
1 School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China;School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, China
2 School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 12, p. 1313-1330.

Voir la notice de l'article provenant de la source International Scientific Research Publications

This paper is concerned with the existence and non-existence of traveling wave solutions for a diffusive SIR model with delay and nonlinear incidence. First, we construct a pair of upper and lower solutions and a bounded cone. Then we prove the existence of traveling wave by using Schauder's fixed point theorem and constructing a suitable Lyapunov functional. The nonexistence of traveling wave is obtained by two-sided Laplace transform. Moreover, numerical simulations support the theoretical results. Finally, we also obtain that the minimal wave speed is decreasing with respect to the latent period and increasing with respect to the diffusion rate of infected individuals.
DOI : 10.22436/jnsa.011.12.03
Classification : 35K57, 35C07, 92D30
Keywords: SIR model, traveling wave, time delay, nonlinear incidence

Wang, Yanmei  1 ; Liu, Guirong  2 ; Zhao, Aimin  2

1 School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China;School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, China
2 School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China 
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Wang, Yanmei ; Liu, Guirong ; Zhao, Aimin . Traveling waves for a diffusive SIR model with delay and nonlinear incidence. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 12, p. 1313-1330. doi : 10.22436/jnsa.011.12.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.12.03/

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