A diffusive SIS epidemic model incorporating the media coverage impact in the heterogeneous environment

Jing Ge; Ling Lin; Lai Zhang

doi:10.3934/dcdsb.2017134

Article Contents

2017, Volume 22, Issue 7: 2763-2776. Doi: 10.3934/dcdsb.2017134

This issue Previous Article Adaptive methods for stochastic differential equations via natural embeddings and rejection sampling with memory Next Article Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems

A diffusive SIS epidemic model incorporating the media coverage impact in the heterogeneous environment

1.
School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China
2.
School of Mathematical Science, Yangzhou University, Yangzhou 225002, China
3.
Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
4.
Department of Mathematics and Mathematical Statistics, Umeå University, SE-90187, Umeå, Sweden

* Corresponding author
* Corresponding author

Received: July 31, 2016

Revised: October 31, 2016

Published: October 2017

The work is partially supported by the NSF of China (Grant No. 11501494,11571301), NSF of Jiangsu Province (BK20151305, BK20151288).

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Abstract

To explore the impact of media coverage and spatial heterogeneity of environment on the prevention and control of infectious diseases, a spatial-temporal SIS reaction-diffusion model with the nonlinear contact transmission rate is proposed. The nonlinear contact transmission rate is spatially dependent and introduced to describe the impact of media coverage on the transmission dynamics of disease. The basic reproduction number associated with the disease in the heterogeneous environment is established. Our results show that the degree of mass media attention plays an important role in preventing the spreading of infectious diseases. Numerical simulations further confirm our analytical findings.

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Mathematics Subject Classification: Primary:35B40;Secondary:92D30.

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Figure 1. For $m=1$, the solution $(S(x,t),I(x,t))$ stabilizes to a positive equilibrium.

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Figure 2. For $m=5$, the infected individuals $I(x,t)$ with the given initial condition decays to zero quickly(left); the susceptible individuals $S(x,t)$ stabilizes to a positive steady-state (right).

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