Global $L^\infty$-bounds and long-time behavior of a diffusive epidemic system in heterogeneous environment

Rui Peng; Yixiang Wu

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arXiv · 1906.11699

Global $L^\infty$-bounds and long-time behavior of a diffusive epidemic system in heterogeneous environment

Rui Peng·Yixiang Wu

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Abstract

In this paper, we are concerned with an epidemic reaction-diffusion system with nonlinear incidence mechanism of the form $S^qI^p\,(p,\,q>0)$. The coefficients of the system are spatially heterogeneous and time dependent (particularly time periodic). We first establish the $L^\infty$-bounds of the solutions of a class of systems, which improve some previous results in [58]. Based on such estimates, we then study the long-time behavior of the solutions of the system. Our results reveal the delicate effect of the infection mechanism, transmission rate, recovery rate and disease-induced mortality rate on the infection dynamics. Our analysis can be adapted to some other types of infection incidence mechanisms.

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Rui Peng, Yixiang Wu. 2019-06-27. Global $L^\infty$-bounds and long-time behavior of a diffusive epidemic system in heterogeneous environment. https://arxiv.org/abs/1906.11699

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