Threshold dynamics of a reaction-diffusion cholera model with seasonality and nonlocal delay

Wenjing Wu; Tianli Jiang; Weiwei Liu; Jinliang Wang

doi:10.3934/cpaa.2022099

Article Contents

2022, Volume 21, Issue 10: 3263-3282. Doi: 10.3934/cpaa.2022099

This issue Previous Article Multiplicity of periodic solutions for second-order perturbed Hamiltonian systems with local superquadratic conditions Next Article Circular average relative to fractal measures

Threshold dynamics of a reaction-diffusion cholera model with seasonality and nonlocal delay

1.
School of Mathematical Science, Heilongjiang University, Harbin 150080, China
2.
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

^*Corresponding author
^*Corresponding author

Received: October 31, 2021

Revised: April 30, 2022

Early access: June 2022

Published: October 2022

W. Wu was supported by Graduate Students Innovation Research Program of Heilongjiang University, P. R. China (no. YJSCX2021-213HLJU). J. Wang was supported by National Natural Science Foundation of China (nos. 12071115, 11871179), Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, and Fundamental Research Funds for the Heilongjiang Education Department (no. 2021-KYYWF-0034)

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Abstract

In this paper, we investigate the threshold results for a nonlocal and time-delayed reaction-diffusion system involving the spatial heterogeneity and the seasonality. Due to the complexity of the model, we rigorously analyze the well-posedness of the model. The basic reproduction number $ \Re_0 $ is characterized with the next generation operator method. We show that the disease-free $ \omega $-periodic solution is globally attractive when $ \Re_0 < 1 $; while the system is uniformly persistent and a positive $ \omega $-periodic solution exists when $ \Re_0 > 1 $. In a special case that the parameters are all independent of the spatial heterogeneity and the seasonality, the global attractivity of the constant equilibria of the model is investigated by the technique of Lyapunov functionals.

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Mathematics Subject Classification: 92D30, 35K57, 35B40.

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