# American Institute of Mathematical Sciences

September  2021, 26(9): 4867-4885. doi: 10.3934/dcdsb.2020316

## Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model

 1 School of Mathematical Science, Heilongjiang University, Harbin 150080, China 2 Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5 Canada

* Corresponding author: Yuming Chen

Received  December 2019 Revised  July 2020 Published  September 2021 Early access  November 2020

Fund Project: This research was partially supported by the Graduate Students Innovation Research Program of Heilongjiang University (No. YJSCX2020-211HLJU) (WL); the National Natural Science Foundation of China (Nos. 12071115, 11871179), Natural Science Foundation of Heilongjiang Province (Nos. LC2018002, LH209A021), Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems (JW); and NSERC of Canada (No. RGPIN-2019-05892) (YC)

Taking account of spatial heterogeneity, latency in infected individuals, and time for shed bacteria to the aquatic environment, we build a delayed nonlocal reaction-diffusion cholera model. A feature of this model is that the incidences are of general nonlinear forms. By using the theories of monotone dynamical systems and uniform persistence, we obtain a threshold dynamics determined by the basic reproduction number $\mathcal {R}_0$. Roughly speaking, the cholera will die out if $\mathcal{R}_0<1$ while it persists if $\mathcal{R}_0>1$. Moreover, we derive the explicit formulae of $\mathcal{R}_0$ for two concrete situations.

Citation: Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 4867-4885. doi: 10.3934/dcdsb.2020316
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