# American Institute of Mathematical Sciences

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## Dynamics of a vector-host model under switching environments

 1 Department of Mathematics, The University of Alabama, Tuscaloosa, Alabama 35487-0350, USA 2 Faculty of Basic Sciences, Ho Chi Minh University of Transport, 2 Vo Oanh, Ho Chi Minh, Vietnam

** Corresponding author: Tran D. Tuong

Received  January 2020 Revised  November 2020 Published  February 2021

Fund Project: This author is supported in part by NSF grant DMS-1853467

In this paper, the stochastic vector-host model has been proposed and analysed using nice properties of piecewise deterministic Markov processes (PDMPs). A threshold for the stochastic model is derived whose sign determines whether the disease will eventually disappear or persist. We show mathematically the existence of scenarios where switching plays a significant role in surprisingly reversing the long-term properties of deterministic systems.

Citation: Harrison Watts, Arti Mishra, Dang H. Nguyen, Tran D. Tuong. Dynamics of a vector-host model under switching environments. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021029
##### References:

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##### References:
Sample paths of $I_H(t)$ (Example 4.1). In the deterministic systems (LEFT) there is persistence in state 1 and extinction in state 2. In the switched system (RIGHT), the infection persists
Sample paths of $I_H(t)$ (Example 4.2). In both deterministic systems (LEFT), $I_H(t)$ converges exponentially fast to 0. Switching makes the disease persist (RIGHT)
Joint density of $(S_H(t),I_H(t),\xi_t)$ in state 1 (LEFT) and state 2 (RIGHT), according to the invariant measure (Example 4.2)
Sample paths of $I_H(t)$ (Example 4.3). In both deterministic systems, $I_H(t)$ converges to a positive equilibrium (LEFT). Switching allows for extinction (RIGHT)
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