Stationary distribution, extinction and density function for a stochastic HIV model with a Hill-type infection rate and distributed delay

Autor:	Wenjie Zuo, Mingguang Shao
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	stochastic hiv model hill function stationary distribution extinction density function Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 30, Iss 11, Pp 4066-4085 (2022)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2022206?viewType=HTML
Popis:	In this article, we investigate the dynamics of a stochastic HIV model with a Hill-type infection rate and distributed delay, which are better choices for mass action laws. First, we transform a stochastic system with weak kernels into a degenerate high-dimensional system. Then the existence of a stationary distribution is obtained by constructing a suitable Lyapunov function, which determines a sharp critical value $ R_0^s $ corresponding to the basic reproduction number for the determined system. Moreover, the sufficient condition for the extinction of diseases is derived. More importantly, the exact expression of the probability density function near the quasi-equilibrium is obtained by solving the Fokker-Planck equation. Finally, numerical simulations are illustrated to verify the theoretical results.
Databáze:	Directory of Open Access Journals
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