Open AccessDynamics and approximation of positive solution of the stochastic SIS model affected by air pollutants
Author(s) -
Qi Zhou,
Huaimin Yuan,
Qimin Zhang
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022207
Subject(s) - mathematics , stationary distribution , convergence (economics) , kernel (algebra) , operator (biology) , extinction (optical mineralogy) , semigroup , markov chain , moment (physics) , rate of convergence , markov process , mathematical optimization , mathematical analysis , statistics , computer science , pure mathematics , physics , computer network , biochemistry , chemistry , channel (broadcasting) , repressor , classical mechanics , transcription factor , optics , economics , gene , economic growth
In this paper, we develop a stochastic susceptible-infective-susceptible (SIS) model, in which the transmission coefficient is a function of air quality index (AQI). By using Markov semigroup theory, the existence of kernel operator is obtained. Then, the sufficient conditions that guarantee the stationary distribution and extinction are given by Foguel alternative, Khasminsk$\check{\rm l}$ function and Itô formula. Next, a positivity-preserving numerical method is used to approximate the stochastic SIS model, meanwhile for all $ p > 0 $, we show that the algorithm has the $ p $th-moment convergence rate. Finally, numerical simulations are carried out to illustrate the corresponding theoretical results.