Approximations of Quasi-Stationary Distributions of the Stochastic <i>SVIR</i>Model for the Measles

作     者：Moussa Seydou Moussa Tessa Moussa Seydou;Moussa Tessa

作者机构：Department of Mathematics and Informatics Abdou Moumouni University Niamey Niger 

出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)

年 卷 期：2021年第9卷第9期

页      面：2277-2289页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Compartment Models SIR Markov Chains Stochastic Simulation Basic Reproduction Number Quasi-Stationary Distribution Measles 

摘      要：In this paper, we analyze the quasi-stationary distribution of the stochastic SVIR (Susceptible, Vaccinated, Infected, Recovered) model for the measles. The quasi-stationary distributions, as discussed by Danoch and Seneta, have been used in biology to describe the steady state behaviour of population models which exhibit discernible stationarity before to become extinct. The stochastic SVIR model is a stochastic SIR (Susceptible, Infected, Recovered) model with vaccination and recruitment where the disease-free equilibrium is reached, regardless of the magnitude of the basic reproduction number. But the mean time until the absorption (the disease-free) can be very long. If we assume the effective reproduction number Rp , the quasi-stationary distribution can be closely approximated by geometric distribution. β and δ stands respectively, for the disease transmission coefficient and the natural rate.