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(Department of Mathematics and Informatics, Abdou Moumouni University, Niamey, Niger)

机构地区：[1]Department of Mathematics and Informatics, Abdou Moumouni University, Niamey, Niger

出　　处：《Journal of Applied Mathematics and Physics》2021年第9期2277-2289,共13页应用数学与应用物理（英文）

摘　　要：In this paper, we analyze the quasi-stationary distribution of the stochastic <em>SVIR</em> (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 <em>SVIR</em> model is a stochastic <em>SIR</em> (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 <em>R</em><em>_p</em> < 1 or <img src="Edit_67da0b97-83f9-42ef-8a00-a13da2d59963.bmp" alt="" />, the quasi-stationary distribution can be closely approximated by geometric distribution. <em>β</em> and <em>δ</em> stands respectively, for the disease transmission coefficient and the natural rate.In this paper, we analyze the quasi-stationary distribution of the stochastic <em>SVIR</em> (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 <em>SVIR</em> model is a stochastic <em>SIR</em> (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 <em>R</em><em>_p</em> < 1 or <img src="Edit_67da0b97-83f9-42ef-8a00-a13da2d59963.bmp" alt="" />, the quasi-stationary distribution can be closely approximated by geometric distribution. <em>β</em> and <em>δ</em> stands respectively, for the disease transmission coefficient and the natural rate.

关 键 词：Compartment Models SIR Markov Chains Stochastic Simulation Basic Reproduction Number Quasi-Stationary Distribution MEASLES 

分 类 号：O17[理学—数学]