TITLE:
Approximations of Quasi-Stationary Distributions of the Stochastic SVIR Model for the Measles
AUTHORS:
Moussa Seydou, Moussa Tessa
KEYWORDS:
Compartment Models, SIR, Markov Chains, Stochastic Simulation, Basic Reproduction Number, Quasi-Stationary Distribution, Measles
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.9,
September
16,
2021
ABSTRACT: 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.