TITLE:
A Stochastic SVIR Model for Measles
AUTHORS:
Moussa Seydou, Ousmane Moussa Tessa
KEYWORDS:
Measles, Compartmental Model, SVIR, Basic Reproductive Number, Markov Chains, Lyapunov Function, Stochastic Stability, Stochastic Simulation, Niger
JOURNAL NAME:
Applied Mathematics,
Vol.12 No.3,
March
30,
2021
ABSTRACT: In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average of the stochastic solution in the case of small population size. The choice of this model takes into account the random fluctuations inherent to the epidemiological characteristics of rural populations of Niger, notably a high prevalence of measles in children under 5, coupled with a very low immunization coverage.