Bayesian inference of a stochastic diffusion process for the dynamic of HIV in closed heterosexual population with simulations and application to Morocco case

Abstract

A model of the HIV dynamic in a heterosexual population of fixed size is considered in this paper. We represent the dynamic by a multidimensional SIR model. We formulate the stochastic diffusion approximation process to describe the dynamic of HIV by using strong approximation theorems for density-dependent Markov chains. Our aim is to estimate the parameters of this model; to reach this goal, we use Bayesian inference with Markov chain Monte Carlo (MCMC) simulations. We prove that the posterior distributions of the parameters are shifted Generalized Inverse Gaussian (GIG). The obtained results are well illustrated by simulations and real application of Morocco’s case.