The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm

Abstract

Mathematical modeling of disease has been an indispensable tool in accounting for disease transmission dynamics as well as disease spread. Epidemiological disease models have been used to explain the dynamics of HIV/AIDS in the population from the early 1900s. The models developed however faced considerable challenges ranging from inaccurate representation of natural data for deterministic models, to methods of forecasting such as statistical extrapolation which assumes that current conditions will prevail which is not always the case. Despite the spread of HIV/AIDS having been explored widely, not much literature is available on the Gillespie Algorithm based SIR model. This algorithm is able to give a statistically correct of the course of a disease with initial conditions to begin with and propensity functions to update the system. The purpose of this paper is to build on the concept of Gillespie's Algorithm based SIR models by developing a stochastic SIR model to simulate disease evolution in the population setting. The values produced through simulation by the model developed in this paper using a tau value as the time step of the model were compared to HIV/AIDS data from 1985 to 2018, given by NACC. We conclude that the simulated model reflects reality.