Model Selection and Parameter Estimation for Stochastic Differential Equations for the Prevalence of HIV Average in the Arab World

Abstract

    Dynamic systems arise in a variety of domains, including economics, physics, biology, and engineering, In addition to random phenomena. As a result, stochastic differential equations are an important mathematical tool for modeling dynamic systems in various fields. In this study, we examined the linear (transformation) reduction method, which transforms some non-linear stochastic differential equations(SDEs) into linear ones using Ito's integrated formula, and subsequently identified the analytical solution. We utilized the maximum likelihood estimation method to estimate the parameters, reflecting the realistic data of the HIV prevalence rate in the Arab world from 1990 - 2022. We study the time series of Human Immunodeficiency Virus )HIV( prevalence in the Arab world from 1990 - 2022, utilizing non-linear models such as SDE models . Maple software was used to compare the outcomes.