Optimal Control Strategies and Sensitivity Analysis of an HIV/AIDS-Resistant Model with Behavior Change

Abstract

Despite several research on HIV/AIDS, it is still incumbent to investigate more effective control measures to mitigate its infection level. Therefore, we introduce an HIV/AIDS-resistant model with behavior change and study its basic properties. In order to determine the most sensitive parameters that are responsible for disease transmission with respect to the basic reproduction number and those responsible for disease prevalence with respect to the endemic equilibrium, the sensitivity analysis was established and it was confirmed that the influx rate of people into the infected population and total abstinence from all risk practices and endemic areas are some of the most sensitive parameters for disease spread and disease eradication, respectively. Furthermore, by considering controls denoting the government’s intervention in promoting and encouraging behavior change, representing intake of balanced nutritional supplementation, and connoting antiretroviral therapy (ART), an optimal control problem was developed and analyzed. Before the establishment of the necessary conditions of the optimal control using Pontryagin’s Maximum Principle, we proved the existence of the optimal control triplet where is the control set at time t ,) which has been neglected by many researchers in recent years. Using the Runge–Kutta scheme, the optimal control problem was solved to understand the best combination of control strategies. Using the demographic and epidemiological data for South Africa on HIV/AIDS, a numerical simulation was carried out and results are presented on 3D surface plots. The obtained results suggested that the combination of all the considered control measures is the best method to ensure disease eradication.

A Statistical Moment-Based Spectral Approach to the Chance-Constrained Stochastic Optimal Control of Epidemic Models

“…In practice, different approaches can be followed in order to solve the integral (10), such as Galerkin projection, collocation, or numerical integration [50]. A Gaussian quadrature rule based on the statistical moments of 𝝃 = (𝜉 1 , … , 𝜉 𝑁 𝑈 ) is used is this paper.…”

“…A dynamic model of the dengue strain is used in [9] to formulate an OCP, in which the number of people infected is minimized by applying mosquito removal measures. The optimal control of a HIV/AIDS-resistant model with behaviour change is proposed in [10], which considers as controls the government's intervention in encouraging behaviour change, the intake of balanced nutritional supplementation, and the antiretroviral therapy. The effectiveness of antidotes and vaccination in restraining viral creation and decelerating the production of new influenza infections is studied in [11], in which a structured model based on urban and rural areas is considered.…”

Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation

“…Their analysis recommended that the combination of all the control strategies is the most cost-effective strategy. Furthermore, notice that optimal control modeling and cost-effectiveness analysis model have been applied in recent infectious diseases models like [55,56].…”