Work

A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative

Year: 2025

Type: article

Abstract: In this paper, we are concerned with a deterministic Caputo fractional derivative mathematical model of HIV/AIDS with treatment and optimal control. We formulate a mathematical model that contains six compartments (including primary infection and treatment) and show that the model is well‐posed. We calculate the reproduction number and free and endemic equilibrium points. We prove the stability of free and endemic equilibrium points. The local stability is carried out by the linearization method, whereas the global stability is performed by Mittag–Leffler stability. We consider four control mechanisms and show their impact on the prevalence of HIV infection. Numerical solutions are performed using the optimal case of the two‐stage explicit fractional order Runge–Kutta methods.

Source: International Journal of Mathematics and Mathematical Sciences

DOI: 10.1155/ijmm/9342227

Authors: Abdul-Aziz Hussein, Benyam Mebrate

Institution: Wollo University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $1,240