Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate

TL;DR

This paper extends the classical HIV-AIDS epidemic model by incorporating fractional derivatives to account for memory effects, analyzes stability, and proposes an optimal control strategy to minimize disease spread.

Contribution

It introduces a fractional differential equation approach to the SICA model, providing new insights into stability and control strategies for HIV-AIDS dynamics.

Findings

Stability of equilibrium points depends on the basic reproduction number.

A fractional optimal control problem is formulated and solved.

Numerical simulations demonstrate effective disease spread minimization.

Abstract

We investigate the celebrated mathematical SICA model but using fractional differential equations in order to better describe the dynamics of HIV-AIDS infection. The infection process is modelled by a general functional response and the memory effect is described by the Caputo fractional derivative. Stability and instability of equilibrium points are determined in terms of the basic reproduction number. Furthermore, a fractional optimal control system is formulated and the best strategy for minimizing the spread of the disease into the population is determined through numerical simulations based on the derived necessary optimality conditions.