Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955, Sidi Othman, Casablanca, Morocco
2 Instituto de Telecomunicações and Department of Mathematics, Universidade da Beira Interior, 6201-001, Covilhã, Portugal
3 Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal
Accepted: 9 December 2020
Published online: 19 January 2021
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021