Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate
Boukhouima, A.
; Lotfi, E.
; Mahrouf, M.
;
Rosa, S.
; Torres, D. F. M. T.
; Yousfi, N.
European Physical Journal Plus Vol. 136, Nº 1, pp. 1 - 20, January, 2021.
ISSN (print): 2190-5444
ISSN (online):
Scimago Journal Ranking: 0,61 (in 2021)
Digital Object Identifier: 10.1140/epjp/s13360-020-01013-3
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.
