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.
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Acknowledgements
Rosa was funded by The Portuguese Foundation for Science and Technology (FCT–Fundação para a Ciência e a Tecnologia) through national funds under the Project UIDB/EEA/50008/2020; Torres by FCT through CIDMA, reference UIDB/50008/2020. The authors would like to acknowledge the comments and suggestions from three anonymous reviewers, which helped them to enriched their work.
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Boukhouima, A., Lotfi, E.M., Mahrouf, M. et al. Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate. Eur. Phys. J. Plus 136, 103 (2021). https://doi.org/10.1140/epjp/s13360-020-01013-3
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DOI: https://doi.org/10.1140/epjp/s13360-020-01013-3