A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

  • El Mehdi Lotfi Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco
  • Marouane Mahrouf Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco
  • Mehdi Maziane Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco
  • Cristiana J. Silva Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
  • Delfim F. M. Torres Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
  • Noura Yousfi Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco
DOI: https://doi.org/10.19139/soic.v7i3.834
Keywords: SICA compartmental model, General incidence function, Global stability, Lyapunov functionals.

Abstract

We study the global dynamics of a SICA infection model with general incidence rate. The proposed model is calibrated with cumulative cases of infection by HIV–AIDS in Morocco from 1986 to 2015. We first prove that our model is biologically and mathematically well-posed. Stability analysis of different steady states is performed and threshold parameters are identified where the model exhibits clearance of infection or maintenance of a chronic infection. Furthermore, we examine the robustness of the model to some parameter values by examining the sensitivity of the basic reproduction number. Finally, using numerical simulations with real data from Morocco, we show that the model predicts well such reality.

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Published
2019-08-17
How to Cite
Lotfi, E. M., Mahrouf, M., Maziane, M., J. Silva, C., Torres, D. F. M., & Yousfi, N. (2019). A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data. Statistics, Optimization & Information Computing, 7(3), 588-603. https://doi.org/10.19139/soic.v7i3.834
Issue
Vol 7 No 3 (2019)
Section
Research Articles
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