Math. Model. Nat. Phenom.
Volume 16, 2021
Mathematical Models and Methods in Epidemiology
|Number of page(s)||32|
|Published online||26 May 2021|
Optimal intervention strategies of staged progression HIV infections through an age-structured model with probabilities of ART drop out
University Cheikh Anta Diop, Department of Mathematics and Informatics, Faculty of Science and Technic,
2 MIVEGEC, Univ. Montpellier, IRD, CNRS, Montpellier, France.
3 University of Yaounde I, National Advanced School of Engineering, Yaoundé, Cameroon.
* Corresponding author: firstname.lastname@example.org
Accepted: 22 April 2021
In this paper, we construct a model to describe the transmission of HIV in a homogeneous host population. By considering the specific mechanism of HIV, we derive a model structured in three successive stages: (i) primary infection, (ii) long phase of latency without symptoms, and (iii) AIDS. Each HIV stage is stratified by the duration for which individuals have been in the stage, leading to a continuous age-structure model. In the first part of the paper, we provide a global analysis of the model depending upon the basic reproduction number ℜ0. When ℜ0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable and the infection is cleared in the host population. On the contrary, if ℜ0 > 1, we prove the epidemic’s persistence with the asymptotic stability of the endemic equilibrium. By performing the sensitivity analysis, we then determine the impact of control-related parameters on the outbreak severity. For the second part, the initial model is extended with intervention methods. By taking into account antiretroviral therapy (ART) interventions and the probability of treatment drop out, we discuss optimal intervention methods which minimize the number of AIDS cases.
Mathematics Subject Classification: 35Q92 / 49J20 / 35B35 / 92D30
Key words: HIV / ART / age structure / non-linear dynamical system / stability / optimal control
© The authors. Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.