Ba M. auteur aut IRD Djidjou-Demasse Ramsès auteur aut IRD Lam M. auteur aut IRD Tewa J.J. auteur aut IRD text report Litérature grise eng text/pdf reformatted digital access 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 equilibriumis globally asymptotically stable and the infection is cleared in thehost 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 of the outbreak severity. For the second part, the initial model is extended with intervention methods. By taking into account ART interventions and the probability of treatment drop out, we discuss optimal interventions methods which minimize the number of AIDS cases. specialized 052MALTRA03 020MATH01 2019 1911.06703 en ligne [43 ] en ligne [43 ] en ligne [43 ] https://www.documentation.ird.fr/hor/fdi:010076968 [F B010076968] https://www.documentation.ird.fr/hor/fdi:010076968 https://horizon.documentation.ird.fr/exl-doc/pleins_textes/divers20-01/010076968.pdf IRD - Base Horizon / Pleins textes 2019-11-20 2021-06-08 fdi:010076968 fre