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In this paper, we construct a model to describe the transmission of HIV in ahomogeneous host population. By considering the specific mechanism of HIV, wederive a model structured in three successive stages: (i) primary infection,(ii) long phase of latency without symptoms and (iii) AIDS. Each HIV stage isstratified 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, weprovide a global analysis of the model depending upon the basic reproductionnumber R 0. When R 0 $\le$ 1, then the disease-free equilibrium is globallyasymptotically stable and the infection is cleared in the host population. Onthe contrary, if R 0 > 1, we prove the epidemic's persistence with theasymptotic stability of the endemic equilibrium. By performing the sensitivityanalysis, we then determine the impact 1 of control-related parameters of theoutbreak severity. For the second part, the initial model is extended withintervention methods. By taking into account ART interventions and theprobability of treatment drop out, we discuss optimal interventions methodswhich minimize the number of AIDS cases.

Optimal intervention strategies of staged progression HIV infections through an age-structured model with probabilities of ART drop out