Abstract
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.
Highlights
human immunodeficiency virus (HIV) weakens your immune system by destroying cells that are essential for fighting diseases and infections
The complexity of HIV infection is linked to many elements that involve the specific mechanism of infection [22]
In the absence of treatment, the HIV infection goes through three successive stages
Summary
In the absence of treatment, the HIV infection goes through three successive stages. Primary infection: The risk of transmission is high during this phase because of the high viral load at this stage of the infection [21, 40, 51]. This stage is characterized by occurrence of symptoms similar to those of a cold or mild influenza (fever, rashes, fatigue, headaches) which disappear spontaneously after a few weeks [1, 51]. AIDS stage: Because of its constant solicitation, the immune system becomes weaker and weaker until it can no longer defend itself against many pathogen agents and prevent the occurrence of serious or fatal diseases [1, 51]
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