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Modelling the effect of treatment and behavioral change in HIV transmission dynamics. (English) Zbl 0792.92023

Summary: We analyze a model for the HIV-infection transmission in a male homosexual population. In the model we consider two types of infected individuals. Those that are infected but do not know their serological status and/or are not under any sort of clinical/therapeutical treatment, and those who are. The two groups of infectives differ in their incubation time, contact rate with susceptible individuals, and probability of disease transmission. The aim of this article is to study the roles played by detection and changes in sexual behavior in the incidence and prevalence of HIV.
The analytical results show that there exists a unique endemic equilibrium which is globally asymptotically stable under a range of parameter values whenever a detection/treatment rate and an indirect measure of the level of infection risk are sufficiently large. However, any level of detection/treatment rate coupled with a decrease of the transmission probability lowers the incidence rate and prevalence level in the population. In general, only significant reductions in the transmission probability (achieved through, for example, the adoption of safe sexual practices) can contain effectively the spread of the disease.

MSC:

92D30 Epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
34D99 Stability theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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