Mathematical Transmission of HIV/AID with Early Treatment

Abstract

In this paper, a mathematical model for the transmission of HIV/AIDS with early treatment is developed and analyzed to gain insight into early treatment of HIV/AIDS and other epidemiological features that cause the progression from HIV to full blown AIDS. We established the basic reproduction number which is the average number of new secondary infection generated by a single infected individual during infectious period. The analysis shows that the disease free equilibrium is locally and globally asymptotically stable whenever the threshold quantity is less than unity i.e. Numerical analysis shows that the early treatment of latently infected individuals reduces the dynamical progression to full blown AIDS. The result also showed that immunity boosted substances increase the red blood cells, sensitivity analysis of basic reproduction number with respect to parameters showed that effective contact rate must not exceed 0.3 to avoid endemic stage.

A Mathematical Model for HIV/AIDS Under Pre-Exposure and Post-Exposure Prophylaxis

“…In recent years, there has been an increase in the number of studies on HIV/AIDS transmission [12][13][14][15][16][17][18][19][20][21][22]. For example, Moya and Marrero [12] presented a stochastic model using Markov chains to study the transmission of HIV/AIDS and control chain elements proposed control strategies.…”

“…Akinwumi et al [17] formulated and studied a mathematical model for the transmission of HIV/AIDS with early treatment. Ogunlaran and Noutchie [18] proposed a mathematical model with two control variables, where the uninfected CD4+T cells follow the logistic growth function and the incidence term is saturated with free virus and apply optimal control approach to maximize the concentration of uninfected CD4+T cells in the body by using minimum drug therapies.…”