A mathematical model of HIV/AIDS population dynamics with treatment failure and treatment dropouts in the era of universal test and treat approach

Abstract

Antiretroviral therapy is currently the major intervention against HIV infection.However, with increased access to treatment through the universal test and treat approach, potential barriers to the overall success of this strategy such as treatment dropouts and treatment failure arise. We constructed a deterministic mathematical model of HIV/AIDS to study the possible effects of treatment failure and treatment dropouts on the population dynamics of the infection. The model incorporated a universal test and treat scenario and a separate sub population of treatment dropouts. The disease free and endemic equilibria is computed and the basic reproduction number R0 of the model, is determined using the next generation matrix method. Numerical simulations are presented to investigate the effect of treatment failure and treatment dropouts on the dynamics of the model and on the R0. From the expression of R0 it is shown that the treatment dropout class contributes to the overall model reproduction number. Results of the numerical simulations show that an increase in treatment dropouts leads to an increased transimission of the HIV infection in a population. Also, the results indicate that even in the absence of treatment dropouts and treatment failure the basic reproduction number remains above unit, highlighting the need for several control measures to end the epidemic. Treatment failure is shown to increase the maximum size of the AIDS class. The results from this study demonstrate the need to focus on increasing efforts of reducing treatment dropouts in combination with other intervention strategies, through monitoring adherence and identifying and enrolling back to antiretroviral therapy(ART) of treatment dropouts. Also there is need to improve on early diagnosis of treatment failure such that those on treatment do not progress to AIDS before they are put on second or third line ART.