Mathematical modelling of the impact of testing, treatment and control of HIV transmission in Kenya

Abstract The control of spread of HIV to reduce its effects on a population is an important role of public health. HIV testing and counselling (HTC) and eventual enrolment of infected individuals on anti retro-viral treatment (ART) as soon as possible to reduce the risk of dying is currently the main intervention against HIV. Mathematical models can be used to study the effects of HIV prevention, testing and treatment with ART on HIV patients. In this study, we employ a deterministic model to provide a quantification of HIV prevention, testing and treatment with ART as public health measurements in the fight against HIV infection. Lyapunov function has been used to derive a condition that ensures that the model system is globally asymptotically stable when R0 is less than unity. Through sensitivity analysis, we determine the relative importance of model parameters for disease transmission. The sensitivity analysis results suggest that the effective contact rates are mechanisms fuelling HIV epidemic proliferation while ART efficacy reduces the incidence. The model is fitted to HIV surveillance data obtained from world in data website. Although the results show a high proportion of individuals with HIV in Kenya, the incidence curve is indicative of a declining HIV infection and settling at an endemic steady state. The results are suggestive of the need to promote preventive mechanism against the occurrence of new infections. Moreover, the results show that the combination of several control mechanisms would significantly reduce the spread of the disease, if we maintain the level of each control high.