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 deterministic model for the transmission dynamics of Tuberculosis (TB) under Direct ObservationTherapy Strategy (DOTS)

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New challenges like the outbreak of new diseases, government policies, war and insurgency etc. present distortion, delay and denial of persons’ access to ART, thereby fuelling the spread and increasing the burden of HIV/AIDS. A mathematical model is presented to study the transmission dynamics and control of HIV infection. The qualitative and quantitative analyses of the model are carried out. It is shown that the disease-free equilibrium of the model is globally asymptotically stable whenever the basic reproduction number is less than unity. It is also shown that a unique endemic equilibrium exists whenever the basic reproduction number exceeds unity and that the model exhibits a forward bifurcation. Furthermore, the Lyapunov function is used to show that the endemic equilibrium is globally asymptotically stable for a special case of the model whenever the associated basic reproduction number is greater than unity. The model is calibrated to the data on HIV/AIDS prevalence in Nigeria from 1990 to 2019 and it represents reality. The numerical simulations on the global stability of disease-free equilibrium and endemic equilibrium justify the analytic results. The fraction of the detected individuals who stays in the treatment class plays a significant role as it influences the population of the latently-infected individuals and AIDS class by preventing individuals from progressing into the AIDS class.