Drug-sensitivity and passive immunity mathematical epidemiological model for tuberculosis

Regardless of many decades of research, the widespread availability of a vaccine and more recently highly visible WHO efforts to promote a unified global control strategy, Tuberculosis remains a leading cause of infectious mortality. In this paper, a Mathematical Model for Tuberculosis Epidemic with Passive Immunity and Drug-Sensitivity is presented. We carried out analytical studies of the model where the population comprises of eight compartments: passively immune infants, susceptible, latently infected with DS-TB. The Disease Free Equilibrium (DFE) and the Endemic Equilibrium (EE) points were established. The next generation matrix method was used to obtain the reproduction number for drug sensitive () Tuberculosis. We obtained the disease-free equilibrium for drug sensitive TB which is locally asymptotically stable when < 1 indicating that tuberculosis eradication is possible within the population. We also obtained the global stability of the disease-free equilibrium and results showed that the disease-free equilibrium point is globally asymptotically stable when ≤ 1 which indicates that tuberculosis naturally dies out

Mathematical Modelling of Dynamics of HIV Transmission Depicting the Importance of Counseling and Treatment

Human immunodeficiency virus is an incurable disease which attacks and destroys the human immunesystem thereby making the body susceptible to all kinds of illnesses. If left unattended to, it can lead to the damaging ofbody organs such as the brain, kidney and the heart which can result to death. Unfortunately this disease has no knowncure till date but through counseling and administering of antiretroviral drugs, the likelihood of dying from it becomesminimal. This study presents the deterministic HIV transmission model. The model has a unique endemic equilibrium point which is locally asymptotically stable if R0  > 1 , DFE of the model was obtained and is shown to be Localasymptotically stable when the associated basic reproduction number was R > 1. We established the numerical simulation of the model which shows that the effective use of condom, counseling or the use of anti-retrovirus drug can lead to effective reduction on HIV transmission. Finally, we discussed that the ART treatment rate will reduce the basic reproduction number R0 hence, leading to the extinction of HIV/AIDS