Coinfection Dynamics of HBV-HIV/AIDS with Mother-to-Child Transmission and Medical Interventions

Abstract

In this study, we analyzed the effect of mother-to-child transmission (MTCT) of hepatitis B virus (HBV) and human immunodeficiency virus (HIV) on the transmission dynamics of their coinfection to make a recommendation based on reasons to public health sector, policy makers, and programme implementers. We proved that the solutions of the sub and full models are positive and bounded. The effective reproduction numbers of the models are derived using the next generation matrix method. The disease-free and endemic equilibria of the submodels and the coinfection model are computed, and the stability of those equilibria is analyzed using Routh-Hurwitz criteria after computing the associated effective reproduction numbers. We performed a sensitivity analysis to show the influence of different parameters on the effective reproduction number of HBV-HIV/AIDS coinfection model, and we identified the most sensitive parameters are <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mtext> </a:mtext> <a:msub> <a:mrow> <a:mi>τ</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:msub> <c:mrow> <c:mi>α</c:mi> </c:mrow> <c:mrow> <c:mn>1</c:mn> </c:mrow> </c:msub> </c:math> , which are the rate of MTCT of HIV and treatment rate for HBV infected class, respectively. The numerical simulation of the model is done using MATLAB and the findings from the simulations are discussed. From the results of numerical simulations, we observed that an increase in the rates of MTCT of HBV and HIV exacerbated HBV-HIV/AIDS coinfection, while a decrease in the rates of MTCT of these infections would decline the number of cases, minimize the spread, and help to eliminate HBV-HIV/AIDS coinfection from the society gradually.