Nonlinear dynamics model of HIV/AIDS: Assessing the impacts of condoms, vaginal microbicides, and optimized treatment - Reuben Iortyer Gweryina; Cicik Alfiniyah; Chinwendu Emilian Madubueze; Kenneth Ojotogba Achema (Partial Differential Equations in Applied Mathematics)
HIV/AIDS remains one of the main global causes of morbidity and mortality. While antiretroviral drugs are still the only treatment for HIV patients, their accessibility and efficient delivery in resource-poor nations constitute a major concern, and no epidemiological model has considered this. Based on this, we create a model for HIV/AIDS that considers condoms and vaginal microbicides alongside saturated treatment. We consider the constant control case, in which theoretical results show that the delay factor in the antiretroviral therapy (ART) regimen can induce backward bifurcation, which consequently distorts the global effort to end HIV incidence. We use the Castillo-Chavez stability to ensure that the disease-free equilibrium is globally asymptotically stable whenever the associated reproduction number is less than one. Uncertainty and sensitivity analysis using the Latin hypercube sampling technique was also carried out on the parameters and state variables of the model equations, and the result shows that half of the most highly influential parameters are capable of reducing cases of HIV and AIDS. For time-dependent control cases, our findings suggest that, in countries with low income, directing resources to either condom use or vaginal microbicides is more effective than a regular intake of antiretrovirals alone. Furthermore, results without ART delay have shown to be more effective in HIV control than others where the inaccessibility of the therapy encouraged outbursts of AIDS cases. Thus, as reliable as antiretrovirals are in HIV/AIDS treatment, early administration and regular intake are key to their continued success.