An optimal control analysis of HIV-Visceral Leishmaniasis co-infection model

In this paper, we develop and analyze a novel mathematical model that captures the co-infection dynamics of HIV/AIDS and Visceral Leishmaniasis (VL) in a population where a reservoir host is present—marking the first study to explicitly incorporate reservoir-mediated transmission into HIV-VL interactions. Our analysis reveals that reducing the basic reproduction number below unity does not guarantee disease eradication due to the occurrence of backward bifurcation, highlighting the complex nature of disease persistence. Through global sensitivity analysis, we identify the sandfly biting rate as the most influential factor driving VL transmission, while the natural death rate of sandflies emerges as the most critical parameter in curbing disease spread. Based on these insights, we implement optimal control strategies tailored to the most sensitive parameters, demonstrating effective pathways to mitigate the burden of both infections in the presence of a reservoir host.