A Deterministic Approach to the Dynamics of Visceral Leishmaniasis and HIV Co-infection with Optimal Control

Visceral leishmaniasis (VL) is considerably more severe among individuals infected with human immunodeficiency virus (HIV), leading to higher parasite loads, frequent relapse, and increased mortality. To examine the epidemiological interaction between the two diseases, we develop a comprehensive VL-HIV co-infection model that incorporates transmission pathways, treatment effects, and relapse dynamics. The model is parameterized using real-time data from Bihar, India, including monthly VL-only and VL-HIV co-infected cases and annual HIV prevalence data. Our analysis shows that HIV infection drives the resurgence and persistence of VL even in settings where VL alone would not sustain transmission, underscoring the amplifying effect of HIV-induced immunosuppression on VL dynamics. We further demonstrate that increasing HIV treatment coverage substantially reduces co-infection prevalence and lowers VL relapse rates. Numerical simulations and optimal control analysis highlight the effectiveness of integrated intervention strategies that combine awareness, treatment enhancement, and vector control. Overall, this study emphasizes the need for coordinated VL and HIV control programs and provides data-driven guidance for designing sustainable intervention strategies in endemic regions.