Mathematical modeling of filariasis and HIV/AIDS co-infection in the context of vector dynamics

Abstract

This study develops a unique fractional-order model comprising nine compartments to explore the dynamical behavior of the progression of filariasis and the immunosuppressive retrovirus (HIV) comorbidity under explicit vector influence. The study utilizes fractional order stochastic to examine the dynamics of randomness in the epidemiological model. Using fractional stability theory, we determined the reproduction number, the pathogen-absent state equilibrium, and the requirements for dual-level stability analytically. A center manifold approach is used to investigate bifurcation behavior at the critical threshold, demonstrating the forward bifurcation which the disease transmission can be early controlled by reducing R₀ less than zero. A fractional optimal control framework is developed; utilizing Pontryagin’s Maximum Principle in the context of fractional order to provide the best strategy to manage the spread of the co-infection. We then did the numerical simulations to verify the theoretical findings and demonstrated how fractional stochastic models provide better understanding of the fluctuations in epdermiological models, and how fractional order can affect disease persistence and the effectiveness of combination therapies. According to our findings, in areas where HIV/AIDS and filariasis are endemic, memory effects play a crucial role in co-infection dynamics and provide guidance for developing integrated, economically sound public health programs. We also found out that, the strategic implementation of intense initial interventions is crucial in managing filariasis and HIV/AIDS co-infection. Thus, by prioritizing early intervention measures, the overall burden of the diseases would be significantly minimized. Therefore, the insights from our study will inform targeted interventions, optimize resource allocation, and improve the overall efficacy of public health strategies in regions burdened by multiple endemic diseases.