A fractional order model of Lymphatic Filariasis and Visceral Leishmaniasis coinfection

Abstract

Lymphatic filariasis and visceral leishmaniasis are parasitic diseases that cause serious public health issues, especially in tropical and subtropical areas. Effective disease control requires an understanding of their co-infection dynamics. In this study, we construct a fractional-order model to analyze the transmission patterns of lymphatic filariasis and visceral leishmaniasis co-infection. The existence and uniqueness of the model’s solution were confirmed by using the fixed point theory; in addition, the model was proven to be positive and bounded. The stability of the fractional coinfection model is proven using the Hyers–Ulam and Hyers–Ulam–Rassias stability procedures. Sensitivity analysis was conducted using the Latin hypercube sampling technique and partial rank correlation coefficient with 10,000 runs using the reproduction number for lymphatic filariasis and visceral leishmaniasis as the response functions per time. It was observed that the parameters that had a significant influence on the spread of the diseases were $a_m$ and $a_s$, thus, the biting rates of mosquitoes and sandflies respectively, the progression rate of lymphatic filariasis in mosquitoes $b_m$, the progression rate of visceral leishmaniasis in sandflies $b_s$, the progression rate of lymphatic filariasis in humans $c_m$ and the progression rate of visceral leishmaniasis in humans and reservoirs $c_s$. Therefore, policymakers are encouraged to focus on reducing the occurrence of these parameters and also use these results as a guide in developing control strategies to mitigate the spread of both disease in the population. We also observed that memory significantly impacts the dynamics of the population’s transmission patterns of lymphatic filariasis and visceral leishmaniasis co-infection.