A Mathematical Model of Lymphatic Filariasis Incorporating the Protected Humans

Lymphatic filariasis is a major cause of long-term disability worldwide, caused by infected female mosquitoes. To manage and control the disease, a deterministic model of ordinary differential equations that includes protected human and treatment compartments is developed, accounting for how access to treatment and movement between affected and unaffected areas influence disease spread. The analysis of the model is carried out by examining the computation of the basic reproduction number utilizing the Next-generation approach and the equilibrium states through the fixed-point and Lyapunov methods. The analysis established the conditions for the local and global stability of the equilibrium states. The sensitivity analysis is further performed using normalized forward sensitivity indices, Latin hypercube sampling and Partial Rank Correlation Coefficient (LHS/PRCC) techniques. The findings from the sensitivity analysis suggest that the rates at which mosquitoes bite and die influence lymphatic filariasis disease dynamics. This is supported by numerical simulation outcomes showing that increasing mosquito mortality and reducing the biting rate can significantly lower infection rates in both human and mosquito populations. It is recommended that public awareness campaigns on the use of insecticide-treated nets, indoor residual spraying, and mass drug administration be implemented to reduce the burden of lymphatic filariasis in the population.