Stability Analysis of the Disease-Free Equilibrium State for Lymphatic Filariasis with Chemical and Biological Control on Vector

In this paper, we develop a mathematical model to analyze the transmission dynamics and control strategies for Lymphatic Filariasis (LF), incorporating both chemical and biological control measures targeting the disease vector. The model is proven to be both mathematically and epidemiologically sound. By determining the basic reproduction number (\(R_0\)), we establish the conditions for local and global stability of the disease-free equilibrium (DFE). The model highlights the impact of Wolbachia bacteria on mosquito populations and the role of drug resistance and recovery in human populations. Our results demonstrate that reducing \(R_0\) below 1 is crucial to eradicating LF from an endemic population, and thus, preventive measures, including vector control, are essential. Further research is recommended to optimize the combined use of chemical and biological controls to achieve long-term stability and disease eradication.