Mathematical modeling of lumpy skin disease: New perspectives and insights

Abstract

This research presents a new mathematical structure featuring two compartments representing cows and flies. It aims to comprehensively understand the dynamics of Lumpy Skin Disease (LSD), incorporating a temperature-dependent mortality rate for flies. We thoroughly examine the model to establish the presence of a positive solution that remains bounded. By evaluating the disease's contamination potential and inspecting the model's stability concerning both local and global equilibrium points—namely, disease-free and endemic—we calculate the reproduction number. Theoretical analysis shows that a stable disease free equilibrium co-exists with a stable endemic equilibrium whenever the basic reproduction number is less than one implying the possibility of having backward bifurcation. Numerical simulation also supports this. Furthermore, through sensitivity analysis, we explore how various model parameters affect the basic reproduction number. Our numerical investigations underscore the critical importance of regulating specific parameters, such as the disease-induced mortality rate of cows, the temperature-dependent mortality rate of flies, and the rate of transition from infected to recovered cows, in effectively managing the disease system. Numerical results also show that controlling flies population and spraying adulticide, LSD spread can be prevented.