Mathematical Analysis of the Dynamics of Lumpy Skin Epidemics within Delay Differential Equations

Cattle are susceptible to an infectious condition called lumpy skin disease (LSD). The disease has caused a drop in dairy products and, occasionally, the death of sick cattle, damaging the economies of the affected countries. Thus, a mathematical model is required to aid the disease's optimal eradication. To address this, we offer a novel mathematical model that helps comprehend disease transmission patterns and provides recommendations for the best ways to manage illness. We verify that the solutions are bounded and positive by looking at the suggested model for the presence of a unique solution. To identify the contagiousness of disease and evaluate the proposed model's local and global stability at equilibrium places, we calculate the reproduction number by the next-generation matrix method. Moreover, figures that confirm the theoretical findings of global stability at equilibrium sites are presented. For local stability, we investigate the well-known result as Routh-Hurwitz criteria for the lumpy skin delayed epidemic model. For global stability, we analyze the notable Lyapunov function stability for the lumpy skin delayed epidemic model. We use sensitivity analysis to identify the reproduction number's most important parameters and visually represent their effects. This study aims to examine different illness prevention strategies to determine which works best.