Mathematical Analysis and Optimal Control Investigation of Lumpy Skin Disease Transmission with Heterogeneous Host Susceptibility

Lumpy Skin Disease (LSD) remains a major challenge to livestock production and cattle farming, causing substantial economic losses and adverse health effects despite existing disease management strategies. This study develops a nonlinear mathematical model with two susceptible cattle groups to investigate the role of varying susceptibility in LSD transmission. Rigorous mathematical analysis is conducted to establish the fundamental properties of the proposed model, derive the basic reproduction number, determine the LSD-free and LSD-present equilibria, investigate their local stability, and establish global stability using Lyapunov function theory. A structure-preserving Nonstandard Finite Difference (NSFD) scheme is developed to validate the analytical results while preserving the essential properties of the continuous model. Numerical simulations investigate the individual effects of vaccination, farmer awareness, and treatment, demonstrating their potential to reduce disease transmission. Furthermore, sensitivity and numerical bifurcation analyses identify key parameters influencing disease dynamics and reveal critical thresholds associated with qualitative changes in transmission. An optimal control problem incorporating time-dependent interventions is formulated to determine cost-effective strategies for reducing infection prevalence and intervention costs. The principal contribution of this study is the integration of a bi-susceptible modelling framework, a structure-preserving numerical scheme, and optimal control analysis to provide a comprehensive mathematical approach to understanding LSD transmission and informing effective disease management strategies.