Optimal control of a lumpy skin disease transmission model with disinfection and culling strategies

Abstract

Lumpy skin disease (LSD) is a viral infection that affects buffaloes and cattle across various regions, including both tropical and temperate climates, and has been reported in some wild ruminants. It is caused by the Lumpy Skin Disease Virus (LSDV), a member of the Capripoxvirus genus. This study presents a mathematical model of lumpy skin disease (LSD) that captures the transmission dynamics among multiple cattle populations, mosquito vectors, and environmental viral loads. To effectively curb the spread of the infection, an optimal control framework is applied for evaluating various parameters to identify the best transmission-reduction strategy. Specifically, the interventions include environmental disinfection to lower viral presence and the culling of infected cattle. The proposed strategy aims to simultaneously minimize the number of infected cows, the environmental virus concentration, and the economic expenses associated with these interventions. Utilizing Pontryagin’s minimum principle, the study successfully resolves this optimization problem. The derived strategies are subsequently analyzed through numerical simulations—employing the modified forward-backward sweep method—under four conditions: no action, solely disinfection, solely culling, and a combined approach. The findings indicate that the simultaneous application of disinfection and culling is the most effective strategy for eliminating the disease.