Dynamical study of lumpy skin disease model with optimal control analysis through pharmaceutical and non-pharmaceutical controls

Lumpy skin disease (LSD) is an infectious disease that affects cattle population. The disease has disrupted economy of the affected countries due to decline in dairy products and sometimes due to death of the infected cattle. It is therefore necessary to develop a mathematical model that may help to eradicate the disease in an optimal way. For this, we propose a new mathematical model not only to understand the disease flow patterns but also to suggest strategies to control disease optimally. We examine the proposed model for existence of a unique solution and prove that the solutions are positive and bounded. We estimate the reproduction number ℛ_0 to measure disease contagiousness and to test the proposed model for local and global stability at disease-free and endemic equilibrium points. We also present graphs to verify theoretical results of global stability at equilibrium points. We perform sensitivity analysis to determine the most influential parameters of the reproduction number ℛ_0 and show their impact on ℛ_0 graphically. The primary goal of this research is to test various possible disease prevention methods in order to find the best one. Therefore, we build an optimal control problem to explore the effects of treatment and precautionary measures on disease control in three different cases. In the first case, we analyze the impact of treatment strategy on the disease control and present the corresponding results graphically. In the second control methodology, we study the impact of adopting precautionary measures on sickness with possible end from society. In the third case, we implement treatment and adopting precautionary measure strategies together to observe their combined effect on disease control. Findings of all the three cases along with discussions and graphs will be presented and concluded at the end.