Mathematical study of lumpy skin disease with optimal control analysis through vaccination

Abstract

In this study, we develop a new mathematical model with vaccination to properly comprehend dynamics of the Lumpy Skin Disease (LSD) ailment. We analyze the model for the existence of a unique positive and bounded solution. To assess the contagiousness of the disease and to test the proposed model for local and global stability at the disease-free and endemic equilibrium points, we determine the reproduction number R0. We also investigate the influence of model parameters on reproduction number R0 by performing sensitivity analysis. The main objective of this study is to carry out different disease control techniques to determine the optimal one. As a first strategy, we analyze the effect of different constant vaccination rates and constant exposure rates on disease control. Secondly, we construct an optimal control problem to investigate the influence of vaccination on disease control with possible elimination from society. The numerical findings reveal that the proposed optimal control strategy for control of LSD is more effective in lowering the number of infected animals.

Keywords

• LSD
• Vaccination
• Existence and uniqueness
• Local and global stabilities
• Sensitivity analysis
• Optimal control