A mathematical model of lumpy skin disease incorporating vaccination with nonlinear response and harvesting

Abstract

A significant bio-security threat for the cattle farms is Lumpy Skin Disease (LSD). A five-dimensional non linear system with disease has been developed to portray the spread and control of LSD. It has been demonstrated that in addition to vaccinations, harvesting practices may be significant to the dynamics associated with this disease. After estimating the basic reproduction number $(R_0)$, sensitivity analysis is performed to investigate how system parameters affect $R_0$. The novelty of this model is that it includes the study of continuous harvesting effort with non linear vaccination response for control of the disease. We determine the best possible condition for disease eradication and investigate the impact of vaccination on transmission of the disease employing the optimal control theory. Furthermore, using a graphical illustration, we provide the numerical validation of our analytical results. This study can be applied for diseased large commercial cattle farms.