Dynamics of Lumpy Skin Disease Model With Vaccination and Environmental Transmission

Lumpy skin disease (LSD) is one of the cattle diseases that can spread rapidly, it is caused by lumpy skin disease virus (LSDV). LSDV can spread through direct contact, insect vectors, and contaminated environments. In this article, we propose the dynamics of a lumpy skin disease model that contains seven compartments: susceptible cattle, vaccinated cattle, infected cattle, recovered cattle, susceptible vector, infected vector, and LSDV in the environment. The non-negativity and boundedness of the solution of the proposed LSD model are shown. There are two equilibrium points: the disease-free equilibrium point which always exists, and the endemic equilibrium point which exists conditionally. The disease-free equilibrium point is locally and globally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium is locally asymptotically stable if the Lienard-Chipart criteria is satisfied. In addition, based on the sensitivity analysis, we find that the vaccination rate is the most sensitive parameter. All analytical results have been verified by our numerical simulations.