Mathematical Modelling of Lumpy Skin Disease in Dairy Cow

Abstract

Lumpy skin disease (LSD) is a threatnening disease caused by virus that affects large ruminant animals mainly cattle. LSD is native in many African and Asian countries, having existed for over one hundred years in Africa where it originally started and has recently expanded to the Middle East region. A disease model consisting of six-dimensional system of ordinary differential equations was formulated to properly understand the spread and control of LSD. The classes considered includes the susceptible cow, vaccinated cow, infectious cow, recovered cow, susceptible mosquito and infectious mosquito. This paper captures two modes of transmission of the disease, direct contact and contact through mosquito bites. Inclusion of vaccination parameter makes this model different from existing literature. We show the model is well-posed through positivity and boundedness of the state variables. The basic reproduction number R0 of the model was derived and the disease-free equilibrium points was shown to be locally asymptotically stable when R0 < 1. Sensitivity analysis to identify the most sensitive parameters was conducted and the vaccination parameter was varied using matplotlib module in Python to check the effect of vaccination on both vaccinated and infectious cow. Increase in the vaccination parameter cause the number of vaccinated cow to increase and hence leads to reduction in the number of infected cow.