Mathematical Model for the Transmission Dynamics of Bovine Tuberculosis in Human and Livestock with Control Strategies

Abstract

A deterministic mathematical model for bovine tuberculosis (bovine TB) in humans and livestock is formulated and used to assess the effectiveness of dairy products inspection, human treatment and quarantine of infected livestock as the control of the disease transmission. The computed effective reproduction number shows that the disease can be cleared from the population if Re is less than unity and it persists if Re is greater than unity. It means that if Re<1 the disease-free equilibrium is asymptotically stable which means the disease can be cleared from the population and endemic when Re>1 which implies the disease persists in the population. Numerical analysis was carried out to investigate how the controls can help to minimize the spread of the disease.