Analysis of a mathematical model of the dynamics of contagious bovine pleuropneumonia

Abstract

Contagious bovine pleuropneumonia (CBPP) is a disease of cattle and water buffalo caused by Mycoplasma mycoides subspecies mycoides (Mmm). It attacks the lungs and the membranes that line the thoracic cavity. The disease is transmitted by inhaling droplets disseminated through coughing by infected cattle. In this paper a deterministic mathematical model for the transmission of Contagious Bovine plueropnemonia is presented. The model is a five compartmental model consisting of susceptible, Exposed, Infectious, Persistently infected and Recovered compartments. We derived a formula for the basic reproduction number R₀. For R₀ ≤ 1, the disease free equilibrium is globally asymptotically stable, thus CBPP dies out; whereas for R₀ > 1, the unique endemic equilibrium is globally asymptotically stable and hence the disease persists. Elasticity indices for R₀ with respect to different parameters are calculated; indicating parameters that are important for control strategies to bring R₀ below 1, the effective contact rateВ ОІ has the largest elasticity index. As the disease control options are associated to these parameters, for some values of these parameters, R₀ < 1, thus the disease can be controlled.