A mathematical model of rinderpest infection in cattle populations

Abstract

A mathematical model for the epidemiology of rinderpest was developed, starting from a simplified descriptive analysis of the disease. A formula for the calculation of the probability of infection of a susceptible animal was first established. A deterministic failure threshold of the infection was then deduced. Deterministic and stochastic approaches were adopted using iterative methods on a computer. These allowed a description of the spread and the variability of an infection process in a population to be made. An illustration of the use of this model showed that, in some cases, variability effects due to stochastic factors were very important. In these particular conditions, the use of the deterministic model alone was not adequate for a good description of the infection. Consequently, improvements of the model were proposed in order to make it more realistic and to allow its use for the evaluation of the efficiency of field operations.