Time-delay dynamics for contagious bovine pleuropneumonia

Modelling of contagious disease usually employs compartmental SEIR-like models where the waiting times in respective compartments are exponentially distributed. In this paper, we are interested in investigating how the distributions of sojourn times in infective compartments affect the dynamics and persistence of the contagious bovine pleuropneumonia, a chronic respiratory disease of cattle. Two kinds of extreme distributions of the sojourn times are considered: a Dirac delta-function and truncated Gaussian function leading to a model with (non-constant) delay and the classical exponential distribution that stands for a model without delay. Expressions of the basic reproductive numbers are derived and dynamical behaviours are discussed for the three models. It is found that the spreading of disease exhibits wave-like oscillations for the time-delay dynamics. In contrast, the disease appears to last longer when the spreading is described by the classical dynamics without delay. Subsequently, the time-delay dynamics turns out to be more appropriate for the description of an experimental epidemic of CBPP.