A Mathematical Model of Anthrax Transmission in Animal Populations.

A general mathematical model of anthrax (caused by Bacillus anthracis) transmission is formulated that includes live animals, infected carcasses and spores in the environment. The basic reproduction number [Formula: see text] is calculated, and existence of a unique endemic equilibrium is established for [Formula: see text] above the threshold value 1. Using data from the literature, elasticity indices for [Formula: see text] and type reproduction numbers are computed to quantify anthrax control measures. Including only herbivorous animals, anthrax is eradicated if [Formula: see text]. For these animals, oscillatory solutions arising from Hopf bifurcations are numerically shown to exist for certain parameter values with [Formula: see text] and to have periodicity as observed from anthrax data. Including carnivores and assuming no disease-related death, anthrax again goes extinct below the threshold. Local stability of the endemic equilibrium is established above the threshold; thus, periodic solutions are not possible for these populations. It is shown numerically that oscillations in spore growth may drive oscillations in animal populations; however, the total number of infected animals remains about the same as with constant spore growth.