A Mathematical Model of Anthrax Transmission in Animal Populations

作者：Saad Roy C M^*; van den Driessche P; Yakubu Abdul Aziz

来源：Bulletin of Mathematical Biology, 2017, 79(2): 303-324.

DOI：10.1007/s11538-016-0238-1

• Anthrax
• Hopf bifurcation
• Global stability
• Disease control strategy
• Type reproduction number

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 is calculated, and existence of a unique endemic equilibrium is established for above the threshold value 1. Using data from the literature, elasticity indices for and type reproduction numbers are computed to quantify anthrax control measures. Including only herbivorous animals, anthrax is eradicated if . For these animals, oscillatory solutions arising from Hopf bifurcations are numerically shown to exist for certain parameter values with 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.

• 出版日期2017-2