A Mathematical Model of Anthrax Transmission in Animal Populations

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• 作者：C. M. Saad-Roy ; P. van den Driessche ; Abdul-Aziz Yakubu
• 关键词：Anthrax ; Hopf bifurcation ; Global stability ; Disease control strategy ; Type reproduction number
• 刊名：Bulletin of Mathematical Biology
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：79
• 期：2
• 页码：303-324
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematical and Computational Biology; Life Sciences, general; Cell Biology;
• 出版者：Springer US
• ISSN：1522-9602
• 卷排序：79

文摘

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 \(\mathcal {R}_0\) is calculated, and existence of a unique endemic equilibrium is established for \(\mathcal {R}_0\) above the threshold value 1. Using data from the literature, elasticity indices for \(\mathcal {R}_0\) and type reproduction numbers are computed to quantify anthrax control measures. Including only herbivorous animals, anthrax is eradicated if \(\mathcal {R}_0 < 1\). For these animals, oscillatory solutions arising from Hopf bifurcations are numerically shown to exist for certain parameter values with \(\mathcal {R}_0>1\) 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.