title: A Mathematical Model of Anthrax Transmission in Animal Populations.
abstract: 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.
authors.affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada. saadroy@uvic.ca.
authors.forename: C M
authors.identifier: 0000-0002-2217-3071
authors.initials: CM
authors.lastname: Saad-Roy
authors.affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada.
authors.forename: P
authors.initials: P
authors.lastname: van den Driessche
authors.affiliation: Department of Mathematics, Howard University, Washington, DC, 20059, USA.
authors.forename: Abdul-Aziz
authors.initials: AA
authors.lastname: Yakubu
mesh_terms: D000818:Animals; D000881:Anthrax / Q000382:microbiology / Q000635:transmission / Q000662:veterinary*; D022122:Anthrax Vaccines / Q000494:pharmacology; D001408:Bacillus anthracis / Q000254:growth & development / Q000472:pathogenicity; D050936:Basic Reproduction Number; D060435:Carnivory; D060434:Herbivory; D006801:Humans; D058751:Livestock; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics; D013171:Spores, Bacterial / Q000254:growth & development / Q000472:pathogenicity
chemical_list: D022122:Anthrax Vaccines
keywords: Anthrax; Disease control strategy; Global stability; Hopf bifurcation; Type reproduction number