Abstract
Anthrax is a zoonotic disease caused by bacillus anthraces. In this study a deterministic mathematical model for transmission dynamics of anthrax in humans and animals is presented and quantitatively analyzed. To understand the dynamics of anthrax, the basic reproduction number $R_0$ which measures average new infections is computed using next generation matrix operator and analyzed by normalized forward sensitivity index. Analysis shows that anthrax transmission rate to animals, animals' natural death rate, anthrax natural death rate and animal's birth rate are the most sensitive parameters to the disease transmission dynamics. When animal recruitment and anthrax transmission rates increase, the basic reproduction number $R_0$ also increase proportionally. However, when animal natural and anthrax induced death rates increase, basic reproduction number $R_0$ decreases. Numerical simulations using Runge-Kutta method show that animals drive the dynamics of anthrax. The study suggests control strategies such as vaccination, fumigation and decomposition of carcasses to eradicate the disease.
Highlights
Anthrax is an acute infectious disease caused by bacterium Bacillus anthraces [10]
Analysis shows that anthrax transmission rate to animals, animals’ natural death rate, anthrax natural death rate and animal’s birth rate are the most sensitive parameters to the disease transmission dynamics
Friedman and Yakubu [2] used a mathematical model developed by Hahn and Furnish and study anthrax is transmitted through carcass ingestion, spread of carcasses to the environment and migration rates on the persistence of animal population
Summary
Anthrax is an acute infectious disease caused by bacterium Bacillus anthraces [10]. The disease is transmitted in four different forms that includes, inhalation, ingestion, contact and injection. Omnivorous as well are vulnerable to the disease and they catch the infection through eating meat which is contaminated with anthrax. Keeling and Rohani [7] developed mathematical model for anthrax basing on environmental contamination and contact between uninfected animals and infected carcases. Furniss and Hahn [3] formulated the mathematical model basing on environmental contamination and direct contact between infected animals and non-infected carcasses. Friedman and Yakubu [2] used a mathematical model developed by Hahn and Furnish and study anthrax is transmitted through carcass ingestion, spread of carcasses to the environment and migration rates on the persistence of animal population. By modifying the models developed by [], this work is intending to study the dynamics of anthrax when infection between animals and human being is considered
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