A mathematical model of anthrax epidemic with behavioural change

Elijah B. Baloba; Baba Seidu; Elijah B. Baloba; Baba Seidu

doi:10.3934/mmc.2022023

Mathematical Modelling and Control

2022, Volume 2, Issue 4: 243-256. doi: 10.3934/mmc.2022023

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A mathematical model of anthrax epidemic with behavioural change

Elijah B. Baloba ,
Baba Seidu ^,

Department of Mathematics, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Ghana

Received: 28 July 2022 Revised: 06 December 2022 Accepted: 18 December 2022 Published: 26 December 2022

Anthrax is an acute infectious zonootic disease caused by Bacillus anthracis, a gram-positive, rod-shaped non-motile bacterium. It is a disease that mainly affects herbivorous animals of both domestic and wildlife, and causes devastating spillover infections into the human population. Anthrax epidemic results in serious and fatal infections in both animals and humans globally. In this paper, a non-linear differential equation model is proposed to study the transmission dynamics of anthrax in both animal and human populations taking into accounts saturation effect within the animal population and behavioural change of the general public towards the outbreak of the disease. The model is shown to have two unique equilibrium points, namely; the anthrax-free and endemic equilibrium points. The anthrax-free equilibrium point is globally asymptotically stable whenever the reproduction number is less than unity $ (\mathcal{R}_{0} < 1) $ and the endemic equilibrium point is locally asymptotically stable whenever $ \mathcal{R}_{0} > 1 $. Sensitivity analysis suggests that the most influential factors on the spread of anthrax are the infection force $ \beta_{a} $, pathogen shedding rate $ \xi_{a} $, recruitment rate $ \Lambda_a $, natural death rate in animals $ \mu_{a} $ and recovery rate in animals $ \phi_{a} $. Numerical simulations demonstrate that the saturation effect and behavioural change of the general public towards the outbreak of the disease increase the size of the susceptible population, reduce the size of the infective population and the pathogen levels in the environment. Findings of this research show that anthrax epidemic can be controlled by reducing the rate of anthrax infection and pathogen shedding rate, while increasing the rate of pathogen decay through proper environmental hygiene as well as increasing treatment to ensure higher recovery rate in infected animals. The results also show that positive behavioural change of the general public through mass awareness interventions can help control the spread of the disease.
- saturation effect,
- behavioural change,
- basic reproduction number,
- stability analysis,
- sensitivity analysis
Citation: Elijah B. Baloba, Baba Seidu. A mathematical model of anthrax epidemic with behavioural change[J]. Mathematical Modelling and Control, 2022, 2(4): 243-256. doi: 10.3934/mmc.2022023

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Abstract

Anthrax is an acute infectious zonootic disease caused by Bacillus anthracis, a gram-positive, rod-shaped non-motile bacterium. It is a disease that mainly affects herbivorous animals of both domestic and wildlife, and causes devastating spillover infections into the human population. Anthrax epidemic results in serious and fatal infections in both animals and humans globally. In this paper, a non-linear differential equation model is proposed to study the transmission dynamics of anthrax in both animal and human populations taking into accounts saturation effect within the animal population and behavioural change of the general public towards the outbreak of the disease. The model is shown to have two unique equilibrium points, namely; the anthrax-free and endemic equilibrium points. The anthrax-free equilibrium point is globally asymptotically stable whenever the reproduction number is less than unity $ (\mathcal{R}_{0} < 1) $ and the endemic equilibrium point is locally asymptotically stable whenever $ \mathcal{R}_{0} > 1 $. Sensitivity analysis suggests that the most influential factors on the spread of anthrax are the infection force $ \beta_{a} $, pathogen shedding rate $ \xi_{a} $, recruitment rate $ \Lambda_a $, natural death rate in animals $ \mu_{a} $ and recovery rate in animals $ \phi_{a} $. Numerical simulations demonstrate that the saturation effect and behavioural change of the general public towards the outbreak of the disease increase the size of the susceptible population, reduce the size of the infective population and the pathogen levels in the environment. Findings of this research show that anthrax epidemic can be controlled by reducing the rate of anthrax infection and pathogen shedding rate, while increasing the rate of pathogen decay through proper environmental hygiene as well as increasing treatment to ensure higher recovery rate in infected animals. The results also show that positive behavioural change of the general public through mass awareness interventions can help control the spread of the disease.

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