Mathematical Model for the Dynamics of Anthrax in Human and Animal Populations Incorporating Control Measures

Authors

  • Abdulrahman Abubakar
    Adamawa State Polytechnic, Yola
  • Maigari Jingi Bala
    Adamawa State Polytechnic, Yola
  • Ahmed Goni Umar
    Adamawa State Polytechnic, Yola
  • Musa Abdullahi
    Modibbo Adama University, Yola
  • Umar Gidado
    Government Day Senior Secondary School Hammawa Toungo, Yola

Keywords:

Anthrax, Reproduction Number, Vaccination, Stability, Simulations

Abstract

Anthrax is a zoonotic infectious disease caused by the bacterium Bacillus anthracis. In this study, we develop and analyze a deterministic compartmental model, formulated using ordinary differential equations, to explore the transmission dynamics of anthrax between humans and animals. Fundamental properties of the model, such as positivity, boundedness, and the existence of equilibrium points are established, confirming that the model is mathematically and biologically well-posed. The basic reproduction number, ​, is derived using the next-generation matrix approach. Stability analysis shows that the disease-free equilibrium is both locally and globally asymptotically stable when . Additionally, the model possesses a unique endemic equilibrium when , which is also globally stable when . Numerical simulations are conducted to validate and illustrate the theoretical results.

Dimensions

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Published

2025-09-15

How to Cite

Abubakar, A., Bala, M. J., Umar, A. G., Abdullahi, M., & Gidado, U. (2025). Mathematical Model for the Dynamics of Anthrax in Human and Animal Populations Incorporating Control Measures. Journal of Science Research and Reviews, 2(3), 166-177. https://doi.org/10.70882/josrar.2025.v2i3.94

Issue

Vol. 2 No. 3 (2025): JOSRAR Vol. 2 No. 3 (May - June)

Section

Articles
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How to Cite

Abubakar, A., Bala, M. J., Umar, A. G., Abdullahi, M., & Gidado, U. (2025). Mathematical Model for the Dynamics of Anthrax in Human and Animal Populations Incorporating Control Measures. Journal of Science Research and Reviews, 2(3), 166-177. https://doi.org/10.70882/josrar.2025.v2i3.94

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