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

Authors

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

DOI:

https://doi.org/10.70882/josrar.2025.v2i4.94

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, R0 ​, is derived using the next-generation matrix approach. Stability analysis shows that the disease-free equilibrium is both locally and globally asymptotically stable when R0<1. Additionally, the model possesses a unique endemic equilibrium when R0>1, which is also globally stable when R0<1 . Numerical simulations are conducted to validate and illustrate the theoretical results.

References

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Schematic Diagram of the Model

Published

2025-10-16

Issue

Vol. 2 No. 4 (2025): JOSRAR Vol. 2 No. 4 (July - August)

Section

Articles

License

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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(4), 38-49. https://doi.org/10.70882/josrar.2025.v2i4.94