Author(s)

Shaibu Osman^1*, Dominic Otoo², Oluwole Daniel Makinde³

¹Department of Basic Sciences, School of Basic and Biomedical Sciences, University of Health and Allied Sciences, Ho, Volta Region, Ghana.
²Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, Ghana.
³Faculty of Military Science, Stellenbosch University, Saldanha, South Africa.

Anthrax is an infection caused by bacteria and it affects both human and animal populations. The disease can be categorized under zoonotic diseases and humans can contract infections through contact with infected animals, ingest contaminated dairy and animal products. In this paper, we developed a mathematical model for anthrax transmission dynamics in both human and animal populations with optimal control. The qualitative solution of the model behaviour was analyzed by determining R_hv, equilibrium points and sensitivity analysis. A vaccination class was incorporated into the model with waning immunity. Local and global stability of the model’s equilibria was found to be locally asymptotically stable whenever R_hv < 1 and unstable otherwise. Analysis of parameter contribution was conducted to determine the contribution of each to R_hv. It was revealed that reducing animal and human interaction rate, would decrease R_hv. We extended the model to optimal control in order to find the best control strategy in reducing anthrax infections. It showed that the effective strategy in combating the anthrax epidemics is vaccination of animals and prevention of humans.

Anthrax Model, Stability Analysis, Sensitivity, Optimal Control, Cost Effectiveness

Osman, S. , Otoo, D. and Makinde, O. (2020) Modeling Anthrax with Optimal Control and Cost Effectiveness Analysis. Applied Mathematics, 11, 255-275. doi: 10.4236/am.2020.113020.