Optimal Control Analysis of Anthrax Dynamics in Human and Animal Populations

Anthrax, caused by Bacillus anthracis, is a severe zoonotic disease with substantial health and economic consequences for animal and human populations. This study developed a nonlinear mathematical model to examine anthrax transmission incorporating animal vaccination and extended the model to identify optimal control strategies. The analysis examined equilibrium stability, parameter sensitivity, and intervention strategies. The disease-free equilibrium was stable when the basic reproduction number was below one, whereas the endemic equilibrium was stable when it exceeded one. Sensitivity analysis indicated that reducing cattle infection rates and the probability of human infection, alongside improvements in control-related parameters, could reduce disease levels. Optimal control analysis identified early human intervention, particularly prompt antibiotic treatment (u₂), as essential for achieving elimination within the model. Combining prevention with early treatment was the most cost-effective strategy, while strategies excluding treatment could worsen outbreaks. Although combinations of multiple controls could achieve elimination, they yielded diminishing returns, with the u₁–u₂ combination identified as the most efficient approach. These findings emphasise the importance of integrating prevention with prompt treatment and provide a mathematical basis for prioritising efficient anthrax control strategies.