Optimal Control of Cholera Transmission Dynamics in Areas of High Endemicity

Cholera continues to pose a public health challenge in endemic areas. This study develops a deterministic compartmental model for cholera that includes compartments for Susceptible, Vaccinated, Infected, Recovered, and Environmental bacteria, along with the system’s bacterial dynamics. To assess specific control strategies aimed at these interventions, an optimal control problem is posed, which includes simultaneously defined controls of hygiene education, vaccination, and treatment. Using Pontryagin’s Maximum Principle, the necessary conditions for optimality are derived. The resulting state and adjoint equations are solved numerically via a forward–backward sweep method: the state system is integrated forward using a fourth-order Runge–Kutta method, while the adjoint system is solved backward to update the control profiles iteratively.The results of the simulations show that vaccination considerably curtails the rate of new infections, while treatment strategies best lower long-term prevalence. The near-optimal blend of both methods came very close to achieving the full three-control strategy but with far less complexity. This could be beneficial in situations where employing all strategies is not cost-effective. To sum up, this model helps rethink different strategies that assist targeted, evidence-based policy-making decisions. It offers practical insights into effective cholera mitigation and can be adapted to other high-endemicity settings or extended to include cost-effectiveness analysis and real-time surveillance data.