Modeling the impact of optimal control measures on the dynamics of cholera

Cholera is an infectious disease that causes severe, watery diarrhea that, if not treated, can lead to dehydration and death. Regardless of medical science advancements and the availability of healthcare services, it has been a global public health concern, affecting both children and adults. In this study, we develop and analyze a nonlinear optimal control problem to investigate the effective control of cholera in a human population. Four control variables were added to an already existing cholera model with vital dynamics: adequate cleanliness, oral vaccine, therapeutic care, and public education. The conditions for the existence of optimal cholera disease control were developed using Pontryagin's renowned maximal principle. Furthermore, the fourth-order Runge-Kutta forward-backward sweep method was used to simulate the optimality system to demonstrate the effect of various control methods on the spread of cholera within the human population. The findings show that control costs have a direct and plausible impact on the timeliness and robustness of each regulation.