| Summary: | In this paper, the mathematical models for amebiasis are developed and presented. The first model considers the transmission dynamics of amebiasis coupled with two constant controls: treatment and sanitation. The next-generation matrix calculates the effective reproductive number, which is then used to assess model system stability. A sensitivity analysis is performed to determine the primary factors affecting disease transmission. Nonetheless, the results suggest that indirect transmission is more crucial than direct transmission in spreading disease. In addition, we extended the first model to incorporate time-dependent optimal control measures, namely community awareness, treatment, and sanitation. The aim was to reduce the number of infections emanating from interaction with carriers, infected people, and polluted environments while minimizing the expenses associated with adopting controls. The optimal control problem is solved by applying Pontryagin’s Maximum Principle and forward and backward-in-time fourth-order Runge–Kutta methods. The results indicate that an awareness program is optimal when a single control strategy is the only available option. However, when a combination of two controls is implemented, an approach combining awareness programs and treatment is shown to be optimal. Generally, the best strategy is implementing a combination of all three controls: awareness programs, sanitation, and treatment.
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