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• An existing epidemiological deterministic model for Cholera disease is extended to an optimal control problem. • Parameter estimation of some parameters is carried out for the model. • The sensitivity analysis of the reproduction number is discussed. • Real statistical data for the Cholera epidemic model is used. • The existence and uniqueness of the optimality system are proved. Cholera is an acute, diarrheal infection of the intestine which spreads by the ingestion of contaminated water or food. It is an important health problem, especially in counties with poor sanitation and hygiene. In this paper, the Cholera dynamics model with continuous controls is theoretically investigated using optimal control theory. First, the parameters of the assumed model are estimated using a real data of Cholera from Ethiopia's Oromia Region. Then the sensitivity analyses of the parameters of the deterministic Cholera model is investigated to see the relative importance of parameters. It is observed that the intake rate of Vibrio Cholerae from infected humans (β 2) and the cholera recovery rate (γ) are the most sensitive parameters. The system is then extended into an optimal control problem to investigate how treatment and sanitation should be carried out to reduce the number of infected and pathogenic populations while minimizing the total cost of implementation. To this end, we have designed a control functional having two controls: treatment and sanitation. Next, we have shown that the optimal controls exist for the system. Then the optimal controls are represented in terms of the solutions of the optimality system, and then the uniqueness of the optimality system is proved. The average cost-effectiveness ratio and the incremental cost-effectiveness ratio are used and compared to examine the most cost-effective strategy. The use of treatment as control is found out to be the most cost-effective strategy using both methods. [ABSTRACT FROM AUTHOR]

• A new epidemiological deterministic model for dysentery diarrhea disease is proposed. • Classical and Caputo models are compared and optimized order in the latter case is obtained. • Parameter estimation is carried out for both classical and the Caputo model. • Existence and Uniqueness properties are carried out with positivity analysis. • Basic reproduction number and its sensitivity analysis is discussed. • Real statistical data for the dysentery diarrhea epidemic model is used. Non-Markovian characteristics, possessing memory effects and hereditary properties, play a vital role when it comes to the transmission dynamics of a disease or an epidemic within human society over the course of time. As a result, non-local operators from the field of fractional calculus are the most suitable choices to comprehend dynamics of the disease transmission. This research study is related with formulation of dysentery diarrhea dynamical nonlinear autonomous model via fractional Caputo differential operator with order τ ∈ (0, 1). Using fixed point theory, its solutions are determined to have properties satisfying existence and uniqueness conditions under the Caputo operator. In addition, the non-negative hyperoctant R + 4 is positively invariant region of the proposed fractional dysentery diarrhea model. Biological parameters of the classical and the Caputo fractional model are estimated under nonlinear parameter estimation technique and the optimized value of the fractional order parameter τ in the Caputo dysentery diarrhea model is computed to be 9.995e-01. The sensitivity of the basic reproduction number R 0 is thoroughly investigated for the most and the least sensitive parameter. Numerical simulations are found to be in good agreement with real statistical data and the theoretical predictions about the disease. [ABSTRACT FROM AUTHOR]