Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis.

• 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]