Abstract
Various epidemics have occurred throughout history, which has led to the investigation and understanding of their transmission dynamics. As a result, non-local operators are used for mathematical modeling in this study. Therefore, this research focuses on developing a dysentery diarrhea model with the use of a fractional operator using a one-parameter-Mittag-Leffler kernel. The model consists of three classes of the human population, whereas the fourth one belongs to the pathogen population. The model carefully deals with the dimensional homogeneity among the parameters and the fractional operator. In addition, the model was validated by fitting the actual number of dysentery diarrhea infected cases covering 52 weeks in 2017, which occurred in Ethiopia. The biological parameters were fitted, and fractional order. was optimized. The basic reproduction numbers R-0 were 1.7031 and 1.9581, which correspond to the fractional and integer-order models, respectively. The fractional model showed smaller discrepancies compared to the integer-order model when the models were fitted and validated with the actual cases of infected humans. Qualitative theory for the existence and uniqueness of the solutions was extensively explored, and the stability of equilibria was investigated. The most influential parameters were found via forward sensitivity indices. This multidisciplinary research shows and explains the results of numerical simulations applied to a biological issue.