Modeling the transmission dynamics of flagellated protozoan parasite with Atangana-Baleanu derivative: Application of 3/8 Simpson and Boole's numerical rules for fractional integral

A multi-analysis of transmission dynamic of Trichomonas was undertaken in this study. A model describing the spread dynamic of flagellated protozoan parasite with a triadic considered. A sensitivity analysis study of parameters involved in the mathematical model with local differentiation is presented in detail using some statistical methods. Conditions for the existence and unicity of the exact solutions of the non-linear system are constructed and proofs presented in detail. New numerical methods based on the 3/8 Simpson rule and Boole's rule approach for the new fractional differentiation based on the generalized kernel is used to solve the transmission model with non-local operator of differentiation. Some numerical simulations are presented for different values of fractional operators. The numerical simulation of the modified model revealed that, the non-locality of fractional derivative could be used as uncertainties analysis. This explains why the fractional differentiation is a powerful mathematical tool for modeling real world problems.