Analysis of a nonlinear fractional system for Zika virus dynamics with sexual transmission route under generalized Caputo-type derivative

Abstract

This paper establishes a mathematical model of the Zika virus infection with the sexual transmission route under the generalized Caputo-type fractional derivative. The model consists of a system of eleven nonlinear fractional differential equations. The existence and uniqueness results are derived by applying Banach's and Schauder's fixed point theorems. The different types of Ulam's stability results for the fractional model are examined. The corrector-predictor algorithm has been applied to illustrate the approximated solutions and analyze the dynamical behavior of the fractional model under consideration. In addition, various numerical simulations are presented corresponding to different fractional-orders in alpha is an element of [0, 1].