Dynamical analysis of a nonlinear fractional cervical cancer epidemic model with the nonstandard finite difference method
Asma Rashid Butt, Aitzaz Ahmad Saqib, Ali Saleh Alshomrani, Abu Bakar
Abstract
In this paper, we analyze the fractional compartmental model in the sense of Caputo derivative for the dynamics of the novel human papillomavirus, which causes cervical cancer. We study and investigate the dynamical analysis of a nonlinear fractional-order cervical cancer epidemic model with the nonstandard finite difference method. The newly proposed nonlinear fractional model is an extension of an integer-order cervical cancer mathematical model. We demonstrate the solution's existence, uniqueness, non-negativity, and boundedness by utilizing fundamental concepts of the fixed-point theory. The basic reproduction number, which analyzes whether or not the infection spreads to the population, is computed using the next-generation matrix method. We investigate the local and global asymptotic stability of the derived cervical-free and cervical-present equilibrium points and discuss the sensitivity of the basic reproduction number, which depends on the parameters of the proposed model. Furthermore, a mathematical simulation of the suggested continuous model is performed to evaluate the reported theoretical results using the nonstandard finite difference method. The acquired results are displayed, which show that a fractional parameter plays a pivotal role in controlling the cervical cancer.