Mathematical assessment of a fractional‐order vector–host disease model with the Caputo–Fabrizio derivative
Yu‐Ming Chu, Muhammad Farooq Khan, Saif Ullah, Syed Azhar Ali Shah, Muhammad Farooq, Mustafa bin Mamat
Abstract
Vector–host diseases outbreak is a major public health concern, and it has greatly affected human health and economy in various regions around the globe. Different approaches have been adopted to investigate the dynamical behavior and possible control of these diseases. In this study, we present a compartmental transmission model in order to explore the dynamics of vector–host infectious diseases. The saturated incidence rate instead of bilinear (or standard) and saturated treatment function is considered in model formulation which enhance the biological suitability of the proposed model. We first formulate the model based on nonlinear classical integer‐order differential equations. Then, the proposed integer‐order model is reformulated using the fractional‐order operator in Caputo–Fabrizio sense with nonsingular kernel. We investigate the model equilibria and evaluate the expression for the most important threshold parameter known as the basic reproduction number. Furthermore, the existence and uniqueness are presented via the fixed point approach. Additionally, using an efficient numerical scheme, the iterative solution of the model is obtained. Finally, we present the model simulations to illustrate the impact of arbitrary fractional order and some of other important parameters involved in the model on the disease dynamics and minimization.