Dynamics and Linear Feedback Control of a Novel Discrete Fractional‐Order Zika Virus Model With Multiroute Transmission

This study addresses the critical public health challenge posed by the Zika virus (ZIKV), a pathogen with complex multiroute transmission dynamics. We develop a novel discrete fractional‐order mathematical model to accurately capture the intrapopulation spread of ZIKV, enhancing traditional models by incorporating memory effects and long‐range interactions inherent in epidemiological processes. Our primary objective is to analyze the model’s dynamics and propose effective control strategies. The model’s well‐posedness is established by proving the existence and uniqueness of solutions. Through stability analysis, we derive the basic reproduction number ( R 0 ) and characterize the local stability conditions for disease‐free and endemic equilibrium points, which are shown to be dependent on the fractional order ω . A comprehensive sensitivity analysis identifies the key parameters driving ZIKV transmission. Furthermore, we design a novel linear feedback control mechanism to suppress disease dynamics and stabilize the disease‐free state. Extensive numerical simulations confirm our theoretical results and demonstrate the control scheme’s efficacy. Our findings provide deeper insights into ZIKV dynamics and offer a robust mathematical framework for informing effective intervention strategies.