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 R0 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.