A Fractional-Order Model for Zika Virus Transmission Dynamics: Analysis, Control Strategies, and Simulation Insights

Abstract

The Zika virus, characterized by its complex transmission dynamics, poses a significant public health challenge. This study presents a novel mathematical model employing Caputo fractional derivatives to capture the intricate dynamics of the transmission of Zika virus between human and vector populations. Whereas the vector population is split into susceptible, exposed, and infected groups, the human population is classified into susceptible, exposed, asymptomatic, symptomatic, and recovered people. Our model incorporates fractional-order dynamics to better account for memory effects and historical data, which are often overlooked in classical models. Positivity and boundedness analyses verify the validity of the model, guaranteeing that all state variables are bounded and nonnegative throughout time. Furthermore, the Banach contraction mapping theorem is used to prove the solution's existence and uniqueness. The next-generation matrix approach is used to obtain the fundamental reproduction number ( R₀ ), which sheds light on the prerequisites for both disease persistence and outbreak. Numerical simulations illustrate the model's dynamics, revealing the impact of fractional orders on disease spread. Optimal control strategies, including vaccination, treatment, and environmental management, are integrated into the model to assess their effectiveness in mitigating the virus's transmission. The simulations demonstrate that optimal control measures significantly lower the number of infected individuals in both human as well as vector populations, although the complexities of vector management highlight the need for careful calibration of interventions. Our findings underscore the enhanced descriptive power of fractional-order models in capturing the real-world complexities of Zika virus transmission. This model offers a robust framework for public health officials to design and implement more effective control strategies, ultimately contributing to better management of Zika virus outbreaks and other vector-borne diseases.