Mathematical Analysis of a Fractional-Order Model of Zika Virus Transmission with Treatment Effects

Abstract Zika virus is a mosquito-borne viral infection primarily transmitted by Aedes species mosquitoes. It gained global attention due to its rapid spread and its association with neurological complications and congenital abnormalities. Understanding its transmission dynamics is essential for effective control and prevention. In this study, a deterministic compartmental model is developed to investigate the transmission dynamics of Zika virus infection, with particular focus on the roles of treatment and contact rates in disease spread. The model incorporates both human and vector populations and captures key processes such as infection, recovery, and reinfection. Numerical simulations are performed to examine how variations in treatment and contact rates influence the spread of the disease and the distribution of population compartments. The results indicate that higher contact rates lead to a substantial increase in new infections and cumulative case numbers, thereby intensifying transmission. In contrast, increased treatment rates reduce the number of infected individuals and overall disease burden while improving recovery levels within the human population. Further analysis of the basic reproduction number shows a nonlinear inverse relationship with treatment and contact parameters. Specifically, high contact rates combined with low treatment levels result in values of greater than one, indicating sustained epidemic conditions. However, as treatment coverage increases, decreases below unity, suggesting eventual disease elimination. The findings demonstrate that effective treatment strategies can mitigate the adverse effects of high contact rates by stabilizing the susceptible population and reducing infection peaks. This study highlights the importance of improving treatment access and reducing exposure through integrated control strategies as key approaches for controlling the spread of Zika virus infection. Keywords: Zika virus infection, Deterministic compartmental model, Stability analysis, Basic reproduction number, Numerical simulations