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

D. C. Ugo; M. B. Okofu; J. Amos; C. L. Ejikeme; K. A. Onoja; B. C. Agbata

doi:10.5281/zenodo.20374646

D. C. Ugo Department of Mathematics Enugu State University of Science and Technology, Enugu, Nigeria.
M. B. Okofu Department of Mathematics University of Nigeria, Nsukka, Nigeria.
J. Amos Department of Mathematical Sciences Prince Abubakar Audu University, Anyigba, Nigeria.
C. L. Ejikeme Department of Mathematics University of Nigeria, Nsukka, Nigeria.
K. A. Onoja Department of Pharmaceutical and Medicinal Chemistry, Faculty of Pharmaceutical Sciences, Nnamdi Azikiwe University, Awka, Nigeria.
B. C. Agbata Department of Mathematics and Statistics, Faculty of Science, Confluence University of Science and Technology, Osara, Nigeria.

DOI: https://doi.org/10.5281/zenodo.20374646

Keywords: Zika virus infection, Deterministic compartmental model, Stability analysis, Basic reproduction number, Numerical simulations

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.

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