Numerical simulation and fractional-order analysis of COVID-19–Zika co-infection: Impacts of vaccination, treatment, and vector control

Abstract

In light of the global health challenges posed by emerging infectious diseases, this study investigates the co-infection dynamics of COVID-19 and Zika virus through a mathematical modeling framework. The primary objective is to analyze the complex interactions between these two diseases and evaluate the effects of control strategies such as vaccination, treatment, quarantine, and vector management. A novel fractional-order model incorporating demographic interactions between human and vector populations is developed. The model employs Caputo fractional derivatives to extend the classical integer-order system, capturing memory and hereditary properties inherent in disease transmission and recovery. Numerical simulations are conducted using the Adams-Bashforth-Moulton (ABM) scheme in MATLAB, which allows for accurate solution approximations at various fractional orders. The existence and uniqueness of the solution are established through fixed-point theory. Basic reproduction numbers for both COVID-19 and Zika are derived, and threshold conditions necessary for disease eradication are analyzed. A detailed sensitivity analysis is performed to identify the most influential parameters affecting disease spread. Results indicate that vaccination and vector control are the most effective strategies in reducing transmission rates. The study concludes that fractional-order models offer deeper insights into delayed behavioral and biological responses, highlighting their importance in epidemic modeling. The novelty of this work lies in its integrated approach to modeling co-infections at a fractional order, combining control strategies within a unified framework. Key findings emphasize the need for a balanced combination of interventions. The study recommends prioritizing vaccination campaigns and vector control measures to effectively curb the simultaneous spread of COVID-19 and Zika virus.