FRACTIONAL-ORDER MODELING OF ZIKA VIRUS TRANSMISSION: ANALYSIS AND NUMERICAL SIMULATIONS

Year 2026, Volume: 16 Issue: 2, 249 - 265, 03.02.2026

Kunjan Shah , Jayashree Parmar Jaydev S. Patel Himanshu C. Patel

Abstract

This study presents a novel mathematical framework for modeling Zika virus transmission dynamics within human populations and between humans and mosquitoes, utilizing a fractional-order Caputo derivative. The study establishes the system's feasibility region, determines equilibrium points, and analyzes their stability. The existence and uniqueness of the solution are proven using fixed-point theory, and solutions are approximated via the fractional natural decomposition method. A key novelty of this study lies in the comparative analysis of fractional-order and integer-order models, highlighting how fractional derivatives provide greater modeling flexibility and better capture memory effects in disease progression. The numerical simulations demonstrate the significant influence of fractional derivatives on system behavior, illustrating differences in the rate of infection spread and disease persistence compared to integer-order models. This fractional calculus approach offers valuable insights into the complex dynamics of Zika virus transmission. Importantly, this study explores how fractional-order modeling can enhance existing control strategies against Zika virus outbreaks, providing a more refined framework for evaluating intervention measures and improving public health decision-making.

Keywords

Zika Virus , Natural Transform (NT) , Reproduction Number , Caputo Fractional Derivative , Fractional Natural Decomposition Method , Adomian Polynomial

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