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

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

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

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

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Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems, Biological Mathematics

Journal Section

Research Article

Authors

Kunjan Shah ^*
0000-0003-1269-0865
India

Jayashree Parmar This is me
0009-0000-7413-2178
India

Jaydev S. Patel This is me
0000-0001-6979-0272
India

Himanshu C. Patel This is me
0000-0001-7228-7256
India

Publication Date

February 3, 2026

Submission Date

November 27, 2024

Acceptance Date

February 28, 2025

Published in Issue

Year 2026 Volume: 16 Number: 2

IZ

https://izlik.org/JA68KW53KB

Cite

RIS / Bibtex

APA

Shah, K., Parmar, J., Patel, J. S., & Patel, H. C. (2026). FRACTIONAL-ORDER MODELING OF ZIKA VIRUS TRANSMISSION: ANALYSIS AND NUMERICAL SIMULATIONS. TWMS Journal of Applied and Engineering Mathematics, 16(2), 249-265. https://izlik.org/JA68KW53KB

AMA

1.Shah K, Parmar J, Patel JS, Patel HC. FRACTIONAL-ORDER MODELING OF ZIKA VIRUS TRANSMISSION: ANALYSIS AND NUMERICAL SIMULATIONS. JAEM. 2026;16(2):249-265. https://izlik.org/JA68KW53KB

Chicago

Shah, Kunjan, Jayashree Parmar, Jaydev S. Patel, and Himanshu C. Patel. 2026. “FRACTIONAL-ORDER MODELING OF ZIKA VIRUS TRANSMISSION: ANALYSIS AND NUMERICAL SIMULATIONS”. TWMS Journal of Applied and Engineering Mathematics 16 (2): 249-65. https://izlik.org/JA68KW53KB.

EndNote

Shah K, Parmar J, Patel JS, Patel HC (February 1, 2026) FRACTIONAL-ORDER MODELING OF ZIKA VIRUS TRANSMISSION: ANALYSIS AND NUMERICAL SIMULATIONS. TWMS Journal of Applied and Engineering Mathematics 16 2 249–265.

IEEE

[1]K. Shah, J. Parmar, J. S. Patel, and H. C. Patel, “FRACTIONAL-ORDER MODELING OF ZIKA VIRUS TRANSMISSION: ANALYSIS AND NUMERICAL SIMULATIONS”, JAEM, vol. 16, no. 2, pp. 249–265, Feb. 2026, [Online]. Available: https://izlik.org/JA68KW53KB

ISNAD

Shah, Kunjan - Parmar, Jayashree - Patel, Jaydev S. - Patel, Himanshu C. “FRACTIONAL-ORDER MODELING OF ZIKA VIRUS TRANSMISSION: ANALYSIS AND NUMERICAL SIMULATIONS”. TWMS Journal of Applied and Engineering Mathematics 16/2 (February 1, 2026): 249-265. https://izlik.org/JA68KW53KB.

JAMA

1.Shah K, Parmar J, Patel JS, Patel HC. FRACTIONAL-ORDER MODELING OF ZIKA VIRUS TRANSMISSION: ANALYSIS AND NUMERICAL SIMULATIONS. JAEM. 2026;16:249–265.

MLA

Shah, Kunjan, et al. “FRACTIONAL-ORDER MODELING OF ZIKA VIRUS TRANSMISSION: ANALYSIS AND NUMERICAL SIMULATIONS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 2, Feb. 2026, pp. 249-65, https://izlik.org/JA68KW53KB.

Vancouver

1.Kunjan Shah, Jayashree Parmar, Jaydev S. Patel, Himanshu C. Patel. FRACTIONAL-ORDER MODELING OF ZIKA VIRUS TRANSMISSION: ANALYSIS AND NUMERICAL SIMULATIONS. JAEM [Internet]. 2026 Feb. 1;16(2):249-65. Available from: https://izlik.org/JA68KW53KB