Mathematics and Computational Sciences

A Fractional-Order analysis of malaria transmission using a ten-compartmental model with Caputo derivatives‎

Articles in Press

Document Type : Original Article

Authors

Gizachew Tirite Gellow 1
Dayalal Suthar 2, 3

1 Department of Mathematics, College of Natural and Computational Sciences, Debre Tabor University, Debre Tabor, Ethiopia.

2 Department of Mathematics, College of Natural Sciences, Wollo University, P.O. Box 1145, Dessie, Ethiopia.

3 Department of Mathematics, Saveetha School of Engineering, Thandalam 600124, Chennai, Tamil Nadu, India.

https://doi.org/10.30511/mcs.2026.2064952.1395
Abstract
This study presents a fractional-order malaria transmission model based on a ten-compartment structure that incorporates Caputo derivatives to capture memory effects in disease dynamics. The model distinguishes non-immune and semi-immune human populations alongside mosquito compartments. We establish mathematical properties including existence, uniqueness, positivity, and boundedness of solutions within a biologically feasible region. An explicit expression for the basic reproduction number R0 is derived using the next-generation matrix approach, and stability conditions for disease-free and endemic equilibria are analyzed via the Matignon criterion. Numerical simulations under realistic parameter settings demonstrate that decreasing the fractional order α delays epidemic peaks, reduces infection intensity, and prolongs disease persistence, highlighting the significant influence of memory effects on malaria dynamics. These results confirm that fractional-order models provide a more accurate representation of transmission patterns compared to classical integer-order frameworks.

Keywords

Basic Reproduction Number (R0)
Caputo Fractional Calculus
Disease-Free Equilibrium (DFE)
Fractional-Order Differential Equations
Malaria Transmission Model

Subjects

Mathematics and Computational Sciences

Articles in Press, Accepted Manuscript
Available Online from 06 February 2026

  • Receive Date 06 July 2025
  • Revise Date 22 December 2025
  • Accept Date 02 January 2026

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