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. 2025 Aug 11;15(1):29290.
doi: 10.1038/s41598-025-14280-w.

Fractional-order model of malaria incorporating treatment and prevention strategies

Benedict Celestine Agbata  1 , Sander Kovaci  2 , Dennis Ferdinand Agbebaku  3 , Raimonda Dervishi  2 , Emmanuel Abah  4 , Godwin Christopher Ezike Mbah  3 , Homan Emadifar  5   6   7 , Aseel Smerat  8   9
Affiliations

Fractional-order model of malaria incorporating treatment and prevention strategies

Benedict Celestine Agbata et al. Sci Rep. .

Abstract

Malaria, a life-threatening disease responsible for millions of deaths worldwide, remains a major public health issue, especially in under-resourced regions. It is caused by Plasmodium parasites, transmitted through mosquito bites, and disproportionately affects vulnerable groups like children and pregnant women. To improve understanding and management of malaria transmission, we investigated different mathematical models, traditionally based on integer-order derivatives. In this study, we introduced a novel approach using a fractional-order mathematical model to evaluate how treatment strategies impact malaria's spread. Initially, we modeled limited treatment scenarios with integer-order nonlinear differential equations. However, recognizing the complexity of malaria dynamics, we enhanced the model with fractional-order derivatives and power laws to capture a more detailed picture of disease behavior. The research established conditions for solution existence and uniqueness within the fractional framework and assessed the stability of the endemic equilibrium using the Lyapunov function technique. A sensitivity analysis of the basic reproduction number identified key factors influencing malaria transmission. Using the fractional Adams-Bashforth-Moulton method, we simulated various scenarios to explore the effects of model parameters and fractional-order values. Visual tools like surface and contour plots helped illustrate the findings. The results showed that improving treatment strategies and implementing preventive measures, such as mosquito control and timely medication, significantly reduced malaria cases. On the other hand, factors like increased mosquito contact and ineffective treatments aggravated the disease's impact. This study provided valuable insights into malaria dynamics, highlighting the critical need for sustained efforts in treatment and prevention to mitigate its devastating effects on communities.

Keywords: Basic reproduction number; Data fitting; Endemic equilibrium; Malaria dynamics; Sensitivity analysis.

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Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Schematic diagram for the model.
Fig. 2
Fig. 2
(a) Sensitivity indices for various parameters. (b) Data fitting for the malaria sub-model.
Fig. 3
Fig. 3
Surface plot of the basic reproduction number.
Fig. 4
Fig. 4
Surface plot and Effect of formula image on formula image.
Fig. 5
Fig. 5
Effect of formula image on formula image and formula image.
Fig. 6
Fig. 6
Effect of formula image on formula image and formula image.
Fig. 7
Fig. 7
Effect of formula image on the cumulative new cases of Malaria.
See this image and copyright information in PMC

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