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Analysis of the drug resistance level of malaria disease: a fractional-order model

  • Komal Bansal ORCID logo EMAIL logo , Trilok Mathur and Santoshi Kumari
Published/Copyright: October 28, 2025
Epidemiologic Methods
From the journal Epidemiologic Methods Volume 14 Issue 1

Abstract

Despite modern medical developments, infectious diseases continue to impact millions worldwide. Malaria, for instance, is a significant cause of mortality and suffering in developed and developing countries. The most challenging hurdle for scientists to control this disease is the parasite’s propensity to develop resistance to novel medicines and treatment approaches. In response, this study develops a novel compartmental model of malaria transmission with memory between human-to-mosquito and mosquito-to-human that integrates drug resistance development and therapy as a preventative measure. The memory is incorporated using the Caputo fractional derivative. The existence and stability of the disease-free and endemic equilibrium have been investigated using the Routh-Hurwitz criterion. Numerical simulations have been performed to establish the role of different crucial parameters and variables in the proposed model. In addition, sensitivity analysis has been performed to demonstrate the variation of findings for the different parameters. The results demonstrate that decreasing the order of derivative reduces the basic reproduction number and that early detection of resistance levels can help minimize transmission. The research has broad implications for healthcare, including the need to achieve high rates of treatment and immunity development while minimizing the emergence of drug resistance due to treatment failure. In summary, this research sheds light on this terrible pandemic’s nature by assessing the impact of treatment rates and resistance levels.

Keywords: fractional differential equation; mathematical modeling; drug resistance; malaria; stability analysis
MSC 2020: 26A33; 00A71; 34A08; 93A30; 97M10; 97M60
Corresponding author: Komal Bansal, Department of Mathematics, Chandigarh University, Mohali, 140413, India, E-mail:

Acknowledgments

Komal Bansal is thankful to UGC for financial support with 1091/(CSIR-UGC NET DEC. 2018).

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: None declared.

  7. Data availability: Not applicable.

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Received: 2025-06-30
Accepted: 2025-10-08
Published Online: 2025-10-28

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/em-2025-0025
Keywords for this article
fractional differential equation; mathematical modeling; drug resistance; malaria; stability analysis

Articles in the same Issue

  1. Research Articles
  2. Definition, identification, and estimation of the direct and indirect number needed to treat
  3. Sample size determination for external validation of risk models with binary outcomes using the area under the ROC curve
  4. Analysis of the drug resistance level of malaria disease: a fractional-order model
  5. Extending the scope of the capture-recapture experiment: a multilevel approach with random effects to provide reliable estimates at national level
  6. Discrete-time compartmental models with partially observed data: a comparison among frequentist and Bayesian approaches for addressing likelihood intractability
  7. Sensitivity analysis for unmeasured confounding for a joint effect with an application to survey data
  8. Investigating the association between school substance programs and student substance use: accounting for informative cluster size
  9. The quantiles of extreme differences matrix for evaluating discriminant validity
  10. Finite-sample improved confidence intervals based on the estimating equation theory for the modified Poisson and least-squares regressions
  11. Causal mediation analysis for difference-in-difference design and panel data
  12. What if dependent causes of death were independent?
  13. Bot invasion: protecting the integrity of online surveys against spamming
  14. A study of a stochastic model and extinction phenomenon of meningitis epidemic
  15. Understanding the impact of media and latency in information response on the disease propagation: a mathematical model and analysis
  16. Time-varying reproductive number estimation for practical application in structured populations
  17. Perspective
  18. Should we still use pointwise confidence intervals for the Kaplan–Meier estimator?
  19. Leveraging data from multiple sources in epidemiologic research: transportability, dynamic borrowing, external controls, and beyond
  20. Regression calibration for time-to-event outcomes: mitigating bias due to measurement error in real-world endpoints
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