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
[1] Ahmed, I., Tariboon, J., Muhammad, M., & Ibrahim, M. J. (2024). A mathematical and sensitivity analysis of an HIV/AIDS infection model. International Journal of Mathematics and Computer in Engineering, 3(1), 35–46.
[2] Aguegboh, N. S., Agbata, A., Okyere, E., Osman, S., & Andrawus, J. (2025). A novel approach to modeling malaria with treatment and vaccination as control strategies in Africa using the Atangana-Baleanu derivative. Modeling Earth Systems and Environment, 11, 110.
[3] Anderson, R. M., & May, R. M. (1991). Infectious diseases of humans: Dynamics and control. Oxford University Press. 
[4] Bhatter, S., Jangid, K., Kumawat, S., Baleanu, D., Purohit, S. D., & Suthar, D. L. (2024). A new investigation on fractionalized modeling of human liver. Scientific Reports, 14(1), 1636. 1
[5] Bhatter, S., Kumawat, S., Bhatia, B., & Purohit, S. D. (2024). Analysis of COVID-19 epidemic with intervention impacts by a fractional operator. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 14(3), 261275. 
[6] Bhatter, S., Kumawat, S., & Purohit, S. D., & Suthar, D. L. (2025). Mathematical modeling of tuberculosis using Caputo fractional derivative: a comparative analysis with real data. Scientific Reports, 15, 12672. 
[7] Boulkroune, A., Zouari, F., & Boubellouta, A. (2025). Adaptive fuzzy control for practical fixed-time synchronization of fractional-order chaotic systems. Journal of Vibration and Control. Advance online publication. 
[8] Boutiba, M., Baghli-Bendimerad, I. S., & Bouzara-Sahraoui, I. N. E. H. (2024). Numerical solution by finite element method for time Caputo-Fabrizio fractional partial diffusion equation. Advanced Mathematical Models & Applications, 9(2), 316–328. 
[9] Diallo, O., Dasumani, M., Okelo, J. A., Osman, S., Sow, O., Aguegboh, N. S., & Okongo, W. (2025). Fractional optimal control problem modeling bovine tuberculosis and rabies co-infection. Results in Control and Optimization,18, 100523. 
[10] Diabate, A. B., Sangare, B., & Koutou, O. (2022). Mathematical modeling of the dynamics of vector-borne diseases transmitted by mosquitoes: Taking into account aquatic stages and gonotrophic cycle. Nonautonomous Dynamical Systems, 9(1), 205236. 
[11] Diethelm, K. (2010). The analysis of fractional differential equations. Springer. 
[12] Ducrot, A., & Magal, P. (2009). A mathematical model for malaria involving differential susceptibility, exposedness and infectivity of human host. Journal of Biological Dynamics, 3(6), 574598. 
[13] Garrappa, R. (2021). Numerical solution of fractional differential equations. Mathematics, 9(11), 1272. 
[14] Gellow, G. T., Munganga, J. M. W., & Jafari, H. (2023). Analysis of a ten compartmental mathematical model of malaria transmission. Advanced Mathematical Models & Applications, 8(2), 140156.
[15] Golmankhaneh, A. K., Welch, K., Tunç, C., et al. (2023). Classical mechanics on fractal curves. The European Physical Journal Special Topics, 232, 991–999. 
[16] Jafari, H., Tajadodi, H., & Gasimov, Y. S. (2025). Modern computational methods for fractional differential equations. Chapman & Hall/CRC. 
[17] Kachhia, K. B. (2023). Chaos in fractional order financial model with fractal-fractional derivatives. Partial Differential Equations in Applied Mathematics, 7, 100502. 
[18] Khan, M. A., DarAssi, M. H., Ahmad, I., Seyam, N. M., & Alzahrani, E. (2024). Modeling the dynamics of tuberculosis with vaccination, treatment, and environmental impact: Fractional order modeling. Computer Modeling in Engineering Sciences, 141(2), 13651394.
[19] Khirsariya, S. R., Yeolekar, M. A., Yeolekar, B. M., & Chauhan, J. P. (2024). Fractional-order rat bite fever model: A mathematical investigation into the transmission dynamics. Journal of Applied Mathematics and Computing,70(4), 38513878.
[20] Krc, Ö., Agamalieva, L., Gasimov, Y. S., & Bulut, H. (2024). Investigation of the wave solutions of two spacetime fractional equations in physics. Partial Differential Equations in Applied Mathematics, 2024, 100775.
[21] Kumawat, S., Bhatter, S., Bhatia, B., Purohit, S. D., Baskonus, H. M., & Suthar, D. L. (2025). Novel application of q-HAGTM to analyze Hilfer fractional differential equations in diabetic dynamics. Mathematics and Computers in Simulation, 238, 136–149. 
[22] Kumawat, S., Bhatter, S., Bhatia, B., Purohit, S. D., & Suthar, D. L. (2024). Mathematical modeling of allelopathic stimulatory phytoplankton species using fractal-fractional derivatives. Scientific Reports, 14(1), 20019. 
[23] Kumawat, S., Bhatter, S., Suthar, D. L., Purohit, S. D., & Jangid, K. (2022). Numerical modeling on age-based study of coronavirus transmission. Applied Mathematics in Science and Engineering, 30(1), 609–634. 
[24] Li, X., Chen, Y. and Podlubny, I. (2010). Mittag-Leffler stability of fractional order nonlinear dynamic systems. Computers & Mathematics with Applications, 59(5), 18101821. 
[25] Macdonald, G. (1957). The epidemiology and control of malaria. Oxford University Press. 
[26] Mangongo, Y. T., Bukweli, J.-D. K., Kampempe, J. D. B., & Munganga, J. M. W. (2025). Mathematical model of malaria transmission dynamics: Evaluating the impact of asymptomatic and resistant strains in human hosts. Advanced Mathematical Models & Applications, 10(3), 648674. 
[27] Manohara, G., & Kumbinarasaiah, S. (2024). Numerical approximation of fractional SEIR epidemic model of measles and smoking model by using Fibonacci wavelets operational matrix approach. Mathematics and Computers in Simulation, 221, 358396. 
[28] Matignon, D. (1996). Stability results for fractional differential equations with applications to control processing. Computational Engineering in Systems Applications, 2(1), 963968. 
[29] Meena, M., Purohit, M., Shyamsunder, S. D., Purohit, S. D., Baleanu, D., & Suthar, D. L. (2024). A novel fractionalized investigation of tuberculosis disease. Applied Mathematics in Science and Engineering, 32(1), Article 2351229. 
[30] Osman, S., Diallo, O., Dasumani, M., Andrawus, J., Sow, O., & Aguegboh, N. S. (2024). Modeling the transmission routes of hepatitis E virus as a zoonotic disease using fractional-order derivative. Journal of Applied Mathematics, 2024, Article 5168873.
[31] Öztürk, Z., Bilgil, H., & Sorgun, S. (2024). Fractional SAQ alcohol model: stability analysis and Türkiye application. International Journal of Mathematics and Computer in Engineering, 3(2), 125–136.
[32] Shyamsunder, S. D., Purohit, S. D., & Suthar, D. L. (2024). A novel investigation of the influence of vaccination on pneumonia disease. International Journal of Biomathematics, Article ID 2450080. 
[33] Tirite, G., & Suthar, D. L. (2025). A mathematical model for analyzing the spread of Malaria. International Journal of Biomathematics. Advance online publication. 
[34] Ullah, S., Khan, M. A., & Farooq, M. (2018). A fractional model for the dynamics of TB virus. Chaos, Solitons & Fractals, 116, 6371.
[35] Zhang, X. H., Ali, A., Gul, T., Khan, A., & Alshomrani, A. S. (2021). Mathematical analysis of the TB model with treatment via Caputo-type fractional derivative. Discrete Dynamics in Nature and Society, 2021, Article 9512371.
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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