Deep neural network applications in mathematical epidemiology: Case of rabies virus

Mutum Zico Meetei; Ramsha Shafqat; Ahmed H. Msmali; Waleed Hamali; Mutum Zico Meetei; Ramsha Shafqat; Ahmed H. Msmali; Waleed Hamali

doi:10.3934/math.20251032

AIMS Mathematics

2025, Volume 10, Issue 10: 23261-23291. doi: 10.3934/math.20251032

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Research article Special Issues

Deep neural network applications in mathematical epidemiology: Case of rabies virus

1.
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia
2.
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan

Received: 19 March 2025 Revised: 01 August 2025 Accepted: 21 August 2025 Published: 14 October 2025
MSC : 34D20, 34K20, 34K60, 92C60, 92D45

This research uses Susceptible–Exposed–Infectious–Recovered (SEIR) and Susceptible–Exposed–Infectious–Vaccinated (SEIV) models to analyze rabies transmission in human and canine populations. The framework includes eight epidemiological compartments to evaluate intervention strategies. A fractional-order model is employed using the Atangana-Baleanu derivative in the Caputo sense to capture memory and the system's complexity. The model's validity is established through qualitative analysis. Existence and uniqueness are confirmed via fixed-point theory, and Ulam-Hyers criteria assess robustness. Numerical solutions are obtained using the iterative Adams and Adams-Bashforth methods for accurate time-series simulations. Numerical experiments evaluate vaccination effects under a constant rate for a subset of the population. The results show that vaccination effectively reduces disease prevalence, emphasizing its critical role in rabies control. Deep neural network (DNN) techniques are applied for training, validation, and testing. The DNN has three hidden layers (10,100, 10 neurons) and is trained over 1000 epochs using the Levenberg-Marquardt algorithm. The model achieves high predictive accuracy, with mean square errors as low as 0.00027 and root mean square errors under 0.17 across compartments. Overall, combining fractional calculus with deep learning provides a robust framework for modeling complex disease dynamics and offers valuable insights for public health strategies in regions with significant dog populations.
- rabies,
- mathematical modeling,
- fractional derivatives,
- dogs,
- qualitative analysis,
- Adam-Bashforth method,
- stability analysis,
- numerical simulation,
- ABC fractional derivative
Citation: Mutum Zico Meetei, Ramsha Shafqat, Ahmed H. Msmali, Waleed Hamali. Deep neural network applications in mathematical epidemiology: Case of rabies virus[J]. AIMS Mathematics, 2025, 10(10): 23261-23291. doi: 10.3934/math.20251032

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Abstract

This research uses Susceptible–Exposed–Infectious–Recovered (SEIR) and Susceptible–Exposed–Infectious–Vaccinated (SEIV) models to analyze rabies transmission in human and canine populations. The framework includes eight epidemiological compartments to evaluate intervention strategies. A fractional-order model is employed using the Atangana-Baleanu derivative in the Caputo sense to capture memory and the system's complexity. The model's validity is established through qualitative analysis. Existence and uniqueness are confirmed via fixed-point theory, and Ulam-Hyers criteria assess robustness. Numerical solutions are obtained using the iterative Adams and Adams-Bashforth methods for accurate time-series simulations. Numerical experiments evaluate vaccination effects under a constant rate for a subset of the population. The results show that vaccination effectively reduces disease prevalence, emphasizing its critical role in rabies control. Deep neural network (DNN) techniques are applied for training, validation, and testing. The DNN has three hidden layers (10,100, 10 neurons) and is trained over 1000 epochs using the Levenberg-Marquardt algorithm. The model achieves high predictive accuracy, with mean square errors as low as 0.00027 and root mean square errors under 0.17 across compartments. Overall, combining fractional calculus with deep learning provides a robust framework for modeling complex disease dynamics and offers valuable insights for public health strategies in regions with significant dog populations.

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