A data-driven mathematical modeling framework for predicting HIV/HBV coinfection dynamics using machine learning approaches

Muhammad Asad Ullah; Sana Ullah Saqib; Yin-Tzer Shih; Nermeen Abdullah; Nidhal Becheikh; Lioua Kolsi; Kaouther Ghachem; Muhammad Asad Ullah; Sana Ullah Saqib; Yin-Tzer Shih; Nermeen Abdullah; Nidhal Becheikh; Lioua Kolsi; Kaouther Ghachem

doi:10.3934/math.2026916

AIMS Mathematics

2026, Volume 11, Issue 7: 22688-22723. doi: 10.3934/math.2026916

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Research article

A data-driven mathematical modeling framework for predicting HIV/HBV coinfection dynamics using machine learning approaches

1.
Institute for Advanced Study in Nuclear Energy & Safety, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, China
2.
Department of Applied Mathematics, National Chung Hsing University, Taichung 402202, Taiwan
3.
Department of Industrial and Systems Engineering, College of Engineering, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh, 11671, Saudi Arabia
4.
Mining Research Center, Northern Border University, P. O. Box 1321, Arar 91431, Saudi Arabia
5.
Department of Mechanical Engineering, College of Engineering, University of Ha'il, Ha'il City 81451, Saudi Arabia

Received: 11 April 2026 Revised: 02 July 2026 Accepted: 14 July 2026 Published: 28 July 2026
MSC : 26A33, 34A08, 34A34, 65L20, 92D30

Viral coinfections remain a significant global health challenge, particularly when infections like human immunodeficiency virus (HIV) coexist with other diseases, causing coinfection in a single individual. This study develops a fractional-order multi-stage HIV/HBV coinfection model using the Caputo fractional derivative to capture memory effects in disease transmission and progression. The model includes latent, asymptomatic, and symptomatic infection stages, as well as key epidemiological factors, including the effects of HBV vaccination, recovery processes among asymptomatic and fully-infected HBV individuals, and the acquisition of secondary infections by exposed, asymptomatic, and individuals. The qualitative properties of the model, such as positivity, boundedness, and sensitivity of key parameters, are analyzed to evaluate the biological feasibility of the system. The basic reproduction numbers for HIV and HBV are calculated, and a sensitivity analysis is conducted to determine the primary parameters affecting coinfection transmission. The coinfected HIV/HBV model is numerically solved using an artificial neural network optimized by the Levenberg-Marquardt algorithm (ANN-LMA). The performance of the ANN-LMA scheme is evaluated using mean squared error (MSE), root mean square error (RMSE), regression analysis, training-state analysis, error histograms, and comparison of overlap results with reference numerical results, demonstrating minimal absolute error. The results underscore the significance of the proposed network in predicting complex coinfection dynamics. This study provides policymakers and epidemic managers with a reliable modeling tool for developing adaptable and sustainable strategies to control HIV/HBV coinfection transmission.
- HIV/HBV coinfection model,
- comparison analysis,
- machine learning,
- simulation,
- fractional derivative,
- sensitivity analysis
Citation: Muhammad Asad Ullah, Sana Ullah Saqib, Yin-Tzer Shih, Nermeen Abdullah, Nidhal Becheikh, Lioua Kolsi, Kaouther Ghachem. A data-driven mathematical modeling framework for predicting HIV/HBV coinfection dynamics using machine learning approaches[J]. AIMS Mathematics, 2026, 11(7): 22688-22723. doi: 10.3934/math.2026916

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Abstract

Viral coinfections remain a significant global health challenge, particularly when infections like human immunodeficiency virus (HIV) coexist with other diseases, causing coinfection in a single individual. This study develops a fractional-order multi-stage HIV/HBV coinfection model using the Caputo fractional derivative to capture memory effects in disease transmission and progression. The model includes latent, asymptomatic, and symptomatic infection stages, as well as key epidemiological factors, including the effects of HBV vaccination, recovery processes among asymptomatic and fully-infected HBV individuals, and the acquisition of secondary infections by exposed, asymptomatic, and individuals. The qualitative properties of the model, such as positivity, boundedness, and sensitivity of key parameters, are analyzed to evaluate the biological feasibility of the system. The basic reproduction numbers for HIV and HBV are calculated, and a sensitivity analysis is conducted to determine the primary parameters affecting coinfection transmission. The coinfected HIV/HBV model is numerically solved using an artificial neural network optimized by the Levenberg-Marquardt algorithm (ANN-LMA). The performance of the ANN-LMA scheme is evaluated using mean squared error (MSE), root mean square error (RMSE), regression analysis, training-state analysis, error histograms, and comparison of overlap results with reference numerical results, demonstrating minimal absolute error. The results underscore the significance of the proposed network in predicting complex coinfection dynamics. This study provides policymakers and epidemic managers with a reliable modeling tool for developing adaptable and sustainable strategies to control HIV/HBV coinfection transmission.

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