Vaccination and transmission interplay in HAV-HIV co-infection: A predictive study backed by simulation

Shaiza Irum; Kashif Ali Khan; Nauman Raza; Waleed M. Abdelfattah; Wedad Albalawi; Ahmed M. Shehata; Gamal M. Ismail; Shaiza Irum; Kashif Ali Khan; Nauman Raza; Waleed M. Abdelfattah; Wedad Albalawi; Ahmed M. Shehata; Gamal M. Ismail

doi:10.3934/math.2026953

AIMS Mathematics

2026, Volume 11, Issue 8: 23663-23686. doi: 10.3934/math.2026953

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Research article

Vaccination and transmission interplay in HAV-HIV co-infection: A predictive study backed by simulation

1.
Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan
2.
Institute of Mathematics, University of the Punjab, Lahore, Pakistan
3.
College of Engineering, University of Business and Technology, Jeddah 23435, Saudi Arabia
4.
Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt
5.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
6.
Department of Mathematics, College of Sciences, University of Bisha, Bisha 61922, Saudi Arabia
7.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia

Received: 31 January 2026 Revised: 08 May 2026 Accepted: 29 May 2026 Published: 03 August 2026
MSC : 37G35, 37N25

This study proposes an epidemiological model for hepatitis A virus (HAV) and human hmmunodeficiency virus (HIV) co-infection in the United States of America, incorporating an integer-order derivative. The model's mathematical properties, including non-negativity and boundedness, are carefully examined and confirmed. Additionally, equilibrium points at the disease-free states are determined, along with the calculation of the reproduction number. With the aid of partial rank correlation coefficient (PRCC) and Latin hypercube sampling (LHS), sensitivity analyses of the basic reproduction numbers are performed using 1200 simulations. Local and global stability of the disease-free equilibrium point are established by employing a Lyapunov function and LaSalle's invariance principle. Using generated HIV and HAV data for the United States from 2014 to 2023, the model reproduces co-infection dynamics, and the MATLAB's built-in routine bvp4c is used to study the effects of vaccination, transmission, and co-infection on both diseases. These results further support the conclusion that if vaccination coverage increases, co-infection may reduce and disease control improves. To this end, these results show important thresholds that concern how disease persists, and highlight the need to research intervention strategies more and allocate targeted resources to control outbreaks.
- antiretroviral therapy,
- HAV and HIV co-infection,
- sensitivity analysis and parameter estimation
Citation: Shaiza Irum, Kashif Ali Khan, Nauman Raza, Waleed M. Abdelfattah, Wedad Albalawi, Ahmed M. Shehata, Gamal M. Ismail. Vaccination and transmission interplay in HAV-HIV co-infection: A predictive study backed by simulation[J]. AIMS Mathematics, 2026, 11(8): 23663-23686. doi: 10.3934/math.2026953

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Abstract

This study proposes an epidemiological model for hepatitis A virus (HAV) and human hmmunodeficiency virus (HIV) co-infection in the United States of America, incorporating an integer-order derivative. The model's mathematical properties, including non-negativity and boundedness, are carefully examined and confirmed. Additionally, equilibrium points at the disease-free states are determined, along with the calculation of the reproduction number. With the aid of partial rank correlation coefficient (PRCC) and Latin hypercube sampling (LHS), sensitivity analyses of the basic reproduction numbers are performed using 1200 simulations. Local and global stability of the disease-free equilibrium point are established by employing a Lyapunov function and LaSalle's invariance principle. Using generated HIV and HAV data for the United States from 2014 to 2023, the model reproduces co-infection dynamics, and the MATLAB's built-in routine bvp4c is used to study the effects of vaccination, transmission, and co-infection on both diseases. These results further support the conclusion that if vaccination coverage increases, co-infection may reduce and disease control improves. To this end, these results show important thresholds that concern how disease persists, and highlight the need to research intervention strategies more and allocate targeted resources to control outbreaks.

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