A comparative study of disease transmission in hearing-impaired populations using the SIR model

Zeeshan Afzal; Mansoor Alshehri; Zeeshan Afzal; Mansoor Alshehri

doi:10.3934/math.2025512

AIMS Mathematics

2025, Volume 10, Issue 5: 11290-11304. doi: 10.3934/math.2025512

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A comparative study of disease transmission in hearing-impaired populations using the SIR model

Zeeshan Afzal ^{1
,
,},
Mansoor Alshehri ^2,3

1.
Department of Mathematics, Lahore Garrison University, Lahore Campus, Pakistan
2.
Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia
3.
King Salman Center for Disability Research, Riyadh 11614, Saudi Arabia

Received: 25 February 2025 Revised: 25 April 2025 Accepted: 06 May 2025 Published: 19 May 2025
MSC : 34A08, 92B05

The study extends the classical SIR epidemic model by incorporating a hearing impairment (H) compartment, which accounts for individuals who suffer from long-term auditory complications due to infection. The proposed SIR-H model includes one more $ H $ compartment to study the effect of infectious diseases on long-term disability. The model is expressed in terms of fractional-order differential equations to better capture the memory and hereditary nature of disease processes. A stability analysis is conducted to find the equilibrium points along with the basic reproduction number $ R_0 $ that governs the disease spread. Numerical solutions are derived using the Laplace Residual Power Series (LRPS) approach, and a comparative analysis with the Runge-Kutta method guarantees accuracy and efficiency. The Simulation results demonstrate how different values for the fractional order $ \alpha $ influence the disease dynamics, with smaller values reflecting higher memory effects. Additionally, machine learning algorithms such as Sequential Neural Networks are used to enhance the predictive capability and identify long-term epidemiological trends. The findings highlight the importance of incorporating disability-related compartments into epidemic models in order to aid public health strategies and policy formation.
- Laplace residual power series (LRPS) approach,
- fractional SIR-H model,
- Laplace transform operator,
- Caputo's derivative operator,
- stability analysis
Citation: Zeeshan Afzal, Mansoor Alshehri. A comparative study of disease transmission in hearing-impaired populations using the SIR model[J]. AIMS Mathematics, 2025, 10(5): 11290-11304. doi: 10.3934/math.2025512

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Abstract

The study extends the classical SIR epidemic model by incorporating a hearing impairment (H) compartment, which accounts for individuals who suffer from long-term auditory complications due to infection. The proposed SIR-H model includes one more $ H $ compartment to study the effect of infectious diseases on long-term disability. The model is expressed in terms of fractional-order differential equations to better capture the memory and hereditary nature of disease processes. A stability analysis is conducted to find the equilibrium points along with the basic reproduction number $ R_0 $ that governs the disease spread. Numerical solutions are derived using the Laplace Residual Power Series (LRPS) approach, and a comparative analysis with the Runge-Kutta method guarantees accuracy and efficiency. The Simulation results demonstrate how different values for the fractional order $ \alpha $ influence the disease dynamics, with smaller values reflecting higher memory effects. Additionally, machine learning algorithms such as Sequential Neural Networks are used to enhance the predictive capability and identify long-term epidemiological trends. The findings highlight the importance of incorporating disability-related compartments into epidemic models in order to aid public health strategies and policy formation.

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