Open Access

ARTICLE

A Hybrid SIR-Fuzzy Model for Epidemic Dynamics: A Numerical Study

Muhammad Shoaib Arif^1,2,*, Kamaleldin Abodayeh¹, Yasir Nawaz²

1 Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
2 Department of Mathematics, Air University, Islamabad, 44000, Pakistan

* Corresponding Author: Muhammad Shoaib Arif. Email:

(This article belongs to the Special Issue: Mathematical Aspects of Computational Biology and Bioinformatics-II)

Computer Modeling in Engineering & Sciences 2024, 139(3), 3417-3434. https://doi.org/10.32604/cmes.2024.046944

Received 20 October 2023; Accepted 25 December 2023; Issue published 11 March 2024

Abstract

This study focuses on the urgent requirement for improved accuracy in disease modeling by introducing a new computational framework called the Hybrid SIR-Fuzzy Model. By integrating the traditional Susceptible-Infectious-Recovered (SIR) model with fuzzy logic, our method effectively addresses the complex nature of epidemic dynamics by accurately accounting for uncertainties and imprecisions in both data and model parameters. The main aim of this research is to provide a model for disease transmission using fuzzy theory, which can successfully address uncertainty in mathematical modeling. Our main emphasis is on the imprecise transmission rate parameter, utilizing a three-part description of its membership level. This enhances the representation of disease processes with greater complexity and tackles the difficulties related to quantifying uncertainty in mathematical models. We investigate equilibrium points for three separate scenarios and perform a comprehensive sensitivity analysis, providing insight into the complex correlation between model parameters and epidemic results. In order to facilitate a quantitative analysis of the fuzzy model, we propose the implementation of a resilient numerical scheme. The convergence study of the scheme demonstrates its trustworthiness, providing a conditionally positive solution, which represents a significant improvement compared to current forward Euler schemes. The numerical findings demonstrate the model’s effectiveness in accurately representing the dynamics of disease transmission. Significantly, when the mortality coefficient rises, both the susceptible and infected populations decrease, highlighting the model’s sensitivity to important epidemiological factors. Moreover, there is a direct relationship between higher Holling type rate values and a decrease in the number of individuals who are infected, as well as an increase in the number of susceptible individuals. This correlation offers a significant understanding of how many elements affect the consequences of an epidemic. Our objective is to enhance decision-making in public health by providing a thorough quantitative analysis of the Hybrid SIR-Fuzzy Model. Our approach not only tackles the existing constraints in disease modeling, but also paves the way for additional investigation, providing a vital instrument for researchers and policymakers alike.

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