Genetic Algorithm Approaches for Parameter Estimation and Global Stability in Fuzzy Epidemic Modeling

Shirali Kadyrov; Yerimbet Aitzhanov; Nurdaulet Shynarbek

doi:10.26599/FIE.2024.9270038

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Article | Open Access

Genetic Algorithm Approaches for Parameter Estimation and Global Stability in Fuzzy Epidemic Modeling

Shirali Kadyrov^¹(), Yerimbet Aitzhanov^², Nurdaulet Shynarbek^³

1Faculty of Science and Technology, Oxus University, Tashkent 7000001, Uzbekistan

2Department of Mathematics and Natural Sciences, SDU University, Kaskelen 040900, Kazakhstan

3Department of Mathematics Education, SDU University, Kaskelen 040900, Kazakhstan

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Abstract

This paper explores the synergy between fuzzy set theory and genetic algorithms in the domain of epidemic modeling, shedding light on the broader challenges inherent in infectious diseases. In response to the evolving landscape of epidemiology, the study advocates for sophisticated modeling techniques to better understand and predict dynamic scenarios. The research thoroughly investigates the global stability of equilibrium solutions within a fuzzy epidemic model, accompanied by an inventive parameter estimation methodology. Utilizing Lyapunov functions, the paper establishes global stability outcomes for both disease-free and endemic equilibria. The novel approach, integrating continued fraction theory and a genetic algorithm, is applied to fit real-world epidemic data, offering insights crucial for public health planning and control measures. By addressing unexplored facets and bridging gaps in previous research, the paper contributes to a more comprehensive understanding of epidemic dynamics, providing a foundation for effective public health strategies in the face of infectious diseases.

Keywords

fuzzy set theory genetic algorithms epidemic modeling continued fraction parameter estimation global stability analysis Lyapunov functions Susceptible, Infected, and Recovered (SIR) fuzzy model

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Fuzzy Information and Engineering

Volume 16 Issue 2,
June 2024

Pages 144-154

DOI: 10.26599/FIE.2024.9270038

Cite this article:

Kadyrov S, Aitzhanov Y, Shynarbek N. Genetic Algorithm Approaches for Parameter Estimation and Global Stability in Fuzzy Epidemic Modeling. Fuzzy Information and Engineering, 2024, 16(2): 144-154. https://doi.org/10.26599/FIE.2024.9270038

Part of a topical collection:

Advances in Fuzzy Computational Intelligence for Biomedical Applications

Variable	Description	Value	Reference
$N (0)$	Total population on 21 February 2020	59 500 579	[10]
$S (0)$	Number of susceptible on 21 February 2020	59 500 559	[11]
$I (0)$	Number of infectious on 21 February 2020	20	[11]
$R (0)$	Number of recovered on 21 February 2020	0	[11]
$μ_{0}^{C}$	The lowest death rate due to virus	$2.2114 \times 1 0^{- 4}$	[12]
$γ_{0}$	The lowest recovery rate	$1.042 \times 1 0^{- 3}$	[12]
$μ$	Natural birth/death rate	$7.931 \times 1 0^{- 3}$	[10]
$ϑ$	Risk mitigation factor	0.999	[7]
$Ω_{m i n}$	The minimum virus load to infect	0.001	[7]

Method	MSE	Estimated parameter				Membership function value			$R_{0}$
Method	MSE	$θ$	$τ$	$π$	$Ω$	$β (Ω)$	$γ (Ω)$	$μ_{C} (Ω)$	$R_{0}$
Note: PSO: Particle Swarm Optimization; DE: Differential Evolution; NM: Nelder–Mead.
GA	$5.190 \times 10^{- 10}$	0.037	0.012	0.011	0.752	0.751	0.276	$7.851 \times 1 0^{- 4}$	2.132
PSO	$2.399 \times 1 0^{- 6}$	0.124	0.185	0.025	1	1	0.125	$9.034 \times 1 0^{- 4}$	1.693
NM	$2.399 \times 1 0^{- 6}$	0.102	0.103	0.102	0.098	0.097	0.912	$2.899 \times 1 0^{- 4}$	0.064
DE	$2.399 \times 1 0^{- 6}$	0.018	0.057	0.026	0.778	0.778	0.237	$8.159 \times 1 0^{- 4}$	2.058