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Research Article | Open Access

Ergodic property and density function of a stochastic Kawasaki disease model

Ying He1( ), Bo Bi2
School of Mathematics and Statistics, Northeast Petroleum University, Daqing163318, China
School of Public Health, Hainan Medical University, Haikou 571199, China
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Abstract

In this paper, a stochastic Kawasaki disease model was investigated. First, it was theoretically proved that the solution of the stochastic model is positive and global, as well as the existence of an ergodic stationary distribution. Subsequently, we derived the exact expression of the probability density function around a quasi-equilibrium point through the four-dimensional Fokker-Planck equation. Finally, some numerical simulations were introduced to validate the theoretical findings.

Keywords

Kawasaki diseaseergodicityprobability densityFokker–Planck equation
CLC number: 37H05, 37H30, 60H10

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AIMS Mathematics
Volume 10 Issue 8,
August 2025
Pages 18680-18715
DOI: 10.3934/math.2025835

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Cite this article:
He Y, Bi B. Ergodic property and density function of a stochastic Kawasaki disease model. AIMS Mathematics, 2025, 10(8): 18680-18715. https://doi.org/10.3934/math.2025835

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Received: 30 April 2025
Revised: 29 July 2025
Accepted: 13 August 2025
Published: 15 August 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)