Ergodic property and density function of a stochastic Kawasaki disease model

Ying He; Bo Bi; Ying He; Bo Bi

doi:10.3934/math.2025835

AIMS Mathematics

2025, Volume 10, Issue 8: 18680-18715. doi: 10.3934/math.2025835

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Research article

Ergodic property and density function of a stochastic Kawasaki disease model

Ying He ^{1
,
,},
Bo Bi ²

1.
School of Mathematics and Statistics, Northeast Petroleum University, Daqing163318, China
2.
School of Public Health, Hainan Medical University, Haikou 571199, China

Received: 30 April 2025 Revised: 29 July 2025 Accepted: 13 August 2025 Published: 18 August 2025
MSC : 37H05, 37H30, 60H10

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.
- Kawasaki disease,
- ergodicity,
- probability density,
- Fokker–Planck equation
Citation: Ying He, Bo Bi. Ergodic property and density function of a stochastic Kawasaki disease model[J]. AIMS Mathematics, 2025, 10(8): 18680-18715. doi: 10.3934/math.2025835

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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.

References

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