Stationary distribution of reaction-diffusion dengue fever model with mean-reverting white noise

Kangkang Chang; Kangkang Chang

doi:10.3934/math.20261141

AIMS Mathematics

2026, Volume 11, Issue 9: 28665-28685. doi: 10.3934/math.20261141

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Research article

Stationary distribution of reaction-diffusion dengue fever model with mean-reverting white noise

Kangkang Chang ^,

School of Mathematics and Statistics, Xinxiang University, Xinxiang, 453003, China

Received: 17 June 2026 Revised: 22 August 2026 Accepted: 27 August 2026 Published: 07 September 2026
MSC : 35Q92, 37H05, 92B05

In our previous study, we explored the stationary distribution of dengue fever models with Brownian motion, to investigate the differences between Brownian motion and the mean-reverting white noise. In this paper, we establish a dengue model with the mean-reverting white noise. First, we utilize the stochastic comparison theorem to prove solution boundedness, and construct a Lyapunov function to demonstrate the existence of the solution. Following this, sufficient conditions guaranteeing the stationary distribution of solutions are presented. To further validate the analytical derivations, numerical simulations are presented. Under the premise that the parameters remain constant, for case 1, compared with Brownian motion, the values of the system are more concentrated, and the histograms tend to be a normal distribution. For case 2, it was found that compared with Brownian motion, the model with the mean-reverting white noise shows an exponential decrease in the number of the infected population over time, and the distribution of the suspected population is closer to the normal distribution.
- dengue fever model,
- mean-reverting white noise,
- stationary distribution,
- reaction-diffusion
Citation: Kangkang Chang. Stationary distribution of reaction-diffusion dengue fever model with mean-reverting white noise[J]. AIMS Mathematics, 2026, 11(9): 28665-28685. doi: 10.3934/math.20261141

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Abstract

In our previous study, we explored the stationary distribution of dengue fever models with Brownian motion, to investigate the differences between Brownian motion and the mean-reverting white noise. In this paper, we establish a dengue model with the mean-reverting white noise. First, we utilize the stochastic comparison theorem to prove solution boundedness, and construct a Lyapunov function to demonstrate the existence of the solution. Following this, sufficient conditions guaranteeing the stationary distribution of solutions are presented. To further validate the analytical derivations, numerical simulations are presented. Under the premise that the parameters remain constant, for case 1, compared with Brownian motion, the values of the system are more concentrated, and the histograms tend to be a normal distribution. For case 2, it was found that compared with Brownian motion, the model with the mean-reverting white noise shows an exponential decrease in the number of the infected population over time, and the distribution of the suspected population is closer to the normal distribution.

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