Positivity and boundedness preserving numerical scheme for the stochastic epidemic model with square-root diffusion term

Yongmei Cai, Junhao Hu, Xuerong Mao

Research output: Journal PublicationArticlepeer-review

Abstract

This work concerns about the numerical solution to the stochastic epidemic model proposed by Cai et al. [2]. The typical features of the model including the positivity and boundedness of the solution and the presence of the square-root diffusion term make this an interesting and challenging work. By modifying the classical Euler-Maruyama (EM) scheme, we generate a positivity and boundedness preserving numerical scheme, which is proved to have a strong convergence to the true solution over finite time intervals. We also demonstrate that the principle of this method is applicable to a bunch of popular stochastic differential equation (SDE) models, e.g. the mean-reverting square-root process, an important financial model, and the multi-dimensional SDE SIR epidemic model.

Original languageEnglish
Pages (from-to)100-116
Number of pages17
JournalApplied Numerical Mathematics
Volume182
DOIs
Publication statusPublished - Dec 2022

Keywords

  • Positivity and boundedness preserving numerical method
  • Square-root process
  • Stochastic differential equation
  • Strong convergence

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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