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

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Cai, Yongmei and Hu, Junhao and Mao, Xuerong (2022) Positivity and boundedness preserving numerical scheme for the stochastic epidemic model with square-root diffusion term. Applied Numerical Mathematics, 182. pp. 100-116. ISSN 0168-9274 (https://doi.org/10.1016/j.apnum.2022.07.019)

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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.

ORCID iDs

Cai, Yongmei, Hu, Junhao and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
CORE (COnnecting REpositories)