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

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. ISSN 0168-9274

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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.

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