TY - JOUR
T1 - Positivity and boundedness preserving numerical scheme for the stochastic epidemic model with square-root diffusion term
AU - Cai, Yongmei
AU - Hu, Junhao
AU - Mao, Xuerong
N1 - Funding Information:
The authors would like to thank the editors and the referees for their professional comments and suggestions. Y. Cai acknowledges the financial support from Zhejiang Natural Science Foundation ( LQ22A010009 ). J. Hu would like to thank the National Natural Science Foundation of China ( 61876192 ), the Fundamental Research Funds for the Central Universities ( CZT20020 ), and Academic Team in Universities ( KTZ20051 ) for their financial support. X. Mao would like to thank the Royal Society ( WM160014 , Royal Society Wolfson Research Merit Award), the Royal Society of Edinburgh ( RSE1832 ), Shanghai Administration of Foreign Experts Affairs ( 21WZ2503700 , the Foreign Expert Program) for their financial support.
Publisher Copyright:
© 2022 IMACS
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
KW - Positivity and boundedness preserving numerical method
KW - Square-root process
KW - Stochastic differential equation
KW - Strong convergence
UR - http://www.scopus.com/inward/record.url?scp=85135913779&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2022.07.019
DO - 10.1016/j.apnum.2022.07.019
M3 - Article
AN - SCOPUS:85135913779
SN - 0168-9274
VL - 182
SP - 100
EP - 116
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -