A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification
-
Yu Chen
,
Yu Jiang
and
Keji Liu
Abstract
In this paper, we propose a novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China. One typical feature of this epidemic is that it can spread in the latent period, which can therefore be described by time delay process in the differential equations. The accumulated numbers of classified populations are employed as variables, which is consistent with the official data and facilitates the parameter identification. The numerical methods for the prediction of the outbreak of 2019-nCoV and parameter identification are provided, and the numerical results show that the novel dynamic system can well predict the outbreak trend so far. Based on the numerical simulations, we suggest that the transmission of individuals should be greatly controlled with high isolation rate by the government.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11971121
Funding source: Science and Technology Commission of Shanghai Municipality
Award Identifier / Grant number: 19QA1403400
Funding statement: This work was supported in part by National Science Foundation of China (NSFC: No. 11971121) and the Science and Technology Commission of Shanghai Municipality under the “Shanghai Rising-Star Program” No. 19QA1403400.
Acknowledgements
The authors thank for the helpful discussions with Dr. Yue Yan, Dr. Boxi Xu, Ms. Xinyue Luo and Mrs. Jingyun Bian in Shanghai University of Finance and Economics. Stay strong Wuhan!
References
[1] B. Cantó, C. Coll and E. Sánchez, Estimation of parameters in a structured SIR model, Adv. Difference Equ. 2017 (2017), Paper No. 33. 10.1186/s13662-017-1078-5Search in Google Scholar
[2] S. Kabanikhin, Definitions and examples of inverse and ill-posed problems, J. Inverse Ill-Posed Probl. 16 (2008), no. 4, Article ID 317357. 10.1515/JIIP.2008.019Search in Google Scholar
[3] S. Kabanikhin and O. Krivorotko, Identification of biological models described by systems of nonlinear differential equations, J. Inverse Ill-Posed Probl. 23 (2015), no. 5, 519–527. 10.1515/jiip-2015-0072Search in Google Scholar
[4] S. Kabanikhin, O. Krivorotko and V. Kashtanova, A combined numerical algorithm for reconstructing the mathematical model for tuberculosis transmission with control programs, J. Inverse Ill-Posed Probl. 26 (2018), no. 5, Article ID 121131. 10.1515/jiip-2017-0019Search in Google Scholar
[5] S. Kabanikhin, O. Krivorotko, A. Takuadina, D. Andornaya and S. Zhang, Geo-information system of spread of tuberculosis based on inversion and prediction, preprint (2020), https://arxiv.org/abs/2002.02367. 10.1515/jiip-2020-0022Search in Google Scholar
[6] J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Springer, New York, 2005. 10.1007/b138659Search in Google Scholar
[7] B. Kaltenbacher, A. Neubauer and O. Scherzer, Iterative Regularization Methods for Nonlinear Ill-posed Problems, Radon Ser. Comput. Appl. Math. 6, Walter de Gruyter, Berlin, 2008. 10.1515/9783110208276Search in Google Scholar
[8] C. Liu, G. Ding, J. Gong, L. Wang, K. Cheng and D. Zhang, Studies on mathematical models for SARS outbreak prediction and warning, Chinese Sci. Bull. 49 (2004), no. 21, 2245–2251. Search in Google Scholar
[9] E. Ma, Y. Zhou, W. Wang and Z. Jin, Mathematical Models and Dynamics of Infectious Diseases, China Science, Beijing, 2004. Search in Google Scholar
[10] Y. Yan, Y. Chen, K. Liu, X. Luo, B. Xu and Y. Jiang and J. CHENG, Modeling and prediction for the trend of outbreak of 2019-nCoV based on a time-delay dynamic system (in Chinese), Sci. Sin. Math. 50 (2020), no. 3, 1–8. 10.1360/SSM-2020-0026Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Image reconstruction method for exterior circular cone-beam CT based on weighted directional total variation in cylindrical coordinates
- Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in ℝn
- Lipschitz stability for a semi-linear inverse stochastic transport problem
- Inverse problem for elastic body with thin elastic inclusion
- Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source
- Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions
- A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification
- A linear regularization method for a parameter identification problem in heat equation
- A study of frozen iteratively regularized Gauss–Newton algorithm for nonlinear ill-posed problems under generalized normal solvability condition
- Numerics of acoustical 2D tomography based on the conservation laws
- Identification of the diffusion coefficient in a time fractional diffusion equation
- Linear least squares method in nonlinear parametric inverse problems
Articles in the same Issue
- Frontmatter
- Image reconstruction method for exterior circular cone-beam CT based on weighted directional total variation in cylindrical coordinates
- Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in ℝn
- Lipschitz stability for a semi-linear inverse stochastic transport problem
- Inverse problem for elastic body with thin elastic inclusion
- Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source
- Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions
- A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification
- A linear regularization method for a parameter identification problem in heat equation
- A study of frozen iteratively regularized Gauss–Newton algorithm for nonlinear ill-posed problems under generalized normal solvability condition
- Numerics of acoustical 2D tomography based on the conservation laws
- Identification of the diffusion coefficient in a time fractional diffusion equation
- Linear least squares method in nonlinear parametric inverse problems
