Mathematical Theories on Corona Pandemic (COVID-19)

The coronavirus disease 2019 (COVID-19) is an ongoing pandemic all over the world, and the number of infected people increases rapidly daily. This grim situation motivates us to investigate the spreading process of COVID-19. As the fundamental step to understand the spreading process, we utilize various mathematical models to simulate and predict the trend of the epidemic. In this webpage, the works of LSR (Prof. Martin Buss) and ITR (Prof. Sandra Hirche) regarding the COVID-19 are presented, as well as the related works on diffusion processes on social networks and distributed topology design. All data in our website are from Worldometer

 

Contact person: Fangzhou Liu.

Content

  • Related Publications

  • Mathematical Models

Related Publications

  • F. Liu and M. Buss. Optimal control for heterogeneous node-based information epidemics over social networks. IEEE Transactions on Control of Network Systems, In press, 2020. [more...][Bibtex][fulltext(DOI)]
  • F. Liu, S. CUI, X. Li, and M. Buss. Node-based SIRS model on heterogeneous networks: Analysis and control. In the Proceedings of IFAC World Congress, accepted, 2020. [more...][Bibtex]
  • D. Xue; S. Hirche; M. Cao: Opinion Behavior Analysis in Social Networks under the Influence of Coopetitive Media. IEEE Transactions on Network Science and Engineering, In press, 2019. [more...][Bibtex][fulltext(DOI)]
  • F. Liu, D. Xue, S. Hirche, and M. Buss. Polarizability, consensusability and neutralizability of opinion dynamics on coopetitive networks. IEEE Transactions on Automatic Control, 64(8):3339–3346, 2019. [more...][Bibtex][fulltext(DOI)]
  • F. Liu, Z. Zhang, and M. Buss. Robust optimal control of deterministic information epidemics with noisy transition rates. Physica A: Statistical Mechanics and its Applications, 517:577–587, 2019. [more...][Bibtex][fulltext(DOI)]
  • F. Liu and M. Buss. Node-based SIRS model on heterogeneous networks: Analysis and control. In American Control Conference (ACC), 2016, pp. 2852-2857. [more...][Bibtex][fulltext(DOI)]
  • F. Liu and M. Buss. Optimal control for information diffusion over heterogeneous networks. In 55th IEEE Conference on Decision and Control (CDC), 2016, pp. 141-146. [more...][Bibtex][fulltext(DOI)]
  • F. Deroo, M. Meinel, M. Ulbrich, and S. Hirche: Distributed stability tests for large-scale systems with limited model information. IEEE Transactions on Control of Network Systems, 3(3), 298-309, 2015. [more...][Bibtex][fulltext(DOI)]
  • D. Xue and S. Hirche: Distributed Topology Manipulation to Control Epidemic Spreading over Networks. IEEE Transactions on Signal Processing, 67 (5):1163-1174, 2018. [more...][Bibtex][fulltext(DOI)]
  • A. Gusrialdi, Z. Qu, and S. Hirche: Distributed Link Removal Using Local Estimation of Network Topology. IEEE Transactions on Network Science and Engineering, 6 (3):280-292, 2018. [more...][Bibtex][fulltext(DOI)]
  • D. Xue, A. Gusrialdi, and S. Hirche: A Distributed Strategy for Near-Optimal Network Topology Design. 21st International Symposium on Mathematical Theory of Networked and Systems (MTNS 2014), 2014. [more...][Bibtex][fulltext(DOI)]
  • D. Xue, A. Gusrialdi, and S. Hirche: Robust Distributed Control Design for Interconnected Systems under Topology Uncertainty. American Control Conference (ACC), 2013. [more...][Bibtex][fulltext(DOI)]

Power-law with an exponential cutoff

 

Inspired by Anna L. Ziff and Robert M. Ziff 's research, we use the power-law model with an exponential cutoff to simulate and predict the trend of the daily new confirmed cases in several countries. The specfic method and further comparison with classic SIR model are given in our note, "A Power-Law Model for the Spread of COVID-19".

 

A power law with an exponential cutoff is simply a power law multiplied by an exponential function: n(t)=Ktxe-t/t0, where K, and t0 are constant parameters, and all of them are positive. tx represents the power-law term and e-t/t0 is the exponential part. In this evolution, in the early stage, the power law behavior dominates the growth, and the exponential decay term e-t/t0 eventually overwhelms the power-law section at very large values of tPlease note that this model is used to predict the pandemic in the early stage.

The simulation results on above model are illustrated below.

Daily new cases in Germany

The data of the daily new cases in Germany from Mar 1 to Jan 10, 2021 are used in the simulation. By using the power law model, we obtain the parameters for the daily new cases in Germany are: K=0.04, x=4.81 and t0=6.30  .

 

Daily new cases in Italy

The data of the daily new cases in Italy from Feb 22 to Jan 10, 2021 are used in the simulation. By using the power law model, we obtain the parameters for the daily new cases in Italy are:K=0.43, x=3.61 and t0=9.97  . 

 

Daily new cases in USA

The data of the daily new cases in USA from Feb 16 to Jan 10, 2021 are used in the simulation. By using the power law model, we obtain the parameters for the daily new cases in USA are: K=396.25, x=1.12 and t0=169.97.

 

Daily new cases in South Korea

The data of the daily new cases in South Korea are from Feb 19 to Jan 10, 2021. The parameters in the power-law with an exponential cutoff model are: K=2.18, x=4.06 and t0=2.66.

 

Daily new cases in China

The data of the daily new cases used in the simulation are from Jan 23 to Jan 10, 2021 in China. Additionally, the parameters of the power law model are: K=23.77, x=3.17 and t0=4.10.

 

Daily new cases in Spain

The data for Spain are from Mar 06 to Jan 10, 2021, and the values of the parameters K, x, and t0 are 12.27, 2.70 and 10.25, respectively.   

 

Daily new cases in France

The data we utilized to simulate and predict the trend of COVID in France are from Feb 27 to Jan 10, 2021. And 0.04, 5.08 and 5.49 are the values of the three parameters (K, x, and t0 ) in the power-law with an exponential cutoff model.      

 

Daily new cases in Japan

We adopt the data from Feb 16 to Jan 10, 2021 about the COVID-19 in Japan, and the parameters for the model are K=0.893212036, x=1.21 and t0=3257.18, respectively.  

 

Daily new cases in Sweden

The simulation results about Sweden are shown below, where the data are from Feb 27 to Jan 10, 2021. In addition, the parameters are: K=0.26, x=2.31 and t0=34.99.  

 

Daily new cases in the World

To study the epidemic in the whole world, we adopt the daily new confirmed infection cases in the whole world  from Feb 22 to Jan 10, 2021 (second outbreak). The parameters in the model are K=313.01, x=1.33 and t0=852.73, respectively. 

 

 

 

Disclaimer: the models are highly dynamic and change every day.