Solution of SIR Infection Equation Using Data Assimilation

Authors

  • Hiroshi Isshiki Institute of Mathematical Analysis, Osaka, Japan

DOI:

https://doi.org/10.24203/ajet.v9i3.6663

Keywords:

SIR Infection Equation, Data Assimilation, State Space Model, Bayes Inference

Abstract

The new coronavirus infection (COVID-19) is rampant. The most troublesome part of this infection is the time between infection and onset and the infectiveness for several days even in the not-onset state. Therefore, a considerable number of infected persons with infectivity are left unchecked. Therefore, even if the infection status is simulated by the SIR equation or the like, the true values of the infection parameters and the true number of infected persons cannot be grasped. However, it is possible to observe the infection status, and the daily number of infected people and the cumulative number of infected people are announced. These numbers are not true values, but they reflect true values. It is impossible to grasp the true value only by the SIR equation, but it will be possible to estimate the true value by combining it with the observation equation. In short, the data assimilation framework is considered to be effective. We report this effectiveness because we were able to confirm this effectiveness from the numerical results.

References

W. 0. Kermack, A. G. McKendrick, A Contribution to the Mathematical Theory of Epidemics, 1927, Proceedings of the Royal Society A (1927).

https://doi.org/10.1098/rspa.1927.0118.

H. Isshiki, M. Namiki, T. Kinoshita, R. Yano : Effective Infection Opportunity Population (EOIP) Hypothesis in Applying SIR Infection Theory, cornell arXive, arXiv:2009.01837 (2020).

https://arxiv.org/search/?query=Hiroshi+Isshiki&searchtype=all&source=header

G. Kitagawa, Use of a State Space Model in Time Series Analysis,Proceedings of the Institute of Statistical Mathematics, Vol. 67, No. 2 (2019) 181–192, in Japanese.

https://www.ism.ac.jp/editsec/toukei/pdf/67-2-181.pdf

K. Fukaya, Time series analysis by state space models and its application in ecology, Japanese Journal of Ecology, Vol. 66, No. 2 (2016), 375-389 in Japanese.

https://doi.org/10.18960/seitai.66.2_375

K. Law, A. Stuart, K. Zygalakis, Data Assimilation: A Mathematical Introduction, Springer (2015).

Downloads

Published

2021-07-01

How to Cite

Isshiki, H. (2021). Solution of SIR Infection Equation Using Data Assimilation. Asian Journal of Engineering and Technology, 9(3). https://doi.org/10.24203/ajet.v9i3.6663

Issue

Section

Articles