A Logistic Curve in the SEIR Model and the Basic Reproduction Number of COVID-19 in Japan
DOI:
https://doi.org/10.14738/aivp.105.13261Keywords:
Variants of SARS-COV-2, SIR model, Epidemiology, Molecular biologyAbstract
The SEIR model is one of modified models of SIR, especially taken into account of exposed people. SEIR equations can be solved numerically, but it is hard to obtain analytically. Here, we propose some approximate solutions of SEIR equations, one of which is related with the logistic formula in Biology. As the second aim, the SEIR model is applied to the 7th-wave of COVID-19 in Japan. The basic reproduction number (α) in the SEIR model is estimated for the Omicron wave. We make use of data of the removed number rather than that of the infective number, because the latter seems to be ambiguous. This analysis gives α=10 with γ=1 and σ=0.5.
References
W. O. Kermack and A. G. McKendrick, ”A Contribution to the Mathematical Theory of Epidemics”, Proceedings of the Royal Society A115 (1927), 700-721(1927).
M. Li, H. L. Smith and L. Wang, “Global Dynamics of an SEIR Epidemic Model with Vertical Transmission”, SIAM J. Appl. Math. 62(1), 58-69(2001)
W. D. Murray, ”Epidemic models and the dynamics of infectious diseases”, Mathematical Biology 42, 610-650(1993).
H. Hethcote, ”The Mathematics of Infectious Diseases”, SIAM Review 42, 599-653 (2000).
M. J. Keeling and L. Danon, ”Mathematical modelling of infectious diseases ”, British Medical Bulletin 92, 33-42(2009).
S. Pathak, A. Maiti and G. P. Samanta, ”Rich dynamics of an SIR epidemic model”, Nonlinear Analysis: Modelling and Control 15, 71-81(2010).
T. Harko, F. S. N. Lobo, M. K. Mak, ”Exact analytical solutions of the SusceptibleInfected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates”, Applied Mathematics and Computation 236, 184194(2014).
J. C. Miller, ”Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes”, Infectious Disease Modelling 2, 3555(2017).
R. Sameni, ”Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID19 Coronavirus”, [arXiv:2003.11371 [q-bio.PE]](2017).
P-F. Verhulst, ”Notice sur la loi que la population poursuit dans son accroissement”, Correspondance Mathmatique et Physique 10, 113-121(1838).
T. Saito and K. Shigemoto, “A Logistic Curve in the SIR Model and Its Application to Deaths by COVID-19 in Japan”, medRxiv 10.1101/2020.06.25.20139865. European Journal of Applied Sciences 10(5), 157-160(2022).
T. Saito, “An Application of Logistic Formula to Deaths by COVID-19 in Japan”, medRxiv 10.1101/2020. 09.15.20195081.
A. Kokado and T. Saito, “A Logistic Formula and Its Application to Deaths by the Third Wave of COVID-19 in Japan”, medRxiv 10.1101/2021.01.30.21250827,
T. Saito, “Variants of SARS-COV-2 and the Death Toll”, Integ. Mol. Bio. Biotechnol. 1, 1-3(2021).
T. Saito, “Area Theorem of Infection Curves for Large Basic Reproduction Number”, European Journal of Applied Sciences 10(1), 482-486(2022).
T. Saito, “Analyses of COVID-19 in Japan by the Mathematical Model of SIR”, EJAS,10(3), 784-796(2022).
Data published from the Ministry of Health, Labor and Welfare of Japan. See for example, ”Summary of the New Coronavirus Infection”(in Japanese), https://news.yahoo.co.jp/pages/article/20200207; “Status of the Domestic New Coronavirus Infection”(in Japanese), https://toyokeizai.net/sp/visual/tko/covid19/.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Takesi Saito, Kazuyasu Shigemoto

This work is licensed under a Creative Commons Attribution 4.0 International License.