Estimation of the Basic Reproduction Number of Novel Influenza A (H1N1) pdm09 in Elementary Schools Using the SIR Model

Daisuke Furushima1, *, Shoko Kawano2, Yuko Ohno1, Masayuki Kakehashi2
1 Department of Mathematical Health Science, Osaka University Graduate School of Medicine, Japan
2 Institute of Biomedical & Health Sciences, Hiroshima University, Japan

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© 2017 Furushima et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this authors at the Department of Mathematical Health Science, Osaka University Graduate School of Medicine, Osaka, Japan; Tel: +81-6-6879-2526; Fax: +81-6-68-79-2526; E-mail:



The novel influenza A (H1N1) pdm09 (A/H1N1pdm) pandemic of 2009-2010 had a great impact on society.


We analyzed data from the absentee survey, conducted in elementary schools of Oita City, to evaluate the A/H1N1pdm pandemic and to estimate the basic reproductive number (R0 ) of this novel strain.


We summarized the overall absentee data and calculated the cumulative infection rate. Then, we classified the data into 3 groups according to school size: small (<300 students), medium (300–600 students), and large (>600 students). Last, we estimated the R0 value by using the Susceptible-Infected-Recovered (SIR) mathematical model.


Data from 60 schools and 27,403 students were analyzed. The overall cumulative infection rate was 44.4%. There were no significant differences among the grades, but the cumulative infection rate increased as the school size increased, being 37.7%, 44.4%, and 46.6% in the small, medium, and large school groups, respectively. The optimal R0 value was 1.33, comparable with that previously reported. The data from the absentee survey were reliable, with no missing values. Hence, the R0 derived from the SIR model closely reflected the observed R0 . The findings support previous reports that school children are most susceptible to A/H1N1pdm virus infection and suggest that the scale of an outbreak is associated with the size of the school.


Our results provide further information about the A/H1N1pdm pandemic. We propose that an absentee survey should be implemented in the early stages of an epidemic, to prevent a pandemic.

Keywords: A/H1N1pdm, Absentee survey, Basic reproductive number, Elementary school student, School health, SIR model.