Inferring the causes of the three waves of the 1918 influenza pandemic in England and Wales

Abstract

Past influenza pandemics appear to be characterized by multiple waves of incidence, but the mechanisms that account for this phenomenon remain unclear. We propose a simple epidemic model, which incorporates three factors that might contribute to the generation of multiple waves: (i) schools opening and closing, (ii) temperature changes during the outbreak, and (iii) changes in human behaviour in response to the outbreak. We fit this model to the reported influenza mortality during the 1918 pandemic in 334 UK administrative units and estimate the epidemiological parameters. We then use information criteria to evaluate how well these three factors explain the observed patterns of mortality. Our results indicate that all three factors are important but that behavioural responses had the largest effect. The parameter values that produce the best fit are biologically reasonable and yield epidemiological dynamics that match the observed data well.

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Research
Cite this article: He D, Dushoff J, Day T, Ma J,
Earn DJD. 2013 Inferring the causes of the
three waves of the 1918 influenza pandemic in
England and Wales. Proc R Soc B 280:
20131345.
http://dx.doi.org/10.1098/rspb.2013.1345
Received: 28 May 2013
Accepted: 14 June 2013
Subject Areas:
health and disease and epidemiology,
theoretical biology
Keywords:
pandemic influenza, behavioural response,
weather, iterated filtering, school closure,
Spanish flu
Author for correspondence:
Daihai He
e-mail: hedaihai@gmail.com
Electronic supplementary material is available
at http://dx.doi.org/10.1098/rspb.2013.1345 or
via http://rspb.royalsocietypublishing.org.
Inferring the causes of the three waves
of the 1918 influenza pandemic in
England and Wales
Daihai He1, Jonathan Dushoff2,3,TroyDay
5, Junling Ma6
and David J. D. Earn3,4
1
Department of Applied Mathematics, Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong
(SAR), People’s Republic of China
2
Department of Biology,
3
M.G. DeGroote Institute for Infectious Disease Research, and
4
Department of
Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
5
Department of Mathematics and Statistics, Queen’s University, Kingston, Onario, Canada
6
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada
Past influenza pandemics appear to be characterized by multiple waves of
incidence, but the mechanisms that account for this phenomenon remain
unclear. We propose a simple epidemic model, which incorporates three fac-
tors that might contribute to the generation of multiple waves: (i) schools
opening and closing, (ii) temperature changes during the outbreak, and
(iii) changes in human behaviour in response to the outbreak. We fit this
model to the reported influenza mortality during the 1918 pandemic in 334
UK administrative units and estimate the epidemiological parameters. We
then use information criteria to evaluate how well these three factors explain
the observed patterns of mortality. Our results indicate that all three factors
are important but that behavioural responses had the largest effect. The par-
ameter values that produce the best fit are biologically reasonable and yield
epidemiological dynamics that match the observed data well.
1. Introduction
The 1918 influenza pandemic was the deadliest pandemic in history. An estimated
50– 100 million people were killed worldwide, and one-third of the world’s popu-
lation is estimated to have been infected [1]. The incidence of influenza and the
resultant mortality exhibited multiple waves during the 1918 pandemic, with
many regions experiencing up to three peaks in mortality [2– 5]. For example,
figure 1 shows the pattern of mortality in the UK during the 12 month period
beginning in June 1918; three distinct waves are evident throughout the country
during this single year. The recent influenza pandemic in 2009 also displayed
multiple waves of incidence in many Northern Hemisphere countries [6–11].
Identifying the processes that give rise to multiple pandemic waves is impor-
tant for public health. This problem has consequently attracted much attention,
with several mechanisms being proposed, including viral evolution (which mod-
ifies transmissibility, immunological escape or both), environmental change
(primarily weather conditions) and behavioural change of people in response
to the pandemic [12,13]. Several statistical analyses of data from past pandemics
have identified potential causes of mortality patterns. For example, Chowell et al.
[14] found that death rates during the 1918 pandemic in the UK were 30–40%
higher in cities and towns when compared with rural areas; and Pearce et al.
[15] found that the occurrence of epidemic waves in the UK in 1918 was associ-
ated with patterns of socioeconomic status and age, potentially as a result of prior
immunity within some age groups. An analysis by Andreasen et al. [3] suggests
that immunological history might play a role. As many of these authors have
noted, however, these results are strictly correlative and a combination of statisti-
cal analysis and mechanistic mathematical modelling is required to establish a
causal relationship between such factors and the occurrence of multiple waves.
&2013 The Author(s) Published by the Royal Society. All rights reserved.