The Mathematical Modelling of Influenza Epidemics

Spicer, C. C.

doi:10.1093/oxfordjournals.bmb.a071536

Cited by 37 publications

(26 citation statements)

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“…An earlier study proposed estimates higher than ours (range 1.4-2.6) for several consecutive influenza seasons in England and Wales [15,16], however the exact quantity measured in this work remains controversial [14,31]. A particularly high R p estimate (R p > 2.0) has also been reported for the 1951 influenza epidemic in England and Canada, however, this epidemic was associated with unusually high mortality and transmissibility locally [19,22].…”

Section: Discussioncontrasting

confidence: 45%

“…Past studies have estimated the reproduction number of individual influenza seasons, in particular for pandemics [11][12][13][14][15][16][17][18][19]. However, no study has yet reported estimates of the reproduction number for several countries and consecutive influenza seasons in the interpandemic period, where a fraction of the population is immune due to previous influenza exposure or vaccination.…”

Section: Introductionmentioning

confidence: 99%

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Seasonal influenza in the United States, France, and Australia: transmission and prospects for control

2007

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SUMMARYRecurrent epidemics of influenza are observed seasonally around the world with considerable health and economic consequences. A key quantity for the control of infectious diseases is the reproduction number, which measures the transmissibility of a pathogen and determines the magnitude of public health interventions necessary to control epidemics. Here we applied a simple epidemic model to weekly indicators of influenza mortality to estimate the reproduction numbers of seasonal influenza epidemics spanning three decades in the United States, France, and Australia. We found similar distributions of reproduction number estimates in the three countries, with mean value 1.3 and important year-to-year variability (range 0.9-2.1). Estimates derived from two different mortality indicators (pneumonia and influenza excess deaths and influenza-specific deaths) were in close agreement for the United States (correlation = 0.61, P < 0.001) and France (correlation = 0.79, P < 0.001), but not Australia. Interestingly, high prevalence of A/H3N2 influenza viruses was associated with high transmission seasons (P = 0.006), while B viruses were more prevalent in low transmission seasons (P = 0.004). The current vaccination strategy targeted at people at highest risk of severe disease outcome is suboptimal because current vaccines are poorly immunogenic in these population groups. Our results suggest that interrupting transmission of seasonal influenza would require a relatively high vaccination coverage (> 60 %) in healthy individuals who respond well to vaccine, in addition to periodic re-vaccination due to evolving viral antigens and waning population immunity.

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Section: Discussioncontrasting

confidence: 45%

Section: Introductionmentioning

confidence: 99%

Seasonal influenza in the United States, France, and Australia: transmission and prospects for control

2007

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“…Over the last century, some discrete-time epidemic models have been formulated to analyze the spread and control of infectious diseases [1,2,4,[9][10][11][13][14][15]19,21,24,30,31]. In [4], a deterministic discrete-time epidemic model is constructed, under certain assumptions, the stabilities of equilibria for the model are studied and the threshold conditions are obtained.…”

Section: Introductionmentioning

confidence: 99%

“…In [4], a deterministic discrete-time epidemic model is constructed, under certain assumptions, the stabilities of equilibria for the model are studied and the threshold conditions are obtained. In [24], a discrete-time epidemic model is developed to predict the prevalence of the influenza in England and Welsh. Allen [2] formulated three types of discretetime model: SIS model with constant population size, SIS model with variable population size, and SIR model with constant population size.…”

Section: Introductionmentioning

confidence: 99%

Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination

Zhang

2015

Applied Mathematics and Computation

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“…1,2 Several investigations have shown that many economic, physical and biological phenomena are best represented via difference equations. One reason for formulating discrete epidemic models is that data is collected at discrete time intervals -a day, a week, a month or a year -and it may be easier to compare experimental data with the predictions of a model if these predictions are given in discrete form.…”

Section: Introductionmentioning

confidence: 99%

Discrete Time Si and Sis Epidemic Models With Vertical Transmission

Zhang

Jin

2009

J. Biol. Syst.

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Discrete time SI and SIS epidemic models with vertical transmission are presented in this paper. With regard to the SI model with constant or variable population size, we introduce an epidemic threshold parameter, the basic reproductive number R 0 , for predicting disease dynamics. R 0 > 1 implies that the disease tends to an endemic equilibrium, while R 0 < 1 implies disease extinction. On the other hand, for the SIS epidemic model with another form force of infection, the basic reproduction number R 0 determines the persistence or extinction of the disease. In the same time, we also explore the relationship between the demographic equation and the epidemic process. In particular, we show that the epidemic model can exhibit bistability (alternative stable equilibria) over a wide range of parameter values.

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The Mathematical Modelling of Influenza Epidemics

Cited by 37 publications

References 0 publications

Seasonal influenza in the United States, France, and Australia: transmission and prospects for control

Seasonal influenza in the United States, France, and Australia: transmission and prospects for control

Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination

Discrete Time Si and Sis Epidemic Models With Vertical Transmission

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