pubmed.ncbi.nlm.nih.gov

Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1) - PubMed

  • ️Thu Jan 01 2009

Review

Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1)

Brian J Coburn et al. BMC Med. 2009.

Abstract

Here we present a review of the literature of influenza modeling studies, and discuss how these models can provide insights into the future of the currently circulating novel strain of influenza A (H1N1), formerly known as swine flu. We discuss how the feasibility of controlling an epidemic critically depends on the value of the Basic Reproduction Number (R0). The R0 for novel influenza A (H1N1) has recently been estimated to be between 1.4 and 1.6. This value is below values of R0 estimated for the 1918-1919 pandemic strain (mean R0 approximately 2: range 1.4 to 2.8) and is comparable to R0 values estimated for seasonal strains of influenza (mean R0 1.3: range 0.9 to 2.1). By reviewing results from previous modeling studies we conclude it is theoretically possible that a pandemic of H1N1 could be contained. However it may not be feasible, even in resource-rich countries, to achieve the necessary levels of vaccination and treatment for control. As a recent modeling study has shown, a global cooperative strategy will be essential in order to control a pandemic. This strategy will require resource-rich countries to share their vaccines and antivirals with resource-constrained and resource-poor countries. We conclude our review by discussing the necessity of developing new biologically complex models. We suggest that these models should simultaneously track the transmission dynamics of multiple strains of influenza in bird, pig and human populations. Such models could be critical for identifying effective new interventions, and informing pandemic preparedness planning. Finally, we show that by modeling cross-species transmission it may be possible to predict the emergence of pandemic strains of influenza.

PubMed Disclaimer

Figures

Figure 1
Figure 1

Compartmental SIR model of disease transmission. The population is partitioned into three classes: Susceptible (S), Infectious (I), and Recovered (R). Individuals who become infected proceed from class S to class I at a rate which depends on the infectiousness of the virus and the prevalence of infection. Infectious individuals recover and move to class R, at which point they are immune to future infection. The model can be straightforwardly extended to include immunity which wanes over time.

Figure 2
Figure 2

Daily incidence for an influenza outbreak calculated using an SIR model. (a) With constant transmission rate. (b) With small seasonal variation in transmission rate. For a constant transmission rate, after an initial transient period, the system approaches an endemic level (that is, equilibrium) by damped oscillations. If a small amount of seasonal variation in transmission is introduced oscillations are sustained rather than damping out, and the system eventually tends to an annual cycle.

Figure 3
Figure 3

SIR compartmental model of disease transmission incorporating vaccination and treatment. Susceptible individuals (S) who are vaccinated proceed to class V, at which point they are considered immune. Upon treatment, infectious individuals (I) proceed to class T, at which point their infectiousness is reduced.

Figure 4
Figure 4

SEIR compartmental model of infection incorporating quarantine and isolation measures. The class E represents a latent class during which an individual who has been exposed to the pathogen is not yet infectious and is asymptomatic. Individuals who might have been exposed (S and E) are quarantined and proceed to the respective Q classes: QS and QE. When susceptible individuals in quarantine (QS) are determined not to have been infected they are returned to the susceptible class (S). Those in quarantine who develop infection (QE) are isolated and proceed to class (QI), as do infected individuals (I).

Figure 5
Figure 5

Results from a cross-species multi-strain transmission model where pigs act as 'mixing vessels'. This figure shows the severity of the epidemic that occurs when a 'super-strain' emerges into the human population from pigs, as a function of the cross-species interaction and the transmissibility/infectivity of the 'super-strain' in humans. The maximal number of infectives that could occur in any year (estimated over a 150-year time period) is shown in dark red. The contour map illustrates that the greatest outbreak occurs when the transmissibility/infectivity of the 'super-strain' is greater than 0.024 and less than 0.04; this implies 2.3 <R0 < 3.8.

Similar articles

Cited by

References

    1. Centers for Disease Control and Prevention http://www.cdc.gov/H1N1flu/
    1. Kermack WO, McKendrick AG. A contribution to the mathematical theory of epidemics. Proc Roy Soc Lond. 1927;115:700–721. doi: 10.1098/rspa.1927.0118. - DOI
    1. Dushoff J, Plotkin JB, Levin SA, Earn DJD. Dynamical resonance can account for seasonal influenza epidemics. Proc Natl Acad Sci USA. 2004;101:16915–16916. doi: 10.1073/pnas.0407293101. - DOI - PMC - PubMed
    1. Stone L, Olinky R, Huppert A. Seasonal dynamics of recurrent epidemics. Nature. 2007;446:533–536. doi: 10.1038/nature05638. - DOI - PubMed
    1. Rvachev LA. Modeling experiment of a large-scale epidemic by means of a computer. (In Russian.) Trans USSR Acad Sci Ser Mathematics and Physics. 1968;180:294–296.

Publication types

MeSH terms