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Theoretical basis to measure the impact of short-lasting control of an infectious disease on the epidemic peak.

Omori R, Nishiura H - Theor Biol Med Model (2011)

Bottom Line: Empirical influenza data (H1N1-2009) in Japan are analyzed to estimate the effect of the summer holiday period in lowering and delaying the peak in 2009.Decline in peak appears to be a nonlinear function of control-associated reduction in the reproduction number.Analytical findings support a critical need to conduct population-wide serological survey as a prior requirement for estimating the time of peak.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biology, Faculty of Sciences, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan.

ABSTRACT

Background: While many pandemic preparedness plans have promoted disease control effort to lower and delay an epidemic peak, analytical methods for determining the required control effort and making statistical inferences have yet to be sought. As a first step to address this issue, we present a theoretical basis on which to assess the impact of an early intervention on the epidemic peak, employing a simple epidemic model.

Methods: We focus on estimating the impact of an early control effort (e.g. unsuccessful containment), assuming that the transmission rate abruptly increases when control is discontinued. We provide analytical expressions for magnitude and time of the epidemic peak, employing approximate logistic and logarithmic-form solutions for the latter. Empirical influenza data (H1N1-2009) in Japan are analyzed to estimate the effect of the summer holiday period in lowering and delaying the peak in 2009.

Results: Our model estimates that the epidemic peak of the 2009 pandemic was delayed for 21 days due to summer holiday. Decline in peak appears to be a nonlinear function of control-associated reduction in the reproduction number. Peak delay is shown to critically depend on the fraction of initially immune individuals.

Conclusions: The proposed modeling approaches offer methodological avenues to assess empirical data and to objectively estimate required control effort to lower and delay an epidemic peak. Analytical findings support a critical need to conduct population-wide serological survey as a prior requirement for estimating the time of peak.

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Related in: MedlinePlus

Estimated weekly incidence of influenza cases in Japan from 2009-10. The estimates are based on nationwide sentinel surveillance, covering the period from week 31 in 2009 to week 13 in 2010. The estimate follows an extrapolation of the notified number of cases from a total of 4800 randomly sampled sentinel hospitals to the total number of medical facilities in Japan. The case refers to influenza-like illness cases with medical attendance, possibly involving other diseases, but with influenza A (H1N1-2009) dominant among the isolated influenza viruses during the period of interest. Period A corresponds to summer school holiday, followed by autumn semester (period B). Period C covers winter holiday and period D corresponds to winter semester.
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Figure 2: Estimated weekly incidence of influenza cases in Japan from 2009-10. The estimates are based on nationwide sentinel surveillance, covering the period from week 31 in 2009 to week 13 in 2010. The estimate follows an extrapolation of the notified number of cases from a total of 4800 randomly sampled sentinel hospitals to the total number of medical facilities in Japan. The case refers to influenza-like illness cases with medical attendance, possibly involving other diseases, but with influenza A (H1N1-2009) dominant among the isolated influenza viruses during the period of interest. Period A corresponds to summer school holiday, followed by autumn semester (period B). Period C covers winter holiday and period D corresponds to winter semester.

Mentions: Here, we apply the above described theory to empirical influenza A (H1N1-2009) data. Figure 2 shows the estimated number of influenza cases based on national sentinel surveillance in Japan from week 31 (week ending 2 August) 2009 to week 13 (week ending 28 March) 2010. The estimates follow an extrapolation of the notified number of cases from a total of 4800 randomly sampled sentinel hospitals to the actual total number of medical facilities in Japan. The cases represent patients who sought medical attendance and who have met the following criteria, (a) acute course of illness (sudden onset), (b) fever greater than 38.0°C, (c) cough, sputum or breathlessness (symptoms of upper respiratory tract infection) and (d) general fatigue, or who were strongly suspected of the disease undertaking laboratory diagnosis (e.g. rapid diagnostic testing). Although the estimates of sentinel surveillance data involve various epidemiological biases and errors, we ignore these issues in the present study. Prior to week 31, the number of cases was small and the dynamics in the early stochastic phase have been examined elsewhere [17]. We arbitrarily assume that the major epidemic starts in week 31.


Theoretical basis to measure the impact of short-lasting control of an infectious disease on the epidemic peak.

Omori R, Nishiura H - Theor Biol Med Model (2011)

Estimated weekly incidence of influenza cases in Japan from 2009-10. The estimates are based on nationwide sentinel surveillance, covering the period from week 31 in 2009 to week 13 in 2010. The estimate follows an extrapolation of the notified number of cases from a total of 4800 randomly sampled sentinel hospitals to the total number of medical facilities in Japan. The case refers to influenza-like illness cases with medical attendance, possibly involving other diseases, but with influenza A (H1N1-2009) dominant among the isolated influenza viruses during the period of interest. Period A corresponds to summer school holiday, followed by autumn semester (period B). Period C covers winter holiday and period D corresponds to winter semester.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3040699&req=5

Figure 2: Estimated weekly incidence of influenza cases in Japan from 2009-10. The estimates are based on nationwide sentinel surveillance, covering the period from week 31 in 2009 to week 13 in 2010. The estimate follows an extrapolation of the notified number of cases from a total of 4800 randomly sampled sentinel hospitals to the total number of medical facilities in Japan. The case refers to influenza-like illness cases with medical attendance, possibly involving other diseases, but with influenza A (H1N1-2009) dominant among the isolated influenza viruses during the period of interest. Period A corresponds to summer school holiday, followed by autumn semester (period B). Period C covers winter holiday and period D corresponds to winter semester.
Mentions: Here, we apply the above described theory to empirical influenza A (H1N1-2009) data. Figure 2 shows the estimated number of influenza cases based on national sentinel surveillance in Japan from week 31 (week ending 2 August) 2009 to week 13 (week ending 28 March) 2010. The estimates follow an extrapolation of the notified number of cases from a total of 4800 randomly sampled sentinel hospitals to the actual total number of medical facilities in Japan. The cases represent patients who sought medical attendance and who have met the following criteria, (a) acute course of illness (sudden onset), (b) fever greater than 38.0°C, (c) cough, sputum or breathlessness (symptoms of upper respiratory tract infection) and (d) general fatigue, or who were strongly suspected of the disease undertaking laboratory diagnosis (e.g. rapid diagnostic testing). Although the estimates of sentinel surveillance data involve various epidemiological biases and errors, we ignore these issues in the present study. Prior to week 31, the number of cases was small and the dynamics in the early stochastic phase have been examined elsewhere [17]. We arbitrarily assume that the major epidemic starts in week 31.

Bottom Line: Empirical influenza data (H1N1-2009) in Japan are analyzed to estimate the effect of the summer holiday period in lowering and delaying the peak in 2009.Decline in peak appears to be a nonlinear function of control-associated reduction in the reproduction number.Analytical findings support a critical need to conduct population-wide serological survey as a prior requirement for estimating the time of peak.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biology, Faculty of Sciences, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan.

ABSTRACT

Background: While many pandemic preparedness plans have promoted disease control effort to lower and delay an epidemic peak, analytical methods for determining the required control effort and making statistical inferences have yet to be sought. As a first step to address this issue, we present a theoretical basis on which to assess the impact of an early intervention on the epidemic peak, employing a simple epidemic model.

Methods: We focus on estimating the impact of an early control effort (e.g. unsuccessful containment), assuming that the transmission rate abruptly increases when control is discontinued. We provide analytical expressions for magnitude and time of the epidemic peak, employing approximate logistic and logarithmic-form solutions for the latter. Empirical influenza data (H1N1-2009) in Japan are analyzed to estimate the effect of the summer holiday period in lowering and delaying the peak in 2009.

Results: Our model estimates that the epidemic peak of the 2009 pandemic was delayed for 21 days due to summer holiday. Decline in peak appears to be a nonlinear function of control-associated reduction in the reproduction number. Peak delay is shown to critically depend on the fraction of initially immune individuals.

Conclusions: The proposed modeling approaches offer methodological avenues to assess empirical data and to objectively estimate required control effort to lower and delay an epidemic peak. Analytical findings support a critical need to conduct population-wide serological survey as a prior requirement for estimating the time of peak.

Show MeSH
Related in: MedlinePlus