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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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The impact of summer holiday on the transmission dynamics of influenza A (H1N1-2009). A. Comparison of the observed and predicted weekly counts of the estimated number of influenza cases in Japan from week 31 to 42. Grey bars are conditionally expected values during the summer school holiday, while white bars are the conditionally expected values during autumn semester. B. Numerical solutions of the number of infectious individuals in a hypothetical population of 100,000 individuals with initial condition (S0, I0, U0) = (99998, 1, 1). Baseline scenario is compared against intervention scenario under a short-lasting intervention. For both scenarios, assumed R(0) and mean generation time are 1.14 and 3 days, respectively. In the second scenario, the transmission rate is reduced by a factor α = 0.948 due to summer school holiday from time 0 to t1 (=50 days). Although heights of peak prevalence do not greatly differ from each other, the time to observe the peak is clearly delayed in the second scenario.
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Figure 3: The impact of summer holiday on the transmission dynamics of influenza A (H1N1-2009). A. Comparison of the observed and predicted weekly counts of the estimated number of influenza cases in Japan from week 31 to 42. Grey bars are conditionally expected values during the summer school holiday, while white bars are the conditionally expected values during autumn semester. B. Numerical solutions of the number of infectious individuals in a hypothetical population of 100,000 individuals with initial condition (S0, I0, U0) = (99998, 1, 1). Baseline scenario is compared against intervention scenario under a short-lasting intervention. For both scenarios, assumed R(0) and mean generation time are 1.14 and 3 days, respectively. In the second scenario, the transmission rate is reduced by a factor α = 0.948 due to summer school holiday from time 0 to t1 (=50 days). Although heights of peak prevalence do not greatly differ from each other, the time to observe the peak is clearly delayed in the second scenario.

Mentions: Figure 3A compares observed and predicted numbers of influenza cases in Japan from week 31 to 42. Grey bars represent conditionally expected values during summer holiday, and white bars represent the expected values during autumn semester. The estimated growth rate in the absence of summer holiday, r0 is 0.048 (95% CI: 0.029, 0.066) per day. Thus, the estimated reproduction number R(0) is 1.14 (95% CI: 1.09, 1.20) which is likely an underestimate (see below).


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)

The impact of summer holiday on the transmission dynamics of influenza A (H1N1-2009). A. Comparison of the observed and predicted weekly counts of the estimated number of influenza cases in Japan from week 31 to 42. Grey bars are conditionally expected values during the summer school holiday, while white bars are the conditionally expected values during autumn semester. B. Numerical solutions of the number of infectious individuals in a hypothetical population of 100,000 individuals with initial condition (S0, I0, U0) = (99998, 1, 1). Baseline scenario is compared against intervention scenario under a short-lasting intervention. For both scenarios, assumed R(0) and mean generation time are 1.14 and 3 days, respectively. In the second scenario, the transmission rate is reduced by a factor α = 0.948 due to summer school holiday from time 0 to t1 (=50 days). Although heights of peak prevalence do not greatly differ from each other, the time to observe the peak is clearly delayed in the second scenario.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: The impact of summer holiday on the transmission dynamics of influenza A (H1N1-2009). A. Comparison of the observed and predicted weekly counts of the estimated number of influenza cases in Japan from week 31 to 42. Grey bars are conditionally expected values during the summer school holiday, while white bars are the conditionally expected values during autumn semester. B. Numerical solutions of the number of infectious individuals in a hypothetical population of 100,000 individuals with initial condition (S0, I0, U0) = (99998, 1, 1). Baseline scenario is compared against intervention scenario under a short-lasting intervention. For both scenarios, assumed R(0) and mean generation time are 1.14 and 3 days, respectively. In the second scenario, the transmission rate is reduced by a factor α = 0.948 due to summer school holiday from time 0 to t1 (=50 days). Although heights of peak prevalence do not greatly differ from each other, the time to observe the peak is clearly delayed in the second scenario.
Mentions: Figure 3A compares observed and predicted numbers of influenza cases in Japan from week 31 to 42. Grey bars represent conditionally expected values during summer holiday, and white bars represent the expected values during autumn semester. The estimated growth rate in the absence of summer holiday, r0 is 0.048 (95% CI: 0.029, 0.066) per day. Thus, the estimated reproduction number R(0) is 1.14 (95% CI: 1.09, 1.20) which is likely an underestimate (see below).

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