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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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Sensitivity analysis of peak prevalence to the efficacy and length of intervention. A. Sensitivity of relative peak prevalence of infectious individuals to reduction in the reproduction number, α. The vertical axis represents I(tm,1)/I(tm,0), where I(tm,0) and I(tm,1) represent the peak prevalence in the absence and presence of intervention, respectively. The time length of intervention, t1 is fixed at Day 50. B. Sensitivity of relative peak prevalence of infectious individuals to the time length of the intervention, t1. α is fixed at 0.90. For both panels, the lines are truncated to satisfy αR(0) ≥ 1 and t1 <tm,0 where tm,0 is the time to observe peak prevalence in the absence of intervention.
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Figure 4: Sensitivity analysis of peak prevalence to the efficacy and length of intervention. A. Sensitivity of relative peak prevalence of infectious individuals to reduction in the reproduction number, α. The vertical axis represents I(tm,1)/I(tm,0), where I(tm,0) and I(tm,1) represent the peak prevalence in the absence and presence of intervention, respectively. The time length of intervention, t1 is fixed at Day 50. B. Sensitivity of relative peak prevalence of infectious individuals to the time length of the intervention, t1. α is fixed at 0.90. For both panels, the lines are truncated to satisfy αR(0) ≥ 1 and t1 <tm,0 where tm,0 is the time to observe peak prevalence in the absence of intervention.

Mentions: Figure 4A examines the sensitivity of relative peak prevalence to α (i.e. reduction in R(0)) for assumed R(0) of 1.2, 1.4 and 1.6. Because αR(0) <1 prevents major epidemic during the early epidemic phase, possible ranges of α satisfying αR(0) ≥ 1 vary with R(0). It is worth noting that the relative reduction in peak prevalence is a nonlinear function of α. Largest reduction occurs when α lies within the range 0.90 to 0.95, rather than when α is minimum. Figure 4B examines the sensitivity of relative reduction in the peak prevalence as a function of the time length of intervention t1 (e.g. the time required to switch control policy from containment to mitigation). Again, to satisfy t1 <tm,0, possible ranges of t1 vary with R(0). The interpretation of Figure 4B is more straightforward than that of Figure 4A. Essentially, the longer the time period of intervention, the larger the potential reduction of prevalence.


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)

Sensitivity analysis of peak prevalence to the efficacy and length of intervention. A. Sensitivity of relative peak prevalence of infectious individuals to reduction in the reproduction number, α. The vertical axis represents I(tm,1)/I(tm,0), where I(tm,0) and I(tm,1) represent the peak prevalence in the absence and presence of intervention, respectively. The time length of intervention, t1 is fixed at Day 50. B. Sensitivity of relative peak prevalence of infectious individuals to the time length of the intervention, t1. α is fixed at 0.90. For both panels, the lines are truncated to satisfy αR(0) ≥ 1 and t1 <tm,0 where tm,0 is the time to observe peak prevalence in the absence of intervention.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Sensitivity analysis of peak prevalence to the efficacy and length of intervention. A. Sensitivity of relative peak prevalence of infectious individuals to reduction in the reproduction number, α. The vertical axis represents I(tm,1)/I(tm,0), where I(tm,0) and I(tm,1) represent the peak prevalence in the absence and presence of intervention, respectively. The time length of intervention, t1 is fixed at Day 50. B. Sensitivity of relative peak prevalence of infectious individuals to the time length of the intervention, t1. α is fixed at 0.90. For both panels, the lines are truncated to satisfy αR(0) ≥ 1 and t1 <tm,0 where tm,0 is the time to observe peak prevalence in the absence of intervention.
Mentions: Figure 4A examines the sensitivity of relative peak prevalence to α (i.e. reduction in R(0)) for assumed R(0) of 1.2, 1.4 and 1.6. Because αR(0) <1 prevents major epidemic during the early epidemic phase, possible ranges of α satisfying αR(0) ≥ 1 vary with R(0). It is worth noting that the relative reduction in peak prevalence is a nonlinear function of α. Largest reduction occurs when α lies within the range 0.90 to 0.95, rather than when α is minimum. Figure 4B examines the sensitivity of relative reduction in the peak prevalence as a function of the time length of intervention t1 (e.g. the time required to switch control policy from containment to mitigation). Again, to satisfy t1 <tm,0, possible ranges of t1 vary with R(0). The interpretation of Figure 4B is more straightforward than that of Figure 4A. Essentially, the longer the time period of intervention, the larger the potential reduction of prevalence.

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