Limits...
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.

Show MeSH

Related in: MedlinePlus

Assessing approximation of time to observe epidemic peak. A. Comparison of epidemic curves in the absence of intervention between explicit numerical and approximate solutions. The population size is assumed to be 100,000 with initial condition (S0, I0, U0) = (99998, 1, 1). The generation time is exponentially distributed with mean 1/γ = 3 days. B. Comparison of estimated delay in epidemic peak (imposed by a short-lasting intervention) between explicit numerical and approximate solutions. The assumed length of intervention t1 is 50 days.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3040699&req=5

Figure 5: Assessing approximation of time to observe epidemic peak. A. Comparison of epidemic curves in the absence of intervention between explicit numerical and approximate solutions. The population size is assumed to be 100,000 with initial condition (S0, I0, U0) = (99998, 1, 1). The generation time is exponentially distributed with mean 1/γ = 3 days. B. Comparison of estimated delay in epidemic peak (imposed by a short-lasting intervention) between explicit numerical and approximate solutions. The assumed length of intervention t1 is 50 days.

Mentions: Figure 5A compares epidemic curves of infectious individuals in the absence of intervention between explicit numerical and approximate solutions (i.e. solutions to (1) and (19), respectively). The height of epidemic peak is approximated well for smaller R(0), reflecting the fact that Taylor series expansion is a good approximation to the exponential function. The relationship between R(0) and approximation of epidemic peak height is also analytically expressed. Inserting (20) into (19), the approximate peak prevalence is


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)

Assessing approximation of time to observe epidemic peak. A. Comparison of epidemic curves in the absence of intervention between explicit numerical and approximate solutions. The population size is assumed to be 100,000 with initial condition (S0, I0, U0) = (99998, 1, 1). The generation time is exponentially distributed with mean 1/γ = 3 days. B. Comparison of estimated delay in epidemic peak (imposed by a short-lasting intervention) between explicit numerical and approximate solutions. The assumed length of intervention t1 is 50 days.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Assessing approximation of time to observe epidemic peak. A. Comparison of epidemic curves in the absence of intervention between explicit numerical and approximate solutions. The population size is assumed to be 100,000 with initial condition (S0, I0, U0) = (99998, 1, 1). The generation time is exponentially distributed with mean 1/γ = 3 days. B. Comparison of estimated delay in epidemic peak (imposed by a short-lasting intervention) between explicit numerical and approximate solutions. The assumed length of intervention t1 is 50 days.
Mentions: Figure 5A compares epidemic curves of infectious individuals in the absence of intervention between explicit numerical and approximate solutions (i.e. solutions to (1) and (19), respectively). The height of epidemic peak is approximated well for smaller R(0), reflecting the fact that Taylor series expansion is a good approximation to the exponential function. The relationship between R(0) and approximation of epidemic peak height is also analytically expressed. Inserting (20) into (19), the approximate peak prevalence is

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