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Real-time forecast of multiphase outbreak.

Hsieh YH, Cheng YS - Emerging Infect. Dis. (2006)

Bottom Line: The 3 estimated turning points are March 25, April 27, and May 24.The estimated case number during the first phase of the outbreak between February 23 and April 26 is 140.53 (95% confidence interval [CI] 115.88-165.17) if we use the data from February 23 to April 4; and 249 (95% CI: 246.67-251.25) at the end of the second phase on June 12 if we use the data from April 28 to June 4.The second phase can be detected by using case data just 3 days past the beginning of the phase, while the first and third turning points can be identified only approximately 10 days afterwards.

View Article: PubMed Central - PubMed

Affiliation: National Chung Hsing University, Taichung, Taiwan. hsieh@amath.nchu.edu.tw

ABSTRACT
We used a single equation with discrete phases to fit the daily cumulative case data from the 2003 severe acute respiratory syndrome outbreak in Toronto. This model enabled us to estimate turning points and case numbers during the 2 phases of this outbreak. The 3 estimated turning points are March 25, April 27, and May 24. The estimated case number during the first phase of the outbreak between February 23 and April 26 is 140.53 (95% confidence interval [CI] 115.88-165.17) if we use the data from February 23 to April 4; and 249 (95% CI: 246.67-251.25) at the end of the second phase on June 12 if we use the data from April 28 to June 4. The second phase can be detected by using case data just 3 days past the beginning of the phase, while the first and third turning points can be identified only approximately 10 days afterwards. Our modeling procedure provides insights into ongoing outbreaks that may facilitate real-time public health responses.

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Epidemic curves for the second phase of severe acute respiratory syndrome outbreak in Toronto area using multistage Richards model and cases, April 28–June 4, 2003.
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Figure 4: Epidemic curves for the second phase of severe acute respiratory syndrome outbreak in Toronto area using multistage Richards model and cases, April 28–June 4, 2003.

Mentions: Starting with the second phase of the outbreak on April 28, we again fit the cumulative case data from April 28 to the Richards model. As the case number on April 28 is 144, we use a transformation of S(t) = Sreal(t)–143, where Sreal(t) is the actual data at time t, so the initial data on April 28 used here is S(0) = 1. We again fit the model to the cumulative data ending on various dates past May 25; the results are given in Table 3 and Figure 4. The estimates start to converge after June 4, in the last 2 rows of Table 3 in bold, yielding an estimate for K of 248.96 (95% CI 246.67–251.25). Once again, the actual case number of 249 for the Toronto area outbreak (and 250 for Canada) is well approximated by our estimate of K. The estimated turning point ti = 26.36 pinpoints May 24, or a turning point for SARS infections 5 days earlier on May 19. This finding further corroborates Health Canada's assertion that, among the 79 cases that resulted from exposure at the hospital where the index patient of the second phase stayed, 78 had exposures that occurred before May 23 (11). Note also that this estimate is obtained by using data that end just 11 days after the turning point on May 24, giving an accurate prediction of the actual cumulative case number (Figure 4).


Real-time forecast of multiphase outbreak.

Hsieh YH, Cheng YS - Emerging Infect. Dis. (2006)

Epidemic curves for the second phase of severe acute respiratory syndrome outbreak in Toronto area using multistage Richards model and cases, April 28–June 4, 2003.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3293463&req=5

Figure 4: Epidemic curves for the second phase of severe acute respiratory syndrome outbreak in Toronto area using multistage Richards model and cases, April 28–June 4, 2003.
Mentions: Starting with the second phase of the outbreak on April 28, we again fit the cumulative case data from April 28 to the Richards model. As the case number on April 28 is 144, we use a transformation of S(t) = Sreal(t)–143, where Sreal(t) is the actual data at time t, so the initial data on April 28 used here is S(0) = 1. We again fit the model to the cumulative data ending on various dates past May 25; the results are given in Table 3 and Figure 4. The estimates start to converge after June 4, in the last 2 rows of Table 3 in bold, yielding an estimate for K of 248.96 (95% CI 246.67–251.25). Once again, the actual case number of 249 for the Toronto area outbreak (and 250 for Canada) is well approximated by our estimate of K. The estimated turning point ti = 26.36 pinpoints May 24, or a turning point for SARS infections 5 days earlier on May 19. This finding further corroborates Health Canada's assertion that, among the 79 cases that resulted from exposure at the hospital where the index patient of the second phase stayed, 78 had exposures that occurred before May 23 (11). Note also that this estimate is obtained by using data that end just 11 days after the turning point on May 24, giving an accurate prediction of the actual cumulative case number (Figure 4).

Bottom Line: The 3 estimated turning points are March 25, April 27, and May 24.The estimated case number during the first phase of the outbreak between February 23 and April 26 is 140.53 (95% confidence interval [CI] 115.88-165.17) if we use the data from February 23 to April 4; and 249 (95% CI: 246.67-251.25) at the end of the second phase on June 12 if we use the data from April 28 to June 4.The second phase can be detected by using case data just 3 days past the beginning of the phase, while the first and third turning points can be identified only approximately 10 days afterwards.

View Article: PubMed Central - PubMed

Affiliation: National Chung Hsing University, Taichung, Taiwan. hsieh@amath.nchu.edu.tw

ABSTRACT
We used a single equation with discrete phases to fit the daily cumulative case data from the 2003 severe acute respiratory syndrome outbreak in Toronto. This model enabled us to estimate turning points and case numbers during the 2 phases of this outbreak. The 3 estimated turning points are March 25, April 27, and May 24. The estimated case number during the first phase of the outbreak between February 23 and April 26 is 140.53 (95% confidence interval [CI] 115.88-165.17) if we use the data from February 23 to April 4; and 249 (95% CI: 246.67-251.25) at the end of the second phase on June 12 if we use the data from April 28 to June 4. The second phase can be detected by using case data just 3 days past the beginning of the phase, while the first and third turning points can be identified only approximately 10 days afterwards. Our modeling procedure provides insights into ongoing outbreaks that may facilitate real-time public health responses.

Show MeSH
Related in: MedlinePlus