Infectious Diseases

Infectious Diseases - Supplementary Material Lipsitch et...

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Supplementary Material Lipsitch et al. Transmission Dynamics and Control of Severe Acute Respiratory Syndrome Revised 4 June 2003 for Science 1. Estimation of R : Deterministic. In the main text (Fig. 2), we estimated R from the mean serial interval V and the exponential growth rate of the cumulative number of cases in the epidemic ln( ( )) () Yt t t λ = using the formula 2 1( 1 ) ( RV ff V ) =+ + , where f is the ratio of the infectious period to the serial interval. For clarity in Fig. 2 we used a single value of f =0.7 (equivalent to f =0.3). This formula, a generalization of the more commonly used formula 1 R V ( 10 ) from the SIR model, is obtained by linearizing the SEIR model ( 11 ) by assuming no depletion of susceptibles, and obtaining the larger eigenvalue of the linearized system  where E and I are the number of infected but not yet infectious and infectious persons respectively, L is the duration of the latent period, D is the duration of the infectious period, and the mean serial interval is the sum of the mean infectious and mean latent periods, V=L+D . R is the reproductive number. This eigenvalue can be rewritten as 1/ E I  =  ± ± / LRD E LD I 2 1 2 )4 2( 1 ( 1) ) f R Vf f −+ + = , where f = D / V is the ratio of the infectious period to the serial interval. The formula for R above is given by rearranging this equation. Under this equation, the particular second-order dependence of the estimate of R on the relative contributions of latent and infectious period depends on the exponentially distributed sojourn times assumed in the simple, deterministic SEIR model. Fig. S1 below shows that the correction factor is relatively unimportant except for large R s and long serial intervals.
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4 6 8 10 12 14 SerialInterval 1 2 3 4 5 Re tamitse (a) 4 6 8 10 12 14 SerialInterval 1 2 3 4 5 (b) 4 6 8 10 12 14 SerialInterval 1 2 3 4 5 0 (c) 4 6 8 10 12 14 SerialInterval 1 2 3 4 5 (d) FIGURE S1: Sensitivity of deterministic estimates of R to varying values of f , the ratio of the infectious period to the serial interval. Dependence is on the product f (1- f ); hence the results are symmetric. Values of f range from 0 or 1 (red) to 0.5 (black). (a) Y ( t )=1358 cases at t =63 days; (b) Y (t)=425 cases at t =41 days; (c) Y ( t )=7919 cases at t =185 days; (d) Y ( t )=15,000 cases at t =185 days.
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2. Transmission model for the effect of quarantine
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This note was uploaded on 02/10/2012 for the course MTH 487 taught by Professor Jhonopera during the Spring '11 term at Cleveland State.

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Infectious Diseases - Supplementary Material Lipsitch et...

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