Model parameters and outbreak control for SARS

Abstract

Control of the 2002-2003 severe acute respiratory syndrome (SARS) outbreak was based on rapid diagnosis coupled with effective patient isolation. We used uncertainty and sensitivity analysis of the basic reproductive number R0 to assess the role that model parameters play in outbreak control. The transmission rate and isolation effectiveness have the largest fractional effect on R0. We estimated the distribution of the reproductive number R0 under perfect isolation conditions. The distribution lies in the interquartile range 0.19-1.08, with a median of 0.49. Even though the median of R0 is <1, we found that 25% of our R0 distribution lies at R0 > 1, even with perfect isolation. This implies the need to simultaneously apply more than one method of control.

Figure 1

Histograms of the six distributed parameters appearing in equation 1 with sample size 10⁵. The transmission rate was assumed to be exponentially distributed with mean 0.25, our estimated transmission rate in Hong Kong. Here l is assumed to have a beta distribution (l ~ β [1,2]). Alternative distributions for l were also used as described in the text. All other distributions were taken from reference .

Figure 2

Empiric (dots) and stretched exponential estimated probability density function Prob(R₀) = a exp[–(R₀/b)^c] (solid line) (16) of R₀ for the cases of Toronto (a = 0.186, b = 0.803, c = 0.957, after control measures had been implemented), Hong Kong (a = 0.281, b = 1.312, c = 0.858), and Singapore (a = 0.213, b = 1.466, c = 0.883) obtained from our uncertainty analysis. The distribution for the case of perfect isolation (l = 0, a = 0.369, b = 0.473, c = 0.756) is shown as a reference.

Figure 3

(β, l) parameter space when R₀ < 1 obtained from the uncertainty analysis (black dots). The deterministic (β, l) level curve when R₀ = 1 is shown in by the dotted white line. All other parameters in equation 1 were fixed to their baseline values (Table 1). l = 0 denotes perfect isolation; l = 1 denotes no isolation.

Figure 4

Boxplot of the sensitivity of R₀ estimates to varying values of l, the relative infectiousness after isolation has begun. l = 0 denotes perfect isolation while l = 1 denotes no isolation. The boxplot shows the median and the interquartile range of R₀ obtained from Monte Carlo sampling of size 10⁵.

Figure A1

Level curve of (l,α), where l(α+2γ₁+2δ) = δ+γ₂.