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To evaluate the risk of transmission of SARS coronavirus outside of the health-care setting, close household and community contacts of laboratory-confirmed SARS cases were identified and followed up for clinical and laboratory evidence of SARS infection. Individual- and household-level risk factors for transmission were investigated. Nine persons with serological evidence of SARS infection were identified amongst 212 close contacts of 45 laboratory- confirmed SARS cases (secondary attack rate 4·2%, 95% CI 1·5–7). In this cohort, the average number of secondary infections caused by a single infectious case was 0·2. Two community contacts with laboratory evidence of SARS coronavirus infection had mild or sub-clinical infection, representing 3% (2/65) of Vietnamese SARS cases. There was no evidence of transmission of infection before symptom onset. Physically caring for a symptomatic laboratory-confirmed SARS case was the only independent risk factor for SARS transmission (OR 5·78, 95% CI 1·23–24·24).
In this paper, we present sufficient conditions for global optimality of a general nonconvex smooth minimisation model problem involving linear matrix inequality constraints with bounds on the variables. The linear matrix inequality constraints are also known as “semidefinite” constraints which arise in many applications, especially in control system analysis and design. Due to the presence of nonconvex objective functions such minimisation problems generally have many local minimisers which are not global minimisers. We develop conditions for identifying global minimisers of the model problem by first constructing a (weighted sum of squares) quadratic underestimator for the twice continuously differentiable objective function of the minimisation problem and then by characterising global minimisers of the easily tractable underestimator over the same feasible region of the original problem. We apply the results to obtain global optimality conditions for optinusation problems with discrete constraints.
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