# American Institute of Mathematical Sciences

2006, 3(3): 527-544. doi: 10.3934/mbe.2006.3.527

## Sensitivity and uncertainty analyses for a SARS model with time-varying inputs and outputs

 1 Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, MB, Canada R3B 2E9, Canada 2 Department of Statistics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2, Canada 3 Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada 4 Department of Mathematics, Malaspina University-College, Nanaimo, BC, Canada V9R 5S5, Canada

Received  April 2005 Revised  February 2006 Published  May 2006

This paper presents a statistical study of a deterministic model for the transmission dynamics and control of severe acute respiratory syndrome (SARS). The effect of the model parameters on the dynamics of the disease is analyzed using sensitivity and uncertainty analyses. The response (or output) of interest is the control reproduction number, which is an epidemiological threshold governing the persistence or elimination of SARS in a given population. The compartmental model includes parameters associated with control measures such as quarantine and isolation of asymptomatic and symptomatic individuals. One feature of our analysis is the incorporation of time-dependent functions into the model to reflect the progressive refinement of these SARS control measures over time. Consequently, the model contains continuous time-varying inputs and outputs. In this setting, sensitivity and uncertainty analytical techniques are used in order to analyze the impact of the uncertainty in the parameter estimates on the results obtained and to determine which parameters have the largest impact on driving the disease dynamics.
Citation: Robert G. McLeod, John F. Brewster, Abba B. Gumel, Dean A. Slonowsky. Sensitivity and uncertainty analyses for a SARS model with time-varying inputs and outputs. Mathematical Biosciences & Engineering, 2006, 3 (3) : 527-544. doi: 10.3934/mbe.2006.3.527
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