Using Mathematical Models to Assess Responses to an Outbreak of an Emerged Viral Respiratory Disease

2.7 Three ways of judging the effectiveness of interventions

Page last updated: April 2006

We compared the effect of interventions on the basis of three different criteria. An intervention was assessed by its effect on the reproduction number (R), its effect on the probability (q) that an outbreak initiated by a single case fades out before becoming an epidemic and its effect on the dynamics of transmission in either calendar-time or in terms of generations. Assessments based on R and q have the advantage that only the mean number infected needs to be modeled, which means that the modeling can incorporate a considerable amount of community structure and a combination of interventions is more easily accommodated for these outcome measures. The information about q contained in the measure R is limited to the fact that q = 1 when R < 1, so q provides a useful alternative means of comparison when R > 1. Describing the complete dynamics of the spread of disease is very much more labour and computer intensive, particularly when community structure and a combination of interventions are accommodated. Time constraints for this work have therefore meant that models to describe the dynamics of transmission are generally based on models with more simplifying assumptions.

To assist with interpreting results on the effect of interventions on R we now point out how R typically relates to the dynamics of an epidemic. Consider four simple SIR models, with R= 10, 5, 2.5 and 1.25. That is, we start with R =10 and successively halve its value. Graphs of the number of infectives and removals over time are shown in Figure 2.2.

Note that halving the reproduction number diminishes and delays the peak of the epidemic, with the greatest gain occurring when R is reduced from a low value (2.5) to an even lower value (1.25). Note also that halving the reproduction numbers has very little effect on the eventual number of people infected when R is large (almost everyone is infected when R = 10, 5, and 2.5). However, reducing a value of R that is already small (<2.5) reduces the eventual number of cases substantially.


The impact of halving the reproduction number in an SIR model

    Figure 2.2 The impact of halving the reproduction number in an SIR model
(a) The number of infectives over time. (b) The number of removals over time.

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