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

Mass gatherings were prohibited during some stages of previous pandemics in an attempt to reduce disease transmission. To assess how effective this is we can think of the number of ‘offspring’ an infective produces as consisting of a mixture of regular contacts and close contacts that arise when the individual attends a mass gathering event during the infectious period. Such events include attending a concert, a major sporting event or the cinema.

As an illustration, suppose that *R*_{0 } =2.5. This means that the mean number infected during the infectious period, including infectious contacts made in the course of everyday life and those made at a mass gathering, is 2.5. We assume that for each infective the probability of attending a mass gathering event during the infectious period is ω, and that if a mass gathering event is attended then the mean number infected at the event is m_{G }. Figure 4.8(a) illustrates a probability distribution for the number infected by a single infective if *R*_{0 } =2.5, ω=0.1 and m_{G }=10. Nearly all of the probability mass near 10 arises from infections at a mass gathering. One way to view this is to say that the mean *R*_{0 } =2.5 is made up of a mean of ω×m_{G }=1.0 attributable to mass gathering events and a mean of 1.5 attributable to everyday contacts. When mass gatherings are banned, the part attributable to mass gatherings is removed.

**Figure 4.8** For *R*_{0 }=2.5, the impact of mass gatherings on the effective *R* is illustrated. The solid line shows *R* for the case when gatherings are allowed, and the dashed curves the reduction in the effective *R* when such gatherings are prohibited. Parameter m_{G} is the mean number of infections at a gathering.

In Figure 4.8(b) we show the effect of banning mass gathering events for various values of m_{G } over the range of values [0, 0.5] for ω. It is evident that the prohibition of mass gatherings reduces the effective *R* significantly, but is highly dependent on the values of ω and m_{G }. Data to guide us on plausible values for ω and m_{G } are scarce.

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