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

7.6 What would happen if R0 is much larger?

Page last updated: April 2006

We can not know with any certainty what the value of R0 will be. The illustrative calculations in this report have generally used values in the range 1.5–3.5. Let us take a more pessimistic scenario and see what might happen in the event that everyone is highly susceptible and R0 large. Suppose that R0 for the newly emerged pandemic influenza is 10, say, and the latent, incubation and infectious periods are similar to those of currently circulating influenza strains. What would happen?

The first point to make is that for this scenario the attempt by WHO to eliminate the newly emerged pandemic influenza in the source region is highly likely to fail. The epidemic will grow at an amazing rate in the source region and the infection is likely to be imported into Australia within a fortnight. Consider the growth of such an epidemic in terms of generations, where a generation occurs about 3 days after the previous generation (because of the short latent and infectious periods). A crude calculation for the first few generations, which ignores the depletion of susceptible individuals, is as follows:

Generation
1 2 3 4 5 6 7
Approx day
0 3 6 9 12 15 18
Cases
1 10 100 1000 10,000 100,000 1,000,000

In the absence of interventions an epidemic like this would infect virtually everyone in the location within a month. This is also evident from Figure 2.2, where the depletion of susceptibles is allowed for. The same is true for any infectious disease with such a large basic reproduction number. For example, in some populations measles is thought to have a value of R0 near 15. A similarly dramatic epidemic would happen if measles were initiated in a fully susceptible population, with two differences. First, incidences in successive generations would rise even more rapidly. Second, generations would be more separated in calendar time, because the latent and infectious periods are longer for measles. The generation interval for measles is about 14 days.

The results about the relative effectiveness of interventions in this report have application to the R0 = 10 scenario, provided the progression characteristics of the infection in an infected individual are similar to those we have assumed in the report. For example, with the peaked infectiousness function, isolating diagnosed individuals 1–2 days post symptoms could reduce the total infectivity of an infective by a modest 20%. By itself this will reduce R by a factor of 0.8 to 8. This has a minimal effect on the course of the epidemic. Personal infection control and avoiding exposure continues to have more potential to reduce R. For example, with λS = λI = 0.7 personal distancing would reduce R by a factor λS × λI = 0.49 to about 5. In absolute terms, this will not alter the course of the epidemic a great deal either, see Figure 2.2, but in terms of contributing towards bringing R down to 1 personal distancing clearly has more potential than isolating diagnosed cases. Similarly the results for other interventions continue to apply in terms of the factor by which they reduce R. However, it is only when R is brought down to the range 1 to 3, by a combination of interventions, that we see an appreciable effect on the dynamics of the epidemic, i.e. the eventual attack rate and a flatter, delayed epidemic. The closer R is to 1, the bigger the effect.

A major consequence of the observation that interventions do not alter the dynamics of an epidemic a great deal until they, in combination, bring R close to 1 is that the use of antiviral drugs for prophylaxis of traced contacts is justified only if such use brings R close to, or below, 1. Current calculations suggest that the use of antiviral drugs for prophylaxis of traced contacts is not a good strategy for using the stockpile if R0 ≥ 4.

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