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

5.5 How many courses of AV drugs are used in an attempt at elimination?

Page last updated: April 2006

Suppose that during elimination attempts, neuraminidase inhibitors are distributed to probable infectious contacts of diagnosed individuals. In such a situation, prophylactics may be relatively generously distributed without having a substantial impact on the stockpile. For practical purposes we may consider that an elimination attempt has failed when 20 or more new infectives are diagnosed on a single day. When the progress of an epidemic reaches that stage it indicates strongly that R > 1 and, furthermore, the probability of an outbreak fading out with 20 initial infectives and R > 1 is negligible. We say that an elimination attempt has succeeded if number of infections on a single day never reaches 20, in which case the outbreak fades out. With this definition of elimination in mind we simulated 100,000 realisations of an outbreak, starting with one initial case and continuing until there are 20 new infections on a single day or the outbreak fades out, whichever comes first. For example, with R0=1.5 this produced the frequency distribution shown in Figure 5.6 for the total number of cases by the end of the elimination attempt.
Frequency distribution of the total number of cases, in 100,000 simulated outbreaks, up to elimination or 20 new cases on a single day, whichever came first.

Figure 5.6 Frequency distribution of the total number of cases, in 100,000 simulated outbreaks, up to elimination or 20 new cases on a single day, whichever came first. (R =1.5)

Table 5.1 shows the 50th, 95th and 99th percentile of the total number of cases by the end of an elimination attempt, for R=1.5, 2.5 and 3.5. They range from 25 to 55. In other words, the total number of cases by the end of the elimination attempt is very small relative to the population size and relative to the size of the antiviral stockpile.


          R = 1.5
          R = 2.5
          R = 3.5
          50th percentile (median)
          25
          25
          25
          95th percentile
          43
          33
          35
          99th percentile
          55
          36
          39

Table 5.1 Percentiles of the total number of cases, in 100,000 simulated outbreaks, up to elimination or 20 new cases on a single day, whichever came first.

Consider now what this might mean in terms of AV use for an elimination attempt. During an elimination attempt, we assume that the number of courses used for prophylaxis will be proportional to the number of cases diagnosed. This number of courses might be low, perhaps 10, for some diagnosed cases, if it only covers family members and close acquaintances. For some diagnosed cases it might be large, say 100, if there is a need to prophylax an entire child care centre, for example. It seems likely that the number of courses used in an elimination attempt, as defined above, will use less than 2,500 courses of AVs. This is a small number relative to the size of the stockpile, particularly in view of the fact that the targeted use of AVs decreases R to a level where the probability of an elimination attempt succeeding becomes substantial.

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