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

5.2 Evaluating the use of antiviral drugs by its effect on R

Page last updated: April 2006

It may be that using antiviral drugs for treatment against illness is very beneficial for the patient. Strategies that take this into account have not yet been investigated. So far we have considered primarily the effect of AVs on transmission of the infection and maintaining the health care services.

The illustrations shown in Figure 4.12 indicate strongly that the use of antiviral drugs for treatment alone reduces transmission only modestly. Specifically, when R is 1.4, as in Figure 4.12(a), we can see a substantial reduction in the size of the epidemic when we are able to treat more than 70% of cases within 48 hours. The peak of the epidemic is then also delayed. However, this effect dissipates rapidly as the infection spreads more easily. Specifically, already with R = 1.7 (as in Figure 4.13) we see only a minimal effect on the epidemic, even if all cases can be treated within 48 hours.

In Figure 5.1 we support this conclusion with another calculation. It plots the effective reproduction number assuming a basic reproduction number of 1.5, and that individuals are isolated 2 days after onset of symptoms. The left plot shows the effective reproduction number according to the fraction of cases that are given AVs as treatment upon diagnosis. The right plot shows the effective reproduction number according to the fraction of susceptible individuals that are given prophylaxis. The solid line shows the case where no cases are treated with AVs after diagnosis, and the dotted line assumes that all cases are given AVs as treatment after diagnosis.

The strategy of using AVs as treatment is not sufficient to eliminate disease spread even when the basic reproduction number is 1.5. There is more scope to reduce the effective reproduction number by using AVs as prophylaxis, although this strategy is only likely to be practical while potential contacts are small in number and relatively easy to identify. The relative effects of these measures are identical for larger values of the basic reproduction number.

Consider now calculations based on a model that can allow different usage of AVs for health workers and the general public. We also allow diagnosed cases to be isolated, and denote the fraction of the infectivity spent in the community (before being isolated) by ƒ. Consider an SEIR model with three types of individual, namely general practitioners (who are the first health care contact of pandemic influenza cases), influenza-dedicated health care workers (who tend the isolated cases) and general community members.

The effective reproduction number achieved by using AVs for treatment and prophylaxis, assuming a basic reproduction number of 1.5 and that individuals are isolated 2 days after onset of symptoms.

Figure 5.1 The effective reproduction number achieved by using AVs for treatment and prophylaxis, assuming a basic reproduction number of 1.5 and that individuals are isolated 2 days after onset of symptoms.

We define a default strategy for the use of antiviral drugs as follows:

i. Influenza-dedicated health care workers (HCWs) receive antiviral drugs for prophylaxis and use personal protection equipment (PPE),

ii. GPs receive antiviral drugs for prophylaxis following the first time they diagnose a pandemic influenza case, but do not use PPE, and

iii. all individuals are isolated upon diagnosis and treated with AVs.

When an infected person presents to a GP there is a probability p that the case infects the GP, if the latter is susceptible.

Figure 5.2 shows the contours where R =1 as a function of R0 and ƒ, the fraction of the infectivity an individual spends in the community before being isolated. The six contours, going from the lowest curve to the highest curve, correspond to progressively increasing intervention, namely

a. isolation of symptomatic cases, but no protection for HCWs
(labeled ‘neither AVs nor PPE’ in Figure 5.2)

b. add PPE only for influenza-dedicated HCWs
(labeled ‘no AVs - with PPE’)

c. add the default strategy for use of AVs as well
(labeled ‘default AVs’)

d. add targeted use of AVs achieving 20%, 40% and 65% coverage among contacts of infectives
(labeled ‘20%’, ‘40%’ and ‘65%’ respectively)

Each  of the above six curves, corresponding to six different levels of intervention,  is a contour for which R=1

Figure 5.2 Each of the above six curves, corresponding to six different levels of intervention, is a contour for which R=1. For points above the curve (where a point is specified by a value for R0 and a value for ƒ) the effective R exceeds 1, so the probability that an imported outbreak takes off is positive. In contrast, R < 1 for points below the curve, which ensures that an imported outbreak will fade out early.

The lowest curve in Figure 5.2, for which R0 =1, indicates that isolating symptomatic cases will only lead to elimination if R0 < 1. This is because HCWs are offered no protection, so that ‘isolated’ cases will continue to infect people.

Go now to the curve above this, namely the curve labeled ‘no AVs - with PPE’. For the specified intervention, this curve consists of all the points for which R=1. The reason for giving this curve is that it partitions all the potential values of R0 and ƒ into those (below the curve) for which an outbreak will fade out rapidly and those (above the curve) for which the chance of a major outbreak is positive. From the curve labeled ‘no AVs - with PPE’ in Figure 5.2 we see that the early isolation of infected individuals and having them tended by HCWs using personal protective equipment enables elimination of the infection for some moderate values of R0 above 1. For example, if cases spend only 40% of their infectious period in the community, before being isolated, then this isolation strategy is sufficient to achieve elimination as long as R0 < 2.

The third curve from the bottom (labeled ‘default AVs’) indicates that adding antiviral use for health workers to this strategy enables containment of infection for a larger range of R0 values. Note however, that most of the additional benefit occurs for early isolation. For influenza one might expect to achieve ƒ = 0.6, at best, and for values of ƒ greater than 0.6 the benefit of the default use of AVs is minimal in terms of its contribution towards eliminating the infection. However, the default strategy for the use of AVs is an important one for maintaining a sustainable health service during a pandemic of influenza.

In contrast, targeted use of AVs for prophylaxis of individuals exposed to diagnosed cases is seen to have a more substantial effect, even when isolation of diagnosed cases is impractical. This follows from the fact that the curves labeled 25%, 40% and 65% are significantly raised above the other contours. Specifically, it suggests that providing protection to 65% of exposed individuals, by prophylactic use of AVs that targets for example contacts, schools or residents of specific geographic locations, one is likely to be able to contain the epidemic. While this does not acknowledge that the AV stockpile may run out, we must remember that elimination, if it occurs, is likely to occur sooner rather than later (as long as we have not delayed the intervention response very long). More on how long the stockpile might last in Section 5.6.

Document download

This publication is available as a downloadable document.

Using Mathematical Models to Assess Responses to an Outbreak of an Emerged Viral Respiratory Disease(PDF 873 KB)