Mitigation Strategies for Pandemic Influenza A: Balancing Conflicting Policy Objectives

Mitigation of a severe influenza pandemic can be achieved using a range of interventions to reduce transmission. Interventions can reduce the impact of an outbreak and buy time until vaccines are developed, but they may have high social and economic costs. The non-linear effect on the epidemic dynamics means that suitable strategies crucially depend on the precise aim of the intervention. National pandemic influenza plans rarely contain clear statements of policy objectives or prioritization of potentially conflicting aims, such as minimizing mortality (depending on the severity of a pandemic) or peak prevalence or limiting the socio-economic burden of contact-reducing interventions. We use epidemiological models of influenza A to investigate how contact-reducing interventions and availability of antiviral drugs or pre-pandemic vaccines contribute to achieving particular policy objectives. Our analyses show that the ideal strategy depends on the aim of an intervention and that the achievement of one policy objective may preclude success with others, e.g., constraining peak demand for public health resources may lengthen the duration of the epidemic and hence its economic and social impact. Constraining total case numbers can be achieved by a range of strategies, whereas strategies which additionally constrain peak demand for services require a more sophisticated intervention. If, for example, there are multiple objectives which must be achieved prior to the availability of a pandemic vaccine (i.e., a time-limited intervention), our analysis shows that interventions should be implemented several weeks into the epidemic, not at the very start. This observation is shown to be robust across a range of constraints and for uncertainty in estimates of both R0 and the timing of vaccine availability. These analyses highlight the need for more precise statements of policy objectives and their assumed consequences when planning and implementing strategies to mitigate the impact of an influenza pandemic.


No intervention
When no intervention is in place, expressions for the epidemic size and peak prevalence can be derived. The first step is to express y as a function of x. This is done by deriving an expression for / dy dx by dividing the equation for / dy dt by the equation for / dx dt (see equation (1) when there is no intervention in place. And therefore, y may be expressed as function of x by integrating by parts, where c 1 is a constant determined by the initial conditions. So, before interventions, or in the absence of interventions, the relevant initial condition is     0 0, 0 1 yx  and so

Epidemic size
At the end of the epidemic with no intervention, as Which is given as equation (6) in the main text.

Cumulative incidence
Cumulative incidence in the exponential phase of the epidemic may be calculated by approximating 1 x  in the equation for / dy dt (equation (1)). If the transmission rate is constant, the prevalence y(t) is As incidence is equal to xy  , cumulative incidence,   It, is approximated by which is used to derive equation (5) in the main text.

Long term intervention
For a long term intervention, the equation for ln 1 The constants are calculated separately. As in the no intervention case above, And so, the dynamics are given by

Epidemic size
When there is a long term intervention in place the final epidemic size, as t  and   0 y  , is given by   1 LI ax    , and therefore we can use equation (S.13) to derive: which is equation (4) in the main text. The approximation to cumulative incidence from equation (S.9) can be used to give an approximate value of the epidemic size for interventions which start during the exponential phase of the unconstrained epidemic.

Peak prevalence
When there is a long term intervention in place, a localized peak in prevalence can occur before or after the start of the intervention. As derived above, peak prevalence without an intervention in place is given by equation (S.7), and occurs when If the intervention is initiated early, then we can perform a similar calculation for peak prevalence during the intervention using the second part of equation (S.10) when And the value of peak prevalence during the intervention is calculated using equation (S.13) as in the main text. Again, the approximation to cumulative incidence prior to the epidemic can be used for early interventions (equation (S.9)). The next step is to derive conditions under which a peak in prevalence is observed before or during the intervention, or at the time that intervention starts. There are a limited number of scenarios which can occur: ). In this case prevalence will decrease when the intervention is initiated and peak prevalence will be   1 yT . The window of opportunity for this scenario is largest when  is largest.

Short term intervention
For a short term intervention, the equation for ln The constants c 1 and c 2 are as in equation (S.13). For the final part of the curve, the 'initial' conditions are determined by the dynamics before and during the intervention,   2 yT and   2 xT . Thus, And so, the dynamics are given by

Epidemic size
When there is a long term intervention in place the final epidemic size, as t  and   0 y  , is given by   1 SI ax    , and therefore we can use equation (S.20) to derive:  which is equation (8) in the main text.

Peak prevalence
When there is a short term intervention in place, a local peak in prevalence can occur before, during or after the intervention. As derived above, peak prevalence without an intervention in place is given by equation (S.7), and occurs when . Peak prevalence can also occur after the intervention, if there are enough susceptibles. Peak prevalence will occur when 0 1/ xR  (since / dy dx is as before the intervention), and its value will be (from equation (S.20)).
Given general conditions under which peak prevalence can occur before, during or after the intervention, the next step is to derive conditions under which each of these peaks occur. These conditions, expressed in terms of the susceptible pool at the time that an intervention is initiated and lifted, are given in Table 1. Table A1 below gives illustrations of each scenario.
Two additional calculations are required to balance which of pairs of two local peaks in prevalence are highest.
When there is a peak in prevalence after the intervention, it may or not be higher than prevalence when the intervention was initiated, depending on the susceptible pool at the time when the intervention is lifted: When there are peaks during and after the intervention, their relative height also depends on the susceptible pool when the intervention is lifted: And so, the range of outcomes are given by Table 1, A1.