When targeting a vaccination campaign (especially against the 2009 H1N1 influenza strain), there are often two competing priorities: minimization of transmission by immunizing those individuals that are most epidemiologically important; and minimization of the effects of the disease by immunizing those individuals that have the most severe health consequences when infected. (We note that for other infections these two groups may strongly overlap, in which case there is no conflict of priorities to resolve.) To tease apart these conflicting ideals, we extend the simple model above by having three groups [18
]: the dominant transmitter group (denoted by a subscript D
), the group at highest risk of severe health complications if they become infected (denoted by a subscript H
) and the rest of the general population (denoted by a subscript G
). These groups obey the basic equation (2.1
) with two main modifications: firstly, the transmission dynamics are coupled through a ‘who acquires infection from whom’ matrix (β
); and secondly, vaccination is prioritized so that either the dominant transmitter group (D
) or the severe health risk group (H
) is vaccinated first, followed by the other group (either H
), finally followed by the general population (G
), (see electronic supplementary material). Here we have ignored the possibility that there is a group that are both dominant transmitters and at high risk of complications—obviously if such a group exists then it should be prioritized for vaccination before all others.
Obviously, an epidemiological model with three interacting groups has a large number of associated parameters, making a comprehensive sweep of the entire parameter space impractical and difficult to visualize. Instead, we show results from a relatively restricted scenario, but comment that these results are representative of all plausible scenarios that have been considered. In particular, we constrain the number of individuals in the three groups to be ND
= 0.1 N and HG
= 0.8 N, and constrain the transmission rates between all groups, except within the epidemiologically important group, to be equal (βXY
, except when X
). We note that different forms and parameters within this transmission matrix can potentially lead to different optimizations of vaccine [22
We now consider the optimal prioritization (either group D first or group H first), as four key parameters are varied: the transmission rate within the dominant transmitter group, βDD; the relative adverse consequences of infection for the three groups, σH > σD = σG; the timing for the start of the vaccination programme, T; and the speed with which the population is vaccinated, v. Here the consequences of infection could capture a variety of measures, from risk of symptoms if infected, to concepts such as loss of QALYs (auality-adjusted life years), to risk of hospitalization, to risk of mortality associated with infection. The curves shown in separate regions of parameter space where one form of prioritization is optimal, in terms of minimizing the total consequences of infection over the entire epidemic and across all three groups; regions above and to the left of the curves are where it is best to initially target vaccination towards the group with potentially severe health complications.
Two clear conclusions can be drawn. More rapid vaccination (larger v
) generally favours prioritizing vaccination towards the group with potential health consequences, as does a later onset of vaccination (larger T
). However, it should be noted that for either extremely rapid or extremely slow vaccination (or extremely late start of the vaccination programme), the differences between the two prioritization schemes will be minimal. We can obtain some estimate of consequences by examining the figures released by the Chief Medical Officer for England [9
]: of 342 confirmed deaths in England from H1N1 by the middle of March 2010, 52 per cent had severe underlying health problems while only 18 per cent were classified as previously healthy; similarly nearly 50 per cent of hospitalized patients were considered to have underlying conditions. These percentages, together with the fact that only 10 per cent of the general population are considered to have health problems, lead to estimates of σH
of atleast 9:1. Therefore, while there are a range of scenarios in which it would be optimal to target the dominant transmitters first, these tend to be in relatively extreme portions of parameter space, when the transmission rate βDD
is very high and vaccination begins very early in the epidemic; for the vast majority of realistic scenarios, it is generally optimal to target vaccination towards those members of the population with underlying health problems first, before tackling the dominant transmitters and the rest of the general population.