In the absence of incentives, the improved nearest neighbor strategy (INN) is the most effective in reducing influenza incidence, followed by chain vaccination (CV), nearest neighbor (NN), random vaccination (RV), and the baseline strategy of passive vaccination alone (PV) ().
This relative ordering is to be expected, since previous research shows the advantages of targeting individuals with many contacts 
. However, feedbacks due to the dependence of vaccinating decisions on infection history generates some surprises 
. In this system, the feedbacks manifest as policy resistance 
, where the response of the population to an intervention (in this case, pro-active strategies and incentives) tends to reduce the effectiveness of the intervention. In our model simulations, policy resistance arises because increased vaccine coverage in one season reduces incidence due to both direct and indirect (herd) protection, which in turn disincentives vaccination in future seasons, since decisions are based partly on infection history and perceived vaccine failure/complications. An additional source of policy resistance in this system is the tendency for pro-active strategies to waste recruitments on individuals who already decided to get vaccinated under passive vaccination, or who have already been infected (this is a problem especially among superspreaders, who are both targeted more often and tend to get infected earlier in the season) (Table S2
). On average, only
of the population was vaccinated through being contacted through a nearest neighbor under INN; whereas under NN and CV the percentage was
Policy resistance almost completely undermines the benefits of using pro-active strategies: passive vaccination (PV) reduces seasonal influenza incidence from
, but implementing improved nearest neighbour vaccination (INN) on top of that provides only slight additional reductions, down to
. The other pro-active strategies (NN, CV, RV) are even less effective, reducing incidence to
(). Moreover, among pro-active strategies, superspreader strategies are only marginally more effective than random vaccination (RV) (). As expected, the superspreader strategies improve vaccine coverage among superspreaders. However, this is offset by lower coverage among non-superspreaders. As a result, the average vaccine coverage under superspreader strategies is the same as under random vaccination (, ).
Figure 1 Model outcomes as a function of neighborhood size .
The impact of policy resistance is made clear by considering the case where vaccinating behavior is neglected (by assuming that targeted individuals are automatically recruited for vaccination). Neglecting behavior (NB) significantly overestimates both effectiveness and vaccine coverage for the pro-active strategies, both in superspreaders and non-superspreaders (). Hence, without accounting for behavior, we might have concluded that superspreader vaccination strategies can be significantly more effective than their non-targeted counterpart, but if we take behavior into account, their impact is greatly diminished.
We note that the slightly higher effectiveness of the improved nearest neighbor strategy also arises because by preferentially immunizing those individuals with a large number of contacts, susceptible individuals tend to be clustered together on the network, reducing the opportunities for the susceptible-infected contacts necessary for transmission (Table S3
Individuals with more neighbors were more likely to be infected (). This resulted in a higher probability of them getting vaccinated (), but it also caused them to perceive the vaccine to be less effective (), on account of higher infection rates causing higher rates of perceived vaccine failure.
The effect of adding vaccinating incentives is likewise blunted by policy resistance (). Any increase in vaccine coverage due to use of incentives reduces incidence, which in turn disincentivizes future vaccine uptake (especially among superspreaders under passive vaccination, Table S4
). Also, incentives often reach individuals who are already prone to get vaccinated (Table S2
). However, modest improvements in program effectiveness due to the use of incentives are still possible. For example, adding a
incentive to the improved nearest neighbor strategy reduces influenza incidence from
We estimated the net per capita costs (total vaccine costs plus total infection treatment costs per member of the population) for each strategy. The least expensive strategy was the improved nearest neighbor strategy (INN) without incentives, at a cost of
per capita. In contrast, passive vaccination on its own (PV) costs
per individual because infection costs are higher under PV than INN. These results assume the administrative costs of vaccination are the same for passive versus pro-active strategies, although in reality the marginal cost per vaccinated person may be higher under pro-active strategies, especially if they involve targeting superspreaders. We ran additional simulations where there was an additional marginal cost for recruiting contacts (as under NN, CV and INN), finding that the marginal cost for recruiting contacts under INN would have to be at least
per recruited individual before INN becomes more costly than PV.
Using vaccinating incentives increased the total cost of all strategies, but not always significantly. Further details appear in Text S1
and Table S5
On average, most individuals received few incentives and only a few individuals received many incentives (Figure S2
). Superspreaders tended to receive more incentives by virtue of having more contacts, but the benefit of this was partly mitigated by the fact that they are likely to be infected and/or seek vaccination earlier in the season than individuals with few contacts, and hence have less time to accumulate incentives.
Our baseline assumption was that superspreading is driven only by heterogeneity in neighborhood size (node degree). Incorporating heterogeneity into the infectious period, transmission rate, or both did not significantly impact the results (the superspreader strategies become slightly less effective in the absence of incentives). We suspect these forms of heterogeneity did not make a difference because an individual's infectious period and infectiousness were not correlated to their node degree, meaning that superspreader strategies on average do not target individuals with higher infectiousness or longer infectious period. This causes differences in effectiveness between the various strategies to be averaged out. Were correlations to exist between node degree on the one hand, and infectious period or transmission rate on the other hand, then we speculate the results could change qualitatively, either in the direction of greater effectiveness of superspreader strategies, or lesser effectiveness, depending on whether the correlation was positive or negative, respectively.
For simulations on the hypothetical Poisson or exponential networks instead of the empirically-based network, we found that the pro-active strategies continued to provide very small reductions in incidence compared to passive vaccination alone (Table S6
and Table S7
). Results were also qualitatively unchanged when incentives were distributed only to the recruited neighbor of individuals targeted under NN and INN (Tables S2
); however, the cost of the policies was reduced due to fewer incentives being distributed (Table S5