Simulation results are reported in terms of average attack rates, the percentages of the population in the simulation who are infected during the course of the simulation; or average case counts, the numbers of people infected during the course of the simulation. Note that these values are not conditioned on an outbreak occurring but are instead averaged over all trials; thus, average attack rate values will be substantially higher than shown in the event of an outbreak.
shows the results for a series of baseline simulations, where the x-axis indicates the percentage of vaccinated HCWs and the y-axis represents the attack rate. Each data point corresponds to 5 replicates of each of 200 different (static) models (ie, contact networks with p = 1) generated using identical simulation parameters (multiple replications are performed, because the simulations are nondeterministic and vary in their initial conditions). A single individual is drawn at random from a population of N = 1,000 (with HCW types and patient proportions like those of UIHC) and is initially infected, HCWs continue to work without regard to infection status, and patients (who are all unvaccinated) are hospitalized for the duration of the simulation (ie, there is no patient turnover). The disease parameters used mimic generally accepted parameters for influenza—namely, w = 2 days and t = 7 days.
FIGURE 1 Attack rate as a function of vaccination rate for 3 different vaccination strategies using (left) a highly effective vaccine (e =0.95) and (right) a less effective vaccine (e =0.45). The 3 vaccination strategies are a random vaccination strategy, an omniscient (more ...)
We compare the performance of several vaccination strategies with differing vaccine effectiveness; results are shown here for highly effective vaccine (e = 0.95), as well as for less effective vaccine (e = 0.45). The 3 strategies are a random vaccination strategy (where the available vaccine doses are distributed to HCWs selected at random with uniform probability), an omniscient vaccination strategy, and a reverse omniscient vaccination strategy. For the omniscient strategies, we assume that the actual number and type of contacts that an individual will have during the course of the day can be fully known a priori (in practice, this assumption is quite unreasonable). The omniscient strategy greedily vaccinates HCWs with the largest number of contacts first, ensuring that each additional dose maximally “fragments” the contact network, thereby reducing the potential for the infection to spread. In contrast, the reverse omniscient strategy vaccinates HCWs in precisely the opposite order, ensuring that each additional dose has a minimal effect on the spread of infection. These 2 strategies serve to delimit the expected performance range, with the random vaccination strategy lying squarely in the middle. A good vaccination strategy would be one that performs better than the random strategy and nearly as well as or better than the omniscient strategy. Note that, for all strategies, the attack rate decreases steadily as a larger number of HCWs are vaccinated or as the effectiveness of the vaccine increases. Other vaccine effectiveness rates and strategies, although not shown here, behave as expected.
The omniscient vaccination strategies assume that we can have perfect advance knowledge of an individual HCW’s number and type of contacts. Although we cannot possibly know these quantities in practice, it is possible to estimate them on the basis of an agent’s job category and to use the estimates to construct a practical vaccination policy.
shows the results obtained with 2 variants of such a targeted vaccination strategy. First, we rank job categories from most to least densely connected on the basis of the observational data, using Σk nk Pjk as a measure of the connectivity of group j (see ). Second, we administer vaccine to workers from each category in order until the target vaccination rate is attained. When the vaccination budget does not suffice to vaccinate all workers in the next job category, agents in that category are selected for vaccination at random until the vaccination budget is exhausted.
FIGURE 2 Attack rate as a function of vaccination rate for all 3 vaccination strategies. Top left, Simulations with healthcare workers vaccinated (e =0.70) on the basis of the expected number of contacts with patients or other healthcare workers as defined by (more ...)
Healthcare Worker Job Group Ordering According to Expected Connectivity
The first simulation (, top left) compares the performance of the targeted vaccination strategy with that of the random and omniscient vaccination strategies using the same simulation parameters as the baseline experiments and a moderately effective vaccine, e = 0.70 (again, other values of e behave as expected). The second simulation (, top right) uses an alternate contact model that excludes repeated contacts but weights edges accordingly to account for qualitative differences between, for example, intensive care nurses (lots of patient contact, but typically with only 1 or 2 patients) and social workers (fewer contacts per person but with a larger set of people). The second and third simulations (, bottom) show results obtained in simulations performed on dynamic contact networks, with persistence p = 0.98.
First, we note that, in all 4 simulation studies, the performance of the targeted vaccination strategy exceeds that of the random vaccination strategy and approaches that of the omniscient strategy while remaining practical and feasible from an implementation perspective. The relative performance ordering and shape of the attack rate curves are conserved in both contact models (ie, with and without repeated contacts) and for all vaccination effectiveness parameters, although the attack rates themselves may differ substantially. And although the rank order may change slightly depending on the contact model (because the corresponding cjk values will differ) and even from trial to trial (because each nj may itself vary slightly even as N, the total population, remains fixed), workers such as unit clerks and X-ray technicians are typically highly connected, whereas pharmacists and housekeepers are typically not as well connected. Note that ignoring repeated contacts in the input data increases the ranking of, for example, social workers, food service workers, transporters, and staff physicians (who tend to have diverse contacts with few repeats) and decreases the ranking of, for example, intensive care nurses and residents or fellows (who tend to have repeated contacts but with fewer people).
Although they are dependent on the model and simulation parameters used, our results are well behaved. Identical effects are observed over a broad range of parameters for all tested vaccination strategies, and, although the magnitude of these effects may change, the relative performance ordering of the strategies is conserved. For example, shows the results obtained for the targeted vaccination strategy (e = 0.70) when parameters governing the ease of agent-to-agent transmission (top left; 0.01 ≤ ij sk ≤ 0.04) and the duration of the subsequent infection (top right; 3 days ≤ t ≤ 11 days) are modified. As expected, increasing transmissibility and the duration of infections increases the attack rates. also explores the effect of dynamic populations, in which patients are discharged and replaced with average length-of-stay values in the range d = 3–7 days. In general, the shorter the length of stay, the more effective the vaccination policy, because discharging infected patients has an attenuating effect on disease spread within the institution (note that the number of agents in these simulations will grow concomitantly, artificially reducing the attack rate, yet the total number of cases remains stable, limited in part by the structure of interactions between HCWs and patients).
FIGURE 3 Attack rate as a function of vaccination rate as a function of other simulation parameters. Top left, Each curve represents a different probability of transmission from an infected agent to a susceptible agent 0.01 ≤ij sk ≤0.04, where (more ...)
Finally, we address the question of how best to put our results into practice without collecting hundreds of hours of contact data. shows the results obtained when randomly selected subsets of observations are used to order job types for targeted vaccination. A number of different-sized observation sets are used, ranging from 1 hour per job type (a total of only 15 hours of observation) to the complete 606-hour observation set. The results show that even small observational data sets suffice to capture much of the requisite job-type ordering information underlying the targeted vaccination strategy; thus, small investments in data collection can yield large gains in vaccine performance.
FIGURE 4 Results obtained using varying-sized subsets of the original observation data for all 3 vaccination strategies with moderately effective vaccine (e =0.70). Each data point represents the average attack rate over 1,000 simulations (5 replicates for each (more ...)