Disease transmission model

To study the impact of vaccine prioritization strategies using the community networks described above, disease transmission is simulated using each network. The Adaptive Recovery Model developed at Sandia National Laboratories [12] was used to simulate disease transmission with various vaccination strategies. This model builds on the software developed by McGee [16], which integrates network structure into a stochastic compartment model. The model includes compartments that represent susceptible (S), exposed (E), asymptotic (A), infectious (I), hospitalized (H) recovered (R), and dead (D) states. The transmission paths between states are shown in Fig. 5. While additional modeling options have been included to model the impact of quarantine, contact tracing, and surveillance sampling, those options are not used in this analysis.

Disease transmission model states and pathways

The disease transmission parameters used in this analysis are shown in Table 3. Transition times between disease states are based on CDC planning scenarios which define some parameters as a function of age [26]. Age dependent disease progression is an important factor in the study of vaccine strategies, as older individuals have a higher chance of hospitalization and death and therefore benefit from the vaccine more. Note that the time from R state to S state is set to 100 years (TR in Table 3). This means that individuals are rarely reinfected. In reality, this is not true. However, this focuses the analysis on the use of vaccines to reduce first infections. The impact of vaccine strategies on subsequent infections could be included in future analysis.

Disease transmission parameters with age dependent values based on [26]

The community networks are initialized with 0.56% of the population in the I state, 0.02% of the population in the H state, and 6.07% of the population in the R state. These values were derived from data obtained from a COVID-19 tracking dashboard in 2021 for Bernalillo County in New Mexico. Using the cumulative cases, hospitalizations, and recovery counts a relative seroprevalence was estimated to initialize the analysis. Each scenario is simulated for 365 days, or until there is no longer disease within the community. It is important to keep in mind that the disease transmission model has not been calibrated to the communities of interest. Rather, the disease transmission parameters and differences in community structure provide a basis for comparing the relative impact of disease control strategies.

To model the impact of vaccine strategies, individual vaccine status (unvaccinated, partially vaccinated, fully vaccinated) is tracked per network node, where each node represents an individual. A two dose vaccine is modeled in this analysis. The time between doses is set to 3 weeks. The vaccine efficacy is based on the Pfizer vaccine clinical trials (0.82 after the first dose and 0.94 after the second dose) [27]. Vaccination reduces infectiousness by increasing the likelihood that an individual remains asymptomatic (A state). This is nominally set to 0.3 (fA in Table 3). Vaccines are distributed based on the available stock, queue of eligible people, and a prioritization strategy.

Vaccine availability is defined as the percent of the population that could be vaccinated each week, based on available stock. For this analysis, it is assumed that vaccine availability is held constant over the simulation time frame. For example, a peak of 3.38 million doses per day were administered in the U.S. on April 13, 2020 [28]. If this peak rate was sustained, that is equivalent to a vaccine availability of 7.2% of the population each week.

Individuals are vaccine eligible if they are in the S, E, A, or R state. As such, a queue of eligible people changes over time, as a function of disease transmission and vaccine status. Therefore, it is possible for someone to receive a first does and then become ineligible for a second dose if the individual becomes symptomatic (I state) within the three weeks between doses. In situations where resources are limited (the length of the queue is greater than the available vaccine doses for a particular day), only the highest-weighted individuals are selected for vaccination. Those that require a second dose are moved to the top of the queue. Additionally, children under 5 were not eligible for vaccination in the U.S until very recently. Given that the closest age bin in this analysis is 10, anyone under 10 is included as ineligible in this analysis. As mentioned earlier, the time spent in R is very large in this analysis, and therefore very few people transition back into the S state. In that way, vaccines given to people in the R state have very little impact on disease control.

People that are not willing to be vaccinated are removed from the vaccine queue. The fraction of the population willing to receive a vaccine has changed over the course of the pandemic. As of February 2022, 65% of the U.S. population was fully vaccinated [28]. Future research could include vaccine willingness that is a function of age, other demographics, or disease incidence in the population.

Position in the queue is determined by different factors according to a vaccine strategy. In this analysis, factors include age, household size, node degree, and disease state of neighboring nodes (for ring vaccination). Age vaccination sorts the queue based on age, from oldest to youngest. Household size vaccination sorts the queue based on household size, from large households to small households. Node degree vaccination sorts the queue based on the number of contacts a person has per day, from largest to smallest. Based on the way the network is generated, the number of contacts a person has per day is the node degree. Ring vaccination gives priority to people that are connected to someone that became symptomatic (transitioned into the I state). The list of people associated with this “ring” is updated every time step. This assumes the time associated with contact tracing is very small. Random vaccination, with no prioritization, is also included in the study. While information on age and household size is easy to obtain within a population, the number of contacts and the disease state of contacts is less observable. Community-aware centrality measures have also been studied as a way to prioritize immunization to reduce the size of disease outbreaks [29–31]. While centrality is also hard to observe in communities, the framework presented here could be extended to study the impact of vaccine prioritization based on centrality. Additional vaccine strategies, such as occupation and heath status could also be tested within this modeling framework, but would require additional data that is not currently included in this study.

To include the influence of non-pharmaceutical control measures, the use of personal protective equipment in the form of masks is included in the analysis. Masks can offer a wide range of protection, depending largely on the material and how the mask is worn. In this analysis, mask effectiveness is defined as the product of the probability that an individual wears a mask and the protection that the mask offers. For example, if an individual wears a mask 25% of the time and the mask reduces transmission by 50%, then the mask effectiveness is 0.125. In the disease transmission model, mask effectiveness is used to modify the transmission probability such that β~=β∗(1-m) where β~ is the modified transmission probability, β is the original transmission probability (set to 0.08 in this analysis) and m is the mask effectiveness. Masks are assumed to only be used outside of households. Therefore, transmission probability is only modified when people interact with members of different households, as defined by the network structure. While additional non-pharmaceutical control measures could be included in the analysis, including quarantine and contact tracing, the use of these control measures has declined in most communities.