Fig 1.
Individuals decide to vaccinate based on one of three risk measures: The number of infected contacts (local count), the fraction of infected contacts (local prevalence), or the overall fraction infected (global prevalence). In this example, six of the 24 nodes are infected, yielding a global prevalence of 0.25. The white node towards the top has a single contact that happens to be infected; the white node towards the bottom has two of its five contacts infected.
Fig 2.
Disease and vaccination dynamics under different decision models.
Shading indicates the fraction of nodes in each state: susceptible (black), vaccinated (light gray), recovered (dark gray), infected (white). Columns corresponds to different strategies, as labeled above; rows correspond to R0 = 2 (top) and R0 = 5 (bottom).
Fig 3.
Epidemiological impacts of decision strategies change with R0.
(A) The proportion of individuals that are infected increases and then declines slightly as R0 increases, across all three decision strategies. (B) The proportion of individuals that choose to vaccinate initially increases sharply with R0 across all three strategies, but then declines for only the local count strategy. (C) Herd effect is the proportion of infections averted per vaccinated individual, and is highest for the local count strategy across all R0. All values are averages across 500 stochastic simulations.
Fig 4.
Vaccination decisions vary with degree.
(A) For each degree class, we graph the proportion of individuals that vaccinate (top) along with the epidemiological situation at the time a node chooses to vaccinate in terms of the number of its infected neighbors (middle) and the overall disease prevalence in the population (bottom). Epidemiological risks—the chances of both becoming infected and infecting others—generally increase with degree. The local count strategy (light blue) is the only strategy for which the probability of vaccinating consistently increases with risk. Compared to the two other strategies, high degree individuals vaccinate earlier in terms of both local and global disease prevalence and, consequently, are less likely to become infected. (B) The number of individuals infected in each degree class under each decision strategy. The top of the curve indicates the number of individuals in each degree class (i.e., the underlying degree distribution) on a log scale. For each degree class, the stacked values indicate the expected number of individuals infected under the various strategies. The top of the gray area indicates the expected number of infections in the baseline scenario without vaccines; red indicates individuals expected to remain uninfected. Generally, local count has the lowest expected attack rate (light blue), followed by local prevalence (dark blue), and finally global prevalence. This ranking does not hold for the lowest degree individuals; instead, local prevalence has a lower expected attack rate than local count, as indicated by the dark blue line cutting through the light blue region. For all graphs, values are averages across 500 simulations, assuming R0 = 5.
Fig 5.
Decision dynamics across social networks.
We compare three different network structures–homogeneous (top), exponential (middle), and scale-free (bottom)–and show the susceptible (black), infected (dark gray) and vaccinated (light gray) for two different values of R0. Results are averages across 500 stochastic simulations.