A simulation analysis to characterize the dynamics of vaccinating behaviour on contact networks

Abstract

Background: Human behavior influences infectious disease transmission, and numerous "prevalence-behavior" models have analyzed this interplay. These previous analyses assumed homogeneously mixing populations without spatial or social structure. However, spatial and social heterogeneity are known to significantly impact transmission dynamics and are particularly relevant for certain diseases. Previous work has demonstrated that social contact structure can change the individual incentive to vaccinate, thus enabling eradication of a disease under a voluntary vaccination policy when the corresponding homogeneous mixing model predicts that eradication is impossible due to free rider effects. Here, we extend this work and characterize the range of possible behavior-prevalence dynamics on a network.

Methods: We simulate transmission of a vaccine-preventable infection through a random, static contact network. Individuals choose whether or not to vaccinate on any given day according to perceived risks of vaccination and infection.

Results: We find three possible outcomes for behavior-prevalence dynamics on this type of network: small final number vaccinated and final epidemic size (due to rapid control through voluntary ring vaccination); large final number vaccinated and significant final epidemic size (due to imperfect voluntary ring vaccination), and little or no vaccination and large final epidemic size (corresponding to little or no voluntary ring vaccination). We also show that the social contact structure enables eradication under a broad range of assumptions, except when vaccine risk is sufficiently high, the disease risk is sufficiently low, or individuals vaccinate too late for the vaccine to be effective.

Conclusion: For populations where infection can spread only through social contact network, relatively small differences in parameter values relating to perceived risk or vaccination behavior at the individual level can translate into large differences in population-level outcomes such as final size and final number vaccinated. The qualitative outcome of rational, self interested behaviour under a voluntary vaccination policy can vary substantially depending on interactions between social contact structure, perceived vaccine and disease risks, and the way that individual vaccination decision-making is modelled.

Figure 1

Individual payoffs in the Basic Model. Ellipses represent transition states while boxes represent formal states. Parameters on arrows denote transition probabilities and expressions in boxes denote payoffs for entering that state.

Figure 2

Individual Payoffs in the Extended Model. Ellipses represent transition states while boxes represent formal states. Parameters on arrows denote transition probabilities and expressions in boxes denote payoffs for entering that state.

Figure 3

Results from the Basic Model. Dependence of final epidemic size and final number vaccinated on: probability of death due to disease d_inf when d_vac = 0.001 (a), probability of death due to vaccine d_vac when d_inf = 0.03 (b), percentage of population with previous immunity (c), and probability to vaccinate ρ (d) in the Basic Model. Error bars represent two standard deviations from the mean across 20 simulations per data point. Note that d_inf = 0.3 (Table 1) lies to the right of the range illustrated in Figure 1a; we did not plot the results for d_inf > 0.07 because they are qualitatively unchanged from the case d_inf = 0.07.