Results of the Model without Incentives

<div><p>The vaccination coverage dynamic has a memory parameter <i>s</i> = 0.7, an adaptability parameter ε = 1, a critical vaccination coverage level <i>p</i><i>_c</i> = 0.6 (dashed line), and a probability <i>q</i>(0) = 0.8 of getting infected if no one participates in the voluntary vaccination program.</p><p>(A) Dynamics of yearly coverage (<i>p</i>) for a population of <i>N</i> = 10⁵ individuals (black data), and the corresponding dynamics of the prevalence (red data). The dynamics of the yearly coverage is approximately cyclic: as <i>p</i> approaches <i>p_c</i> from below, it eventually fluctuates above <i>p_c</i> and then abruptly drops below <i>p_c</i>.</p><p>(B) The probability that individual <i>i</i> decides to be vaccinated in season <i>n</i> is <i>w</i>^(<i>i</i>)<i>_n</i>. The figure shows <i>w</i>^(<i>i</i>)<i>_n</i> versus time for two individuals in the population. In contrast to the simple dynamics of the coverage, individuals go through complex vaccination decision behavior.</p><p>(C) Normalized distributions <i>ρ</i>(<i>w</i>^(<i>i)</i>) versus <i>w</i>^(<i>i</i>)<i>_n</i> for a population with <i>N</i> = 10⁷ for improved accuracy. The distribution when the coverage fluctuates above <i>p_c</i> is shown by the black data, and the distribution in the successive year when the coverage abruptly drops below <i>p_c</i> is shown by the blue data. Individuals tend to strongly segregate into two groups. The individuals in one group are highly unlikely to get vaccinated the next season. The black data show that the individuals in the other group are highly likely to get vaccinated (i.e., <i>w</i> = 1). The blue data show that the individuals in the second group are less likely to get vaccinated than previously (i.e., given that no epidemic occurred in the previous season, <i>w</i> = <i>s</i>).</p>