Parameters used and their default values.

<p>UT denotes the unit of time which can be expressed in year or ten years.</p><p>Parameters used and their default values.</p

Confirmation bias, conformism and the emergence of oscillations in vaccination coverage.

<p>The emergence of oscillations (o) is depicted as a function of an infection’s reproductive rate (R₀) and the rate of negative side effects from vaccination (<i>δ</i>^<i>v</i>). The emergence of oscillations is contingent on the inclusion of confirmation bias but not conformism and is observed for intermediate values of R₀. Three models are considered: Model 3 (without either confirmation bias or conformism); Model 4 (including confirmation bias) and Model 5 (including both confirmation bias and conformism). If no oscillations emerge, three dynamics can be noted for the distribution of opinions of vaccination: (i) coexistence of 2 opinions with a greater number of individuals with a positive opinion (+), (ii) coexistence of 2 opinions with a greater number of individuals with a negative opinion (-), (iii) all individuals have a positive opinion (*). The models are analysed for 2 different generation times (birth (<i>b</i>) = death (<i>d</i>) = 1 and 0.5) and for different values of the rate of negative side effects from infection (<i>δ</i>^<i>I</i>). 1 million iterations were run with a time step of 0.0001 which correspond to 100 unit of time.</p

Infection and opinion dynamics as a function of the reproductive rate of the infection (model 5).

<p>For each value of R₀ (number of secondary infections which can be understood as the fitness of the pathogen; it must be >1 for the pathogen to invade the population), the time-series of the dynamics of the infection (top panel; the thin line corresponds to the number of infected individuals and the thick line corresponds to the number of vaccinated individuals) and opinion (bottom panel; the dashed grey line indicates the number of individuals who have a positive opinion and the dashed black line indicates individuals who have a negative opinion) are depicted for a rate of negative side effects from vaccination <i>δ</i>^<i>v</i> = 0.7. Alternative changes of opinions of vaccination and oscillations in vaccination coverage emerge for intermediate values of R₀. When the reproductive rate of the disease is large (R₀ >4), the negative opinion of vaccination disappears and vaccination coverage, while reaching high levels, does not reach herd immunity. This is because the infection spreads too quickly. More generally, four dynamics can be observed and a₁ to a₃ represent their limits which can be moved depending of the values of <i>δ</i>^<i>v</i> considered.</p

Components of the different nested models.

<p>Components of the different nested models.</p

Structure of the behaviour-incidence model.

<p>The model is an augmentation of a classic SIR compartmental model [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0142990#pone.0142990.ref030" target="_blank">30</a>]. Individuals are characterized by both their epidemiological status (<i>S</i>: susceptible; <i>I</i>: infected; <i>R</i>^<i>v</i>: recovered through vaccination; <i>R</i>^<i>g</i>: recovered naturally) and for each compartment, their opinion of vaccination (positive: subscript p; non-shaded colours; negative: subscript n; shaded colours). <i>C</i>^<i>V</i> and <i>C</i>^<i>I</i> are compartments that indicate the total recalled number of individuals having suffered negative side effects from vaccination and infection, respectively. <i>β</i> indicates the rate of infection transmission; Ω indicates the rate at which individuals change their opinion (from positive to negative Ω or from negative to positive Ω′); <i>δ</i> indicates the number of individuals suffering side effects from either vaccination <i>δ</i>^<i>V</i> and infection <i>δ</i>^<i>I</i>; <i>θ</i> indicates the rate at which individuals vaccinate. Each individual dies at the same rate <i>d</i>.</p

Conformism and oscillations in vaccination coverage.

<p>The evolution of the number of infected (thin line) and (thick line) vaccinated individuals is depicted. Conformism (illustrated by Model 5) increases the amplitude of oscillations and slows down the rate at which alternative opinions of vaccination alternate. The situation is indicated for infections that are moderately infectious (with a reproductive ratio (R₀) varying from 3 to 5) and with the rate of negative side effects from the vaccination (<i>δ</i>^<i>V</i>) varying from 0.5 to 2.</p