Fig. 1: Illustration of our model.
From: Seasonal social dilemmas
A Schematic of the SIRS model, describing susceptible (S), infected (I), and recovered (R) individuals and the transitions between them. The seasonal transmission rate is β(t), b ≤ 1 is the average effect of adherence to an NPI, γ is the recovery rate, and δ is the rate at which recovered individuals become susceptible again (waning immunity). B SIRS model with constant transmission rate. We show an outbreak of the infection, transient oscillations and the dynamics approaching an endemic equilibrium for the fraction of infected, susceptible, and recovered individuals as a function of time for a constant transmission rate. C SIRS model with seasonal transmission rate. We show the fraction of infected, susceptible, and recovered individuals as a function of time for a seasonal transmission rate after reaching the steady state, where β0 is the baseline transmission rate, and β1 the strength of oscillations. Increasing the oscillation strength, the number of peaks in the infection changes with a damping appearing for high enough values. Model parameters are as in Table 1. D Behavioral dynamics. We show a summary of all dilemma conditions depending on the fraction of infected individuals in the population. Non-adherers are depicted in yellow, and adherers in purple. Each game has a different level of adherence at the steady state, where no one adheres in the NA and PD games, some adhere in the SD game, and everyone adheres in the HG game. We show the thresholds for the number of infected individuals separating the games.
