Effects of vaccine-hesitation on an epidemic: Simulations and meanfield studies of an agent based stochastic model

An elementary model of epidemics (the SIS model) consists of two subgroups in a population: the susceptible (S) and the infected (I), with rates for infection (η) and recovery (γ), showing a transition to a long-term, endemic state when γ/β≤1. In the spirit of the SIR model [Kermack and McKendrick, Proc. R. Soc. A115, 700 (1927)], we introduce a subgroup who takes vaccines (V ) as well as a time-dependent probability of acceptance (α). The evolution of α is based on a simple model of game theory, in which taking the vaccine or getting infected are treated as a "gamble" with risks. Using Monte Carlo techniques, we simulate populations evolving stochastically with N≤100000 individuals. Modeling a typical outbreak (from a small number of I's and V = 0), we find a variety of the epidemic's progression, including monotonic and oscillatory approaches to different steady endemic states. The mean-field equations for our simple model are quite successful in predicting the average behavior of the stochastic system, finding transitions between different phases in the system where the mean-field solutions go from stable to unstable, and boundary conditions for the absorbing state (I→0).