Role of inflexible minorities in the evolution of alcohol consumption - Crokidakis, Nuno (2022)
In this work we study a simple mathematical model for drinking behavior evolution. For this purpose, we considered three compartments, namely Susceptible individuals $S$ (nonconsumers), Moderated drinkers $M$ and Risk drinkers $R$. Inside the $S$ and $R$ compartments, we considered the presence of inflexible or zealot agents, i.e., individuals that never change their behavior (never drink or always drink a lot). These inflexible agents are described by fixed densities $s_I$ and $r_I$, for nonconsumer inflexible and risk drinking inflexible individuals, respectively. We analyze the impact of the presence of such special agents in the evolution of drinking behavior in the population. Specifically, since the presence of inflexible agents are similar to the introduction of quenched disorder in the model, we are interested in the impact of such disorder in the critical behavior of the system. Our analytical and numerical results indicate that the presence of only one class of inflexible agents, $s_I$ or $r_I$, destroys one of the two possible absorbing phases that are observed in the model without such inflexibles, i.e., for $s_i=r_I=0$. In the presence of the both kinds of inflexible agents simultaneously, there are no absorbing states anymore. Since absorbing states are collective macroscopic states with the presence of only one kind of individuals in the population, nonconsumers or risk drinkers, we argue that the inclusion of inflexible agents in the population makes the model more realistic. In addition, the work makes a contribution to studies on the impact of quenched disorder in nonequilibrium phase transitions, that are a subject of interest for Nonequilibrium Statistical Physics.Comment: 19 pages, 7 figures, submitted for publicatio