An SIS model for cultural trait transmission with conformity bias

Abstract

Epidemiological models have been applied to human health-related behaviors that are affected by social interaction. Typically these models have not considered conformity bias, that is the exaggerated propensity to adopt commonly observed behaviors or opinions, or content biases, where the content of the learned trait affects the probability of adoption. Here we consider an interaction of these two effects, presenting an SIS-type model for the spread and persistence of a behavior which is transmitted via social learning. Uptake is controlled by a nonlinear dependence on the proportion of individuals demonstrating the behavior in a population. Three equilibrium solutions are found, their linear stability analyzed and the results compared with a model for unbiased social learning. Our analysis focuses on the effects of the strength of conformity bias and the effects of content biases which alter a conformity threshold frequency of the behavior, above which there is an exaggerated propensity for adoption. The strength of the conformity bias is found to qualitatively alter the predictions regarding whether the trait becomes endemic within the population, and the proportion of individuals who display the trait when it is endemic. As the conformity strength increases, the number of feasible equilibrium solutions increases from two to three, leading to a situation where the stable equilibrium attained is dependent upon the initial state. Varying the conformity threshold frequency directionally alters the behavior invasion threshold. Finally we discuss the possible application of this model to binge drinking behavior.