Mixing and Diffusion in a Two-Type Population

The outbreak of epidemics, the rise of religious radicalization, or the motivational influence of fellow students in classrooms are some of the issues that can be described as diffusion processes in heterogeneous groups. Understanding the role that interaction patterns between groups (e.g. homophily or segregation) play in the diffusion of certain traits or behaviors is a major challenge for contemporary societies. Here, we study the effects on diffusion processes of mixing (or, alternatively, segregating) two different groups –one group that presents some sensitivity or propensity to infection, and another group with a different propensity. We find non-monotonic effects of mixing and Pareto inefficient segregation levels, i.e., situations where a change in the mixing level can benefit both groups, e.g., where an increase in the mixing level can reduce the expected infection levels in both groups. These findings can have fundamental consequences for the design of inclusion policies.