Modelling the dynamics of cross-border ideological competition

Individuals are increasingly exposed to news and opinion from beyond national borders in a world that is becoming more and more globalised. This news and opinion is often concentrated in clusters of ideological homophily such as political parties, factions or interest groups. But how does exposure to cross-border information affect the diffusion of ideas across national and ideological borders? Here we develop a non-linear mathematical model for the cross-border spread of two ideologies by using an epidemiological approach. The populations of each country are assumed to be a constant and homogeneously mixed. We solve the system of differential equations numerically and show how small changes in the influence of a minority ideology can trigger shifts in the global political equilibrium.