  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.
