An Epidemiological Approach to the Spread of Political Third Parties

Third political parties are influential in shaping American politics. In this work we study the spread of third parties ideologies in a voting population where we assume that party members are more influential in recruiting new third party voters than non-member third party voters. The study is conducted using an epidemiological model with nonlinear ordinary differential equations as applied to a case study, the Green Party. Through the analysis of our system we obtain the party-free and member-free equilibria as well as two endemic equilibria. We identify two threshold parameters in our model that describe the different possible scenarios for the political parties and their spread. Our system produces a backward bifurcation that helps identify conditions under which a third party can thrive. We perform a sensitivity analysis to the threshold conditions in order to isolate those parameters to which our model is most sensitive. We explore all results through deterministic simulations and refer to data from the Green Party in the state of Pennsylvania as a case study.