An Epidemiological Math Model Approach to a Political System with Three Parties

Abstract

The United States has proven to be and remains a dual political party system. Each party is associated to its own ideologies, yet work by Baldassarri and Goldberg in Neither Ideologues Nor Agnostics show that many Americans have positions on economic and social issues that don't fall into one of the two mainstream party platforms. Our interest lies in studying how recruitment from one party into another impacts an election. In particular, there was a growing third party presence in the 2000 and 2016 elections. Motivated by previous work, an epidemiological approach is taken to treat the spread of ideologies and political affiliations among three parties, analogous to the spread of an infectious disease. A nonlinear compartmental model is derived to study the movement between classes of voters with the assumption of a constant population that is homogeneously mixed. Numerical simulations are conducted with initial conditions from reported national data with varying parameters associated to the strengths of political ideologies. We determine the equilibria analytically and discuss the stability of the system both algebraically and through simulation, parameters are expressed to stabilize a co-existence between three parties, and numerical simulations are performed to verify and support analysis.