An epidemiological approach to the spread of political third parties

Daniel M. Romero; Christopher M. Kribs-Zaleta; Anuj Mubayi; Clara Orbe

doi:10.3934/dcdsb.2011.15.707

Article Contents

2011, Volume 15, Issue 3: 707-738. Doi: 10.3934/dcdsb.2011.15.707

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An epidemiological approach to the spread of political third parties

1.
Center for Applied Mathematics, Cornell University, Ithaca, NY 14853
2.
University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408
3.
Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1904
4.
Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027

Received: December 31, 2009

Revised: April 30, 2010

Published: September 2011

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Abstract

Third political parties are influential in shaping American politics. In this work we study the spread of a third party ideology in a voting population where we assume that party members/activists are more influential in recruiting new third party voters than non-member third party voters. The study uses an epidemiological metaphor to develop a theoretical model with nonlinear ordinary differential equations as applied to a case study, the Green Party. Considering long-term behavior, we identify three threshold parameters in our model that describe the different possible scenarios for the political party and its spread. We also apply the model to the study of the Green Party's growth using voting and registration data in six states and the District of Columbia to identify and explain trends over the past decade. Our system produces a backward bifurcation that helps identify conditions under which a sufficiently dedicated activist core can enable a third party to thrive, under conditions which would not normally allow it to arise. Our results explain the critical role activists play in sustaining grassroots movements under adverse conditions.

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Mathematics Subject Classification: Primary: 92D25, 91F10; Secondary: 37N99, 91D30.

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