Modeling Dynamics of Political Parties with Poaching from One Party

Abstract

Dynamical social phenomena have been modeled using differential systems employed in mathematical models of epidemiology. In Misra (2012), an epidemiological model is used to study the “spread” of two political parties. In Nyabadzaet. al (2016), the authors point out that the Misra model may be generalized by considering switching between political parties. We take off from these to consider a model in which there are two parties, with a third party recruiting only from one, hence acting as a renegade to one of the two parties. We locate equilibria and consider local stability particularly of the co-existence/endemic equilibrium. Finally, we look at parameter values that result in the recruitment activities of the third party adversely affecting the group it recruits from.