In this paper, a non-linear mathematical model of a political system with two political parties and a group of voters is considered and analyzed by using epidemiological approach. Because party members go door-to-door canvassing and influence people to vote for their party during elections, the epidemic method is more applicable in the modeling process for political parties. During elections, party members can make an offer to voters to join their party based on their party's ideology. The net population is considered to be fixed and homogeneously mixed. In this model we have considered three classes namely susceptible class (those people who vote for parties only), voters class (those people who vote for third party) and members class (party members, workers). We grouped the susceptible and voting classes into two separate parties based on their affection (high or low) for the third party's agenda. Here the model consists of three ordinary differential equations in which the voters join any of two parties and the members of existence parties switch their parties. Equilibria and stability analysis are finded out here. There are now established circumstances that allow for the co-existence of both political parties. We also find numerical simulation to support the analytical results