Modeling Trade Wars: Applying Systems of Ordinary Differential Equations

Abstract

Systems of differential equations have been used to model a variety of situations including population dynamics, reactions between several chemicals, and even the outcome of warfare between two nations. These types of systems are well equipped to model both simple and relatively complex situations involving several interacting parties; however, they seem to have never been used to model the interactions between nations engaged in a trade war. This text was primarily developed to showcase the ability of such systems to broadly model the key features of such a trade conflict. We begin by summarizing the main inputs and outputs of several historical trade wars and proceed forward by developing two models utilizing systems of differential equations that incorporate these inputs and outputs into their terms. Following this, we analyze both systems by finding specific solutions to each, by developing a general formula for each system’s equilibria, and by confirming the stability of these equilibria. After the model’s development and analysis, we apply these systems in the controlled environment of a hypothetical trade war. Finally, we conclude with a brief list of limitations that discuss several factors that hinder the accuracy of the proposed models.