Modelling contagious viral dynamics: a kinetic approach based on mutual utility

The time evolution of a contagious viral disease is modeled as the dynamic progression of different classes of populations that interact pairwise, aiming to improve their condition with respect to a given target. This evolutionary mechanism is based on binary interactions between agents, designed to enhance their utility mutually. To achieve this goal, we introduce kinetic equations of Boltzmann type to describe the time evolution of the probability distributions of the agent system undergoing binary interactions. The fundamental idea is to describe these interactions using principles from price theory, particularly by employing Cobb-Douglas utility functions for the binary exchange and the Edgeworth box to depict the common exchange area where utility increases for both agents.