Co-evolution of viruses and games

Mathematical modeling of virus dynamics is key to depicting the evolutionary pathways that lead to virus emergence, transmission, and persistence. Typically, viruses are populations of closely related genomes that continuously change their configuration and adapt to environmental selection pressures. In this work, we revisit this idea by considering viruses as active particles that dynamically shape their ecological niche. To this end, we adapt the Kinetic Theory of Active Particles to model virus interactions, allowing payoffs to co-evolve as a function of the population’s configuration. We deduce the system of ordinary equations corresponding to the replicator dynamics with frequency-dependent payoffs. Then we obtain a nonlinear integro-differential equation describing the dynamics for a continuum of strategies by passing to the limit in the replicator system when the number of equations grows. Finally, we present some examples of virus dynamics.