The Continuous Time Infection–Immunization Dynamics

Abstract

Recently a new evolutionary game dynamics, the Infection–Immunization Dynamics,has been introduced for discrete time. In this paper a continuous time version of this model is derived and the existence and structure of solutions is analysed. This is a very challenging task, since standard technique existence theorems for Differential Inclusions do not hold in general. An extended solution concept, the notion of Krasovsky solutions, can be applied though. Some stability results are stated and discussed.