In this paper the novel model of diffusion on networks and the experimental environment are presented. We consider the utilization of the graph and network theory in the field of modelling and simulating the dynamics of contagious diseases. We describe basic principles and methods and show how we can use them to fight against the spread of this phenomenon. We also present our software solution – CARE (Creative Application to Remedy Epidemics) that can be used to support decision-making activities.