Stochastic processes on random graphs with
multiple type edges

Abstract. In this paper we examine the spread of an infectious disease on several random graph models with multiple type edges. The introduction of the types of the edges allows us to use more adequate models, because the probabilities of the propagations may depend on the variety of the connections in the graph. At first, we generalize the \(SIR\)-process for graphs with multi-type edges. Then, we further generalize the process by introducing latency (i.e. infected individuals do not show symptoms for a random period of time) and quarantine (i.e. infected individuals who show symptoms are temporarily separated from the population). Finally, the empirical results of some stochastic simulations related to the different processes and underlying structures are presented.