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This paper investigates the effect of the structure of the contact network onthe dynamics of the epidemic outbreak. In particular, we focus on the peaknumber of critically infected nodes (PCIN), determining the maximum workload ofintensive healthcare units which should be kept low. As a model and simulationmethod, we develop a continuous-time Markov chain (CTMC) model and an efficientsimulation-based on Gillespie's Stochastic Simulation Algorithm (SSA). Thismethods combine a realistic approximation of the stochastic process not relyingon the assumptions of mean-field models and large asymptotically largepopulation sizes as in differential equation models, and at the same time anefficient way to simulate networks of moderate size. The approach is analysedfor different scenarios, based on data from the COVID-19 outbreak anddemographic data from Ukraine. From these results we extract network topologyfeatures that need to be considered to effectively decrease the peak number ofinfections. The CTMC simulation is implemented in python and integrated in adashboard that can be used for interactive exploration and it is made openlyavailable.

Efficient Stochastic Simulation of Network Topology Effects on the Peak Number of Infections in Epidemic Outbreaks