  This paper investigates the effect of the structure of the contact network on
the dynamics of the epidemic outbreak. In particular, we focus on the peak
number of critically infected nodes (PCIN), determining the maximum workload of
intensive healthcare units which should be kept low. As a model and simulation
method, we develop a continuous-time Markov chain (CTMC) model and an efficient
simulation-based on Gillespie's Stochastic Simulation Algorithm (SSA). This
methods combine a realistic approximation of the stochastic process not relying
on the assumptions of mean-field models and large asymptotically large
population sizes as in differential equation models, and at the same time an
efficient way to simulate networks of moderate size. The approach is analysed
for different scenarios, based on data from the COVID-19 outbreak and
demographic data from Ukraine. From these results we extract network topology
features that need to be considered to effectively decrease the peak number of
infections. The CTMC simulation is implemented in python and integrated in a
dashboard that can be used for interactive exploration and it is made openly
available.
