Study on the Influence of Direct Contact Network Topology on the Speed of Spread of Infectious Diseases in the Covid-19 Case

The management of epidemics received much interest in recent times, due to devastating outbreaks of epidemic diseases such as Ebola and COVID-19. 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, because this determines the workload of intensive health-care units and should be kept low when managing an epidemic. Simulation of virus propagation in complex networks of different topologies, generated according to the models of Erdős—Rényi, Watts-Strogatz, Barabási—Albert and in complete graph. Continuous-time Markov chains were used to simulate the infection process. The simulation was performed in networks with 200 nodes and different number of edges. The difference between the influence of age- and gender-determined and weighted characteristics of nodes on the number of critically infected nodes that can be used to predict the load on the hospital is analyzed. The analysis used the data of the demographic distribution of Ukraine as of 2020 and data on mortality from COVID-19 in Ukraine, as of December 16, 2020. It is proved that the deterministic characteristics a slightly lower values of critically infected, in small networks. According to the simulation results, it was proven that for one medium degree of connection, the largest peak number of infections is observed in the Barabási—Albert models, slightly less in the Erdős— Rényi models and the smallest in the Watts-Strogatz model. It is established that the main difference between these networks is the average shortest distance. It is proved that the main influence on the propagation rate has the average shortest distance between network nodes, location, clustering coefficient has less influence. It was found that with a large number of edges in the networks, the difference in the prevalence of viruses in the models of the Erdős—Rényi and Barabási—Albert networks is minimized, despite the reduction of the average shortest distance between nodes.