Spreading processes in “post-epidemic” environments. II. Safety patterns on scale-free networks

This paper continues our previous study on spreading processes in inhomogeneous populations consisting of susceptible and immune individuals (Blavatska and Holovatch, 2021). A special role in such populations is played by “safety patterns” of susceptible nodes surrounded by the immune ones. Here, we analyze spreading on scale-free networks, where the distribution of node connectivity k obeys a power-law decay ∼k-λ. We assume, that only a fraction of p individual nodes can be affected by spreading process, while remaining 1 - p are immune. We apply the synchronous cellular automaton algorithm and study the stationary states and spatial patterning in SI, SIS and SIR models in a range 2 ‹ λ ‹ 3. Two immunization scenarios, the random immunization and an intentional one, that targets the highest degrees nodes are considered. A distribution of safety patterns is obtained for the case of both scenarios. Estimates for the threshold values of the effective spreading rate ß_c as a function of active agents fraction and parameter are obtained and efficiency of both vaccination techniques is analyzed quantitatively. The impact of the underlying network heterogeneous structure is manifest e.g. in decreasing the ß_c  values within the random scenario as compared to corresponding values in the case of regular lattices. This result quantitatively confirms the compliance of scale-free networks for disease spreading. On contrary, the vaccination within the targeted scenario makes the complex networks much more resistant to epidemic spreading as compared with regular lattice structures.