Non-Markovian epidemic processes in complex networks - Morán, José Andrés Guzmán (2023)
One of the cornerstones of mathematical epidemic modeling consists in assuming that infection and recovery can be described by Markov processes. This assumption implies that the inter-event times follow a negative exponential distribution. However, real-world epidemics are influenced by complex factors like human behavior and non-exponential incubation periods. As a result, there has been a growing interest in exploring non-Markovian epidemic processes. in the last decade. This work has the goal of exploring different problems concerning non-Markovian epidemics in complex networks. In particular, numerical simulations were conducted to study SIR and SIS non-Markovian epidemics using Weibull infection processes on different network models: (i) regular random networks (Erdos and Renyi model), (ii) scale-free networks (Barabási Albert model), and (iii) small-world networks (Watts Strogatz model). Our results reveal that considering a non-Markovian infection can significantly alter the epidemic size and threshold values. Increasing the shape parameter a, associated with aging in the probability of infection, leads to smaller epidemic sizes and higher critical effective rates. Our investigation also extends to the study of SIR non-Markovian processes in modular networks. For a Weibull infection process, we verify that strong community structures and positive aging contribute to larger epidemic sizes. Furthermore, the results suggest that as long as the critical transition rate remains below the effective rate chosen, positive aging processes can hence the role of communities in hindering the disease propagation to the entire network. This is caused by the slower propagation associated with the positive aging process, which prevents the disease from reaching healthy communities.