Non-recurrent epidemics on complex networks, such as the paradigmatic susceptible-infected-recovered (SIR) model, are often studied by mapping the model to bond percolation. However, the conditions under which this identification is justified have not been fully understood, except in specific cases. Here, we systematically determine when this mapping can be applied, starting from minimal assumptions on the epidemic model and the underlying network. Specifically, we discuss the conditions for three different forms of equivalence between a general non-recurrent epidemic model and Bernoulli bond percolation: isomorphism, equality of marginal infection probabilities, and equality of expected epidemic size. We numerically demonstrate the validity of our findings and examine how epidemiological outcomes are affected when these equivalences are not upheld. Our results establish the methodological basis and limitations of a common tool for analyzing epidemic processes on networks.
Across biological and social complex systems, models of epidemics or contagions incorporate complexity through network correlations, adaptive behavior, higher-order interactions, or co-circulating strains. Tracking these mechanisms lead to high-dimensional mathematical systems that resist analytical treatment. We show...
Laurent Hébert-Dufresne, P'eter L. Simon, István Z. Kiss· 0 citations
In this paper, we study a stochastic Susceptible-Infected-Removed (SIR) model where the infection and the recovery rates depend on individual covariates for susceptibility and infectiousness of the infector and the infectee. Such models allow explicit nonlinearity in the incidence term. They are also important from a p...
Kushankur Dutta, O. Izyumtseva, Wasiur R. KhudaBukhsh et al.· 0 citations
We incorporate stochastic fluctuations into an epidemic-behavior coevolution model and study its threshold dynamics and stationary distributions. By introducing the stochastic basic reproduction number R0σ, the behavioral threshold d, and two potential infection proportions RPσ,1 and RPσ,2, we establish conditions for...
Huan Yang, Sanyi Tang, Lin Wang· Journal of Theoretical Biolo...· 0 citations
A susceptible-infected-recovered model on clustered networks with stochastic behavioral adaptation, which reveals a rich interplay between behavioral adaptation, transmission heterogeneity, and network clustering in shaping both the onset and structure of epidemic outbreaks.
Xiao-Long Peng, Shu-Yan Chang, Li Li et al.· Chaos· 0 citations
Network epidemic simulation enables fine-grained understanding of epidemic behavior. However, empirical samples of interaction networks display properties that are challenging to capture with popular synthetic models of networks. Our empirical results show that epidemic spread behavior is sensitive to a form of multi-s...
Omar Eldaghar, Michael W. Mahoney, D. Gleich· PLOS Complex Systems· 1 citation
Persistence, coexistence, and boundary transcritical relays are usually studied through model-specific analyses in mathematical epidemiology, ecology, population dynamics, and chemical reaction network theory. Although these fields address closely related questions, they have developed largely independently. This separ...
Rim Adenane, Florin Avram, A. Halanay· Mathematics· 0 citations
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