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Guillaume St-Onge
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Proceedings Papers
. isal2020, ALIFE 2020: The 2020 Conference on Artificial Life567-569, (July 13–18, 2020) 10.1162/isal_a_00327
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A standard problem in complex systems science has been to understand how infectious diseases, information, or any other contagion can spread within a system. Simple models of contagions tend to assume random mixing of elements, but real interactions are not random pairwise encounters: they occur within clearly defined higher-order structures. These higher-level structures could represent communities in social systems, cells in organisms or modules in neural networks. For a broader understanding of contagion dynamics in complex networks, we need to embrace higher-order structure, which can itself take many forms such as simplicial complexes or hypergraphs. To accurately describe spreading processes on these higher-order networks and correctly account for the heterogeneity of the underlying structure, we use a set of approximate master equations. This general framework allows us to unveil and characterize important properties of these systems. Here we focus on three of them: the localization of contagions within certain substructures, the bistability of the stationary state and a crossover of the optimal seeding strategies to maximize early spread.
Proceedings Papers
. isal2020, ALIFE 2020: The 2020 Conference on Artificial Life780-782, (July 13–18, 2020) 10.1162/isal_a_00311
Abstract
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Mathematical disease modeling has long operated under the assumption that a single disease is caused by a single pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of contagions and has allowed the community to focus on the complexity of other factors such as population structure. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their evolutionary dynamics with the host immune system, can play a large role in shaping epidemics. Here, we introduce a simple disease model with an underlying genotype network (Wagner, 2014), allowing the disease to mutate along network pathways as it spreads in a well-mixed host population. This genotype network allows us to define a genetic distance across strains and therefore model the transcendence of immunity often observed in real world pathogens (Katzelnick, 2017; Peeters, 2017). We study the emergence of epidemics in this model, or so-called epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases as well as localization around key strains of the associated pathogen. More generally, our model illustrates the richness of behaviors that are possible even in well-mixed host populations once more complex genetic structures are considered to go beyond the “one disease equals one pathogen” paradigm.