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A key scientific challenge during the outbreak of novel infectious diseasesis to predict how the course of the epidemic changes under differentcountermeasures that limit interaction in the population. Most epidemiologicalmodels do not consider the role of mutations and heterogeneity in the type ofcontact events. However, pathogens have the capacity to mutate in response tochanging environments, especially caused by the increase in population immunityto existing strains and the emergence of new pathogen strains poses a continuedthreat to public health. Further, in light of differing transmission risks indifferent congregate settings (e.g., schools and offices), different mitigationstrategies may need to be adopted to control the spread of infection. Weanalyze a multi-layer multi-strain model by simultaneously accounting for i)pathways for mutations in the pathogen leading to the emergence of new pathogenstrains, and ii) differing transmission risks in different congregate settings,modeled as network-layers. Assuming complete cross-immunity among strains,namely, recovery from any infection prevents infection with any other (anassumption that will need to be relaxed to deal with COVID-19 or influenza), wederive the key epidemiological parameters for the proposed multi-layermulti-strain framework. We demonstrate that reductions to existingnetwork-based models that discount heterogeneity in either the strain or thenetwork layers can lead to incorrect predictions for the course of theoutbreak. In addition, our results highlight that the impact ofimposing/lifting mitigation measures concerning different contact networklayers (e.g., school closures or work-from-home policies) should be evaluatedin connection with their effect on the likelihood of the emergence of newpathogen strains.

Spreading Processes with Mutations over Multi-layer Networks