  A key scientific challenge during the outbreak of novel infectious diseases
is to predict how the course of the epidemic changes under different
countermeasures that limit interaction in the population. Most epidemiological
models do not consider the role of mutations and heterogeneity in the type of
contact events. However, pathogens have the capacity to mutate in response to
changing environments, especially caused by the increase in population immunity
to existing strains and the emergence of new pathogen strains poses a continued
threat to public health. Further, in light of differing transmission risks in
different congregate settings (e.g., schools and offices), different mitigation
strategies may need to be adopted to control the spread of infection. We
analyze a multi-layer multi-strain model by simultaneously accounting for i)
pathways for mutations in the pathogen leading to the emergence of new pathogen
strains, 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 (an
assumption that will need to be relaxed to deal with COVID-19 or influenza), we
derive the key epidemiological parameters for the proposed multi-layer
multi-strain framework. We demonstrate that reductions to existing
network-based models that discount heterogeneity in either the strain or the
network layers can lead to incorrect predictions for the course of the
outbreak. In addition, our results highlight that the impact of
imposing/lifting mitigation measures concerning different contact network
layers (e.g., school closures or work-from-home policies) should be evaluated
in connection with their effect on the likelihood of the emergence of new
pathogen strains.
