PhD Defense by Gustav S. Halvorsen

Title: Generalized epidemics in heterogeneous networks and homogeneous metapopulation.

Abstract: Epidemic processes operate on all scales of life – from infectious pathogens to the spread of rumors on social networks. This work is about epidemic spreading in different network substrates. The thesis is apportioned between three related research topics.

The first seeks to estimate the effect of coordinating lockdowns between subnational entities that sustain recurring out-of-phase outbreaks of SARS-CoV-2. The uncoordinated strategy delays longer when given the same disposable resources. This difference is minimal on a metapopulation network with small-world properties. The coordinated strategy is superior if it is only slightly better at reducing transmission.

The second topic explores the dynamics of reactive social behavior on infectious disease outbreaks in a spatially extended system. This model exhibits a critical transition where the disease can no longer spread because reactive behavior changes have depleted the susceptible population around the outbreak. We show that the model can explain the 2014–2016 outbreak of the Ebola virus disease and introduce a statistical measure of spatial heterogeneity.

The final topic concerns the spread of information on a social network. Here we simulate how influencers compete for attention on a social network by new spreading information. The "virality" of information decays over time. Consequently, an influencer must discover new information or appropriate it from other subcultures to retain its subscribers' attention. The collective attention of the network exhibits metastable states in the presence of positive feedback. We consider the model on an assortment of social network topologies and find mutual coexistence between a few dominating influencers on a scale-free social network. Our findings suggest that either fake news or the perception of fake news as ubiquitous is endemic to our society because everyone can become a news outlet (e.g., influencer).