UC Irvine

The study of infectious disease spread is important for the health and security of a population. Compartmental susceptible-infected-recovered (SIR) and susceptible-infected-susceptible (SIS) are a popular tool to study contagion spread. In this thesis, we explored random graphs as a theoretical host population structure where nodes represent individual hosts and edges correspond to contacts between individuals that can result in an infection. We studied the dynamics of an advantageous mutant virus characterized by a higher infectivity compared to the wild-type pathogen and considered the Watts-Strogatz small-world network. The rewiring probability p, increase the number of non-local connections and spans between networks with a strong local structure and non-spatial networks. We also created a modified small-world network where ``superspreaders" were added to represent highly connected individuals. When initially generated by a spreading resident virus, a mutant variant has both an advantage (an assumed higher infectivity) and disadvantage (arriving later than the wild-type, to a shrinking population of susceptible targets). We asked, how do these two factors trade off, and whether the underlying network can influence the fate of a mutant virus. Under an SIR model, we considered two measures of mutant success: the expected height of the peak of mutant infected individuals and the total number of recovered from mutant individuals at the end of the epidemic. Using these measures, we have found the existence of an optimal rewiring probability, p, that enhances the spread of an advantageous mutant. Further, we studied infection dynamics in the presence of a vaccination administered according to two strategies: a random strategy and a chain strategy, which follows the vaccinations individuals' network connections. Using both SIS and SIRS models, we showed that network properties, vaccine efficacy, and vaccine adoption can influence the final quasi-steady state (QSS) of infection dependent on vaccination strategy. In particular we found that for a highly spacial network, while random vaccination strategy corresponds to a lower infection QSS, it tends to promote the rise of advantageous mutants. On the other hand, for a network with superspreaders, chain vaccination leads to a lower infection QSS, but it enhances the spread of advantageous mutants. This trade-off highlights the complexity of the epidemic evolutionary dynamics in the presence of vaccination.