On the Dynamics and Structure of Multiple Strain Epidemic Models and Genotype Networks

Mathematical disease modeling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modeling community to focus on the complexity of other factors such as contact structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. This body of work first explores the role of strain-transcending immunity in mathematical disease models, and how genotype networks may be used to explore the evolution of multistrain pathogens. A model is introduced to follow multistrain epidemics with an underlying genotype network. Consequently, the genotype network structure of the antigenic hemagglutinin protein of influenza A (H3N2) is analyzed, suggesting the important role of strain-transcending immunity in the evolution of the virus. The unique structure of the influenza genotype network is then explored with age-weighted preferential attachment models, utilizing approximate Bayesian computation of the network growth mechanisms. Finally, multistrain vaccination strategies are identified through the application of a genetic algorithm towards minimization of super-critical strains. Altogether, we show the impact of genotype networks on multistrain disease modeling, explore the role of empirical genotype network structure, and identify applications that include network generative models and vaccine strain selection