A New Approach to Modeling Multiple Influenza Strain Dynamics
(December 31, 1969 7:00 PM - 7:00 PM)
Models that incorporate host dynamics to study the evolving nature of pathogens such as influenza face major computational challenges. We develop a mathematical model that allows for the study of several strain structures and show how these may influence disease dynamics. In particular, partial cross-immunity to next-to-kin strains leaves hosts less likely to be infected by antigenically similar strains while providing no immunity against all other strains. The status of the host is determined by immune-competence levels corresponding to all the strains that each host has immunity to. Immunity of the host population is captured by an index-set notation where the index specifies the immune-competence level against each particular strain. In contrast to previous modeling approaches, the population here is structured into non-intersecting subclasses. That is, since multiple infection with influenza strains is uncommon, we do not imbed superinfection with the same or different strains as part of our model. We provide threshold quantities that allows us to determine conditions for the invasion of a single strain or multiple co-existence of strains. Furthermore we provide stability conditions for the disease-free and endemic state equilibrium.