Characterization of the endemic equilibrium and response to mutant injection in a multi-strain disease model. (7th March 2015) - Aquino, Tomás; Bolster, Diogo; Nunes, Ana
Abstract: We explore a model of an antigenically diverse infection whose otherwise identical strains compete through cross-immunity. We assume that individuals may produce upon infection different numbers of antibody types, each of which matches the antigenic configuration of a particular epitope, and that one matching antibody type grants total immunity against a challenging strain. In order to reduce the number of equations involved in the analytic description of the dynamics, we follow the strategy proposed byKryazhimskiy et al. (2007) and apply a low-order closure reminiscent of a pair approximation. Using this approximation, we go beyond the numerical studies ofKryazhimskiy et al. (2007) and explore the analytic properties of the ensuing model in the absence of mutation. We characterize its endemic equilibrium, comparing with the results of agent based simulations of the full model to assess the performance of the closure assumption. We show that a particular choice of immune response leads to a degenerate endemic equilibrium, where different strain prevalences may exist, breaking the symmetry of the model. Finally we study the behavior of the system under the injection of mutant strains. We find that the build up of diversity from a single founding strain is extremely unlikely for different choices of the population׳s immune response. Abstract : Highlights: This work deals with multi-strain systems competing through cross-immunity in an SIR type framework with vital dynamics. We explore this system using a deterministic model that postulates strain immunity cross-correlations, together with stochastic simulations. We study in particular the multi-strain equilibrium, and how diversity may develop from a single founding strain. We show how strain prevalence is reduced because of overall cross-immunity. We find that the build up of diversity from a single founding strain is extremely unlikely for different choices of the population׳s immune response.