title: Characterization of the endemic equilibrium and response to mutant injection in a multi-strain disease model.
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 by Kryazhimskiy et al. (2007) and apply a low-order closure reminiscent of a pair approximation. Using this approximation, we go beyond the numerical studies of Kryazhimskiy 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.
authors.affiliation: Department of Civil & Environmental Engineering and Earth Sciences, University of Notre Dame, 46556 IN, USA; Centro de Física da Matéria Condensada and Departamento de Física, Faculdade de Ciências da Universidade de Lisboa, P-1649-003 Lisboa Codex, Portugal.
authors.forename: Tomás
authors.initials: T
authors.lastname: Aquino
authors.affiliation: Department of Civil & Environmental Engineering and Earth Sciences, University of Notre Dame, 46556 IN, USA.
authors.forename: Diogo
authors.initials: D
authors.lastname: Bolster
authors.affiliation: Centro de Física da Matéria Condensada and Departamento de Física, Faculdade de Ciências da Universidade de Lisboa, P-1649-003 Lisboa Codex, Portugal. Electronic address: anunes@ptmat.fc.ul.pt.
authors.forename: Ana
authors.initials: A
authors.lastname: Nunes
mesh_terms: D000940:Antigenic Variation; D003429:Cross Reactions / Q000276:immunology; D019353:Endemic Diseases; D006801:Humans; D018448:Models, Immunological; D009154:Mutation; D013269:Stochastic Processes; D014777:Virus Diseases / Q000453:epidemiology / Q000276:immunology* / Q000821:virology
keywords: Mathematical epidemiology; Strain competition and evolution; Strain cross-immunity