title: Mathematical analysis of a multiple strain, multi-locus-allele system for antigenically variable infectious diseases revisited.
abstract: Many important pathogens such as HIV/AIDS, influenza, malaria, dengue and meningitis generally exist in phenotypically distinct serotypes that compete for hosts. Models used to study these diseases appear as meta-population systems. Herein, we revisit one of the multiple strain models that have been used to investigate the dynamics of infectious diseases with co-circulating serotypes or strains, and provide analytical results underlying the numerical investigations. In particular, we establish the necessary conditions for the local asymptotic stability of the steady states and for the existence of oscillatory behaviors via Hopf bifurcation. In addition, we show that the existence of discrete antigenic forms among pathogens can either fully or partially self-organize, where (i) strains exhibit no strain structures and coexist or (ii) antigenic variants sort into non-overlapping or minimally overlapping clusters that either undergo the principle of competitive exclusion exhibiting discrete strain structures, or co-exist cyclically.
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom. Electronic address: alhaji.cherif@maths.ox.ac.uk.
authors.forename: Alhaji
authors.initials: A
authors.lastname: Cherif
mesh_terms: D000483:Alleles; D000940:Antigenic Variation; D003141:Communicable Diseases / Q000453:epidemiology / Q000235:genetics / Q000276:immunology*; D019353:Endemic Diseases; D054884:Host-Pathogen Interactions / Q000235:genetics / Q000276:immunology; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological
keywords: Antigenically diverse diseases; Hopf bifurcation; Multiple strain epidemic model; Periodic solutions; Stability analysis; Strain structures