On state-space reduction in multi-strain pathogen models, with an application to antigenic drift in influenza A

Sergey Kryazhimskiy, Ulf Dieckmann, Simon Asher Levin, Jonathan Dushoff

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


Many pathogens exist in phenotypically distinct strains that interact with each other through competition for hosts. General models that describe such multi-strain systems are extremely difficult to analyze because their state spaces are enormously large. Reduced models have been proposed, but so far all of them necessarily allow for coinfections and require that immunity be mediated solely by reduced infectivity, a potentially problematic assumption. Here, we suggest a new state-space reduction approach that allows immunity to be mediated by either reduced infectivity or reduced susceptibility and that can naturally be used for models with or without coinfections. Our approach utilizes the general framework of status-based models. The cornerstone of our method is the introduction of immunity variables, which describe multi-strain systems more naturally than the traditional tracking of susceptible and infected hosts. Models expressed in this way can be approximated in a natural way by a truncation method that is akin to moment closure, allowing us to sharply reduce the size of the state space, and thus to consider models with many strains in a tractable manner. Applying our method to the phenomenon of antigenic drift in influenza A, we propose a potentially general mechanism that could constrain viral evolution to a one-dimensional manifold in a two-dimensional trait space. Our framework broadens the class of multi-strain systems that can be adequately described by reduced models. It permits computational, and even analytical, investigation and thus serves as a useful tool for understanding the evolution and ecology of multi-strain pathogens.

Original languageEnglish (US)
Pages (from-to)1513-1525
Number of pages13
JournalPLoS computational biology
Issue number8
StatePublished - Aug 2007

All Science Journal Classification (ASJC) codes

  • Genetics
  • Ecology, Evolution, Behavior and Systematics
  • Cellular and Molecular Neuroscience
  • Molecular Biology
  • Ecology
  • Computational Theory and Mathematics
  • Modeling and Simulation


Dive into the research topics of 'On state-space reduction in multi-strain pathogen models, with an application to antigenic drift in influenza A'. Together they form a unique fingerprint.

Cite this