Journal of Mathematical Biology

, Volume 35, Issue 7, pp 825–842

The dynamics of cocirculating influenza strains conferring partial cross-immunity

  • Viggo Andreasen
  • Juan Lin
  • Simon A. Levin

DOI: 10.1007/s002850050079

Cite this article as:
Andreasen, V., Lin, J. & Levin, S. J Math Biol (1997) 35: 825. doi:10.1007/s002850050079


 We develop a model that describes the dynamics of a finite number of strains that confer partial cross-protection among strains. The immunity structure of the host population is captured by an index-set notation where the index specifies the set of strains to which the host has been exposed. This notation allows us to derive threshold conditions for the invasion of a new strain and to show the existence of an endemic multi-strain equilibrium in a special case. The dynamics of systems consisting of more than two strains can exhibit sustained oscillations caused by an overshoot in the immunity to a specific strain if cross-protection is sufficiently strong.

Key words: Infectious diseasesCross-immunityInfluenzaMultiple viral strains

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Viggo Andreasen
    • 1
  • Juan Lin
    • 2
  • Simon A. Levin
    • 3
  1. 1.Department of Mathematics and Physics, Roskilde University, DK-4000 Roskilde, Denmark. e-mail: viggo@fatou.ruc.dkDK
  2. 2.Department of Physics, Washington College, Chestertown MD 21620, USAUS
  3. 3.Department of Ecology and Evolutionary Biology, Eno Hall, Princeton University, Princeton NJ 08544, USAUS