Send to

Choose Destination
See comment in PubMed Commons below
J Theor Biol. 2008 May 7;252(1):155-65. doi: 10.1016/j.jtbi.2008.01.014. Epub 2008 Jan 26.

Backward bifurcations and multiple equilibria in epidemic models with structured immunity.

Author information

  • 1Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.


Many disease pathogens stimulate immunity in their hosts, which then wanes over time. To better understand the impact of this immunity on epidemiological dynamics, we propose an epidemic model structured according to immunity level that can be applied in many different settings. Under biologically realistic hypotheses, we find that immunity alone never creates a backward bifurcation of the disease-free steady state. This does not rule out the possibility of multiple stable equilibria, but we provide two sufficient conditions for the uniqueness of the endemic equilibrium, and show that these conditions ensure uniqueness in several common special cases. Our results indicate that the within-host dynamics of immunity can, in principle, have important consequences for population-level dynamics, but also suggest that this would require strong non-monotone effects in the immune response to infection. Neutralizing antibody titer data for measles are used to demonstrate the biological application of our theory.

[PubMed - indexed for MEDLINE]
Free PMC Article
PubMed Commons home

PubMed Commons

How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for Elsevier Science Icon for PubMed Central
    Loading ...
    Write to the Help Desk