TY - JOUR
T1 - Backward bifurcations and multiple equilibria in epidemic models with structured immunity
AU - Reluga, Timothy C.
AU - Medlock, Jan
AU - Perelson, Alan S.
N1 - Funding Information:
The authors thank P. van den Driessche for discussions that initially motivated this work and two anonymous reviewers for their helpful comments. Portions of this work were performed under the auspices of the US Department of Energy under contract DE-AC52-06NA25396. This work was supported in part by NIH Grants AI28433 and RR06555 (A.S.P.) and 2 T32 MH020031-07 (J.M.) and the Human Frontiers Science Program Grant RPG0010/2004.
PY - 2008/5/7
Y1 - 2008/5/7
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jtbi.2008.01.014
DO - 10.1016/j.jtbi.2008.01.014
M3 - Article
C2 - 18325538
AN - SCOPUS:41949112171
SN - 0022-5193
VL - 252
SP - 155
EP - 165
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
IS - 1
ER -
