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Related Experiment Video

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A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness

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

Timothy C Reluga¹, Jan Medlock, Alan S Perelson

¹Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. timothy@reluga.org

Journal of Theoretical Biology

|March 8, 2008

Summary

Waning immunity in hosts does not alone cause backward bifurcation in disease dynamics. Mathematical modeling shows unique endemic equilibria are possible, highlighting immunity

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Area of Science:

Epidemiology
Mathematical Biology
Immunology

Background:

Host immunity to pathogens often wanes over time, influencing disease spread.
Understanding the impact of declining immunity on epidemiological dynamics is crucial.

Purpose of the Study:

To develop an epidemic model structured by immunity level to analyze epidemiological dynamics.
To investigate the role of waning immunity in the stability of disease-free and endemic states.

Main Methods:

Development of a mathematical epidemic model incorporating host immunity levels.
Analysis of the model's steady states, focusing on the disease-free and endemic equilibria.
Application of the model to measles neutralizing antibody titer data.

Main Results:

Waning immunity alone does not cause backward bifurcation of the disease-free steady state.
Two sufficient conditions for the uniqueness of the endemic equilibrium were identified.
These conditions ensure uniqueness in several common epidemiological scenarios.

Conclusions:

Within-host immunity dynamics can significantly impact population-level disease dynamics.
Strong non-monotone immune responses are likely required for complex population dynamics driven by immunity.
The model provides a framework for studying immunity's role in infectious disease epidemiology.