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Epidemiological models with age structure, proportionate mixing, and cross-immunity
C Castillo-Chavez1, H W Hethcote, V Andreasen
1Ecology and Systematics, Cornell University, Ithaca, NY 14853.
Journal of Mathematical Biology
|January 1, 1989
Summary
Cross-immunity between influenza A strains can lead to sustained oscillations in co-circulation, particularly when age-specific mortality rates are considered. This interplay is key to understanding viral variant dynamics.
Area of Science:
- Epidemiology
- Mathematical Biology
- Virology
Background:
- Influenza A virus (H1N1, H3N2) exhibits cross-immunity, where infection by one strain offers protection against related strains.
- Understanding cross-immunity is crucial for explaining the co-circulation of different influenza variants.
Purpose of the Study:
- To investigate the influence of cross-immunity on the co-circulation dynamics of influenza A subtypes.
- To explore the role of age structure and age-specific mortality in maintaining viral oscillations.
Main Methods:
- Formulation of discrete and continuous time mathematical models.
- Inclusion of parameters for two viral strains, cross-immunity, age structure, and infectious disease dynamics.
- Simulation and analysis of model outputs under varying mortality and activity level rates.
Main Results:
- Sustained oscillations in viral co-circulation were not maintained by age-specific infection activity levels alone with constant mortality.
- Age-specific mortalities, even with age-independent activity levels, facilitated sustained oscillations.
- Single-strain models, even with age-specific mortalities, did not produce sustained oscillations.
Conclusions:
- The interplay between cross-immunity and age-specific mortalities is a potential driver for the observed oscillations in co-circulating influenza A variants.
- Mathematical modeling provides insights into the complex dynamics of infectious disease spread and variant selection.