Epidemiological models with age structure, proportionate mixing, and cross-immunity. (English) Zbl 0715.92028
Summary: Infection by one strain of influenza type A provides some protection (cross-immunity) against infection by a related strain. It is important to determine how this influences the observed co-circulation of comparatively minor variants of the H1N1 and H3N2 subtypes. To this end, we formulate discrete and continuous time models with two viral strains, cross-immunity, age structure, and infectious disease dynamics.
Simulation and analysis of models with cross-immunity indicate that sustained oscillations cannot be maintained by age-specific infection activity level rates when the mortality rate is constant; but are possible if mortalities are age-specific, even if activity levels are independent of age. Sustained oscillations do not seem possible for a single-strain model, even in the presence of age-specific mortalities; and thus it is suggested that the interplay between cross-immunity and age-specific mortalities may underlie observed oscillations.
Simulation and analysis of models with cross-immunity indicate that sustained oscillations cannot be maintained by age-specific infection activity level rates when the mortality rate is constant; but are possible if mortalities are age-specific, even if activity levels are independent of age. Sustained oscillations do not seem possible for a single-strain model, even in the presence of age-specific mortalities; and thus it is suggested that the interplay between cross-immunity and age-specific mortalities may underlie observed oscillations.
MSC:
| 92D30 | Epidemiology |
| 35B35 | Stability in context of PDEs |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
proportionate mixing; influenza type A; cross-immunity; H1N1 and H3N2 subtypes; discrete and continuous time models; age structure; infectious disease dynamics; Simulation; sustained oscillations; age-specific infection activity level rates; mortality rate; single-strain model; age- specific mortalitiesReferences:
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