Epidemiological models with age structure, proportionate mixing, and cross-immunity
Identifieur interne : 001747 ( Istex/Curation ); précédent : 001746; suivant : 001748Epidemiological models with age structure, proportionate mixing, and cross-immunity
Auteurs : C. Castillo-Chavez [États-Unis] ; H. W. Hethcote [États-Unis] ; V. Andreasen [États-Unis] ; S. A. Levin [États-Unis] ; W. M. Liu [États-Unis]Source :
- Journal of Mathematical Biology [ 0303-6812 ] ; 1989-05-01.
English descriptors
- KwdEn :
- Teeft :
- Academic press, Activity level, Activity level rates, Activity levels, Andreasen, Berlin heidelberg, Characteristic equation, Characteristic equations, Coefficient, Complete immunity, Constant mortality rate, Constant recovery rate, Contact number, Contact rates, Continuous dependence, Continuous model, Cornell university, Dependent epidemic model, Dietz, Different sets, Different values, Differential equations, Dimensional system, Disease dynamics, Dominant eigenvalues, Dynamics, Eigenvalue, Epidemiological, Epidemiological models, Equilibrium values, Further details, General case, Heterogeneous populations, Hethcote, Human population, Imaginary part, Imaginary parts, Incidence proportionality factors, Infectious diseases, Infectious period, Influenza, Influenza type, Influenza viruses, Initial boundary value problem, Initial conditions, Intermediate amplitude, Larger amplitude, Levin, Local stability analysis, Mathematical approaches, Mathematical ecology, Mathematical models, Minor variants, Mortality rate, Mortality rates, Nontrivial, Nontrivial equilibrium, Notes biomath, Orthant approach, Oscillation, Other strain, Pandemic, Partial immunity, Particular case, Periodic behavior, Periodic solutions, Permanent immunity, Real part, Regular cycles, Relative susceptibility, Resource management, Schenzle, Sect, Simulation, Simulation model, Single host population, Smaller amplitude, Special case, Stability analysis, Strain model, Subtypes, Survivorship curve, Susceptibility, Threshold condition, Threshold quantity, Time approaches infinity, Time step, Transfer diagram, Transmission coefficient, Transmission coefficients, Transmission rates, Viral, Viral strains, York tokyo.
Abstract
Abstract: 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.
Url:
DOI: 10.1007/BF00275810
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<term>Influenza</term>
<term>Proportionate mixing</term>
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<keywords scheme="Teeft" xml:lang="en"><term>Academic press</term>
<term>Activity level</term>
<term>Activity level rates</term>
<term>Activity levels</term>
<term>Andreasen</term>
<term>Berlin heidelberg</term>
<term>Characteristic equation</term>
<term>Characteristic equations</term>
<term>Coefficient</term>
<term>Complete immunity</term>
<term>Constant mortality rate</term>
<term>Constant recovery rate</term>
<term>Contact number</term>
<term>Contact rates</term>
<term>Continuous dependence</term>
<term>Continuous model</term>
<term>Cornell university</term>
<term>Dependent epidemic model</term>
<term>Dietz</term>
<term>Different sets</term>
<term>Different values</term>
<term>Differential equations</term>
<term>Dimensional system</term>
<term>Disease dynamics</term>
<term>Dominant eigenvalues</term>
<term>Dynamics</term>
<term>Eigenvalue</term>
<term>Epidemiological</term>
<term>Epidemiological models</term>
<term>Equilibrium values</term>
<term>Further details</term>
<term>General case</term>
<term>Heterogeneous populations</term>
<term>Hethcote</term>
<term>Human population</term>
<term>Imaginary part</term>
<term>Imaginary parts</term>
<term>Incidence proportionality factors</term>
<term>Infectious diseases</term>
<term>Infectious period</term>
<term>Influenza</term>
<term>Influenza type</term>
<term>Influenza viruses</term>
<term>Initial boundary value problem</term>
<term>Initial conditions</term>
<term>Intermediate amplitude</term>
<term>Larger amplitude</term>
<term>Levin</term>
<term>Local stability analysis</term>
<term>Mathematical approaches</term>
<term>Mathematical ecology</term>
<term>Mathematical models</term>
<term>Minor variants</term>
<term>Mortality rate</term>
<term>Mortality rates</term>
<term>Nontrivial</term>
<term>Nontrivial equilibrium</term>
<term>Notes biomath</term>
<term>Orthant approach</term>
<term>Oscillation</term>
<term>Other strain</term>
<term>Pandemic</term>
<term>Partial immunity</term>
<term>Particular case</term>
<term>Periodic behavior</term>
<term>Periodic solutions</term>
<term>Permanent immunity</term>
<term>Real part</term>
<term>Regular cycles</term>
<term>Relative susceptibility</term>
<term>Resource management</term>
<term>Schenzle</term>
<term>Sect</term>
<term>Simulation</term>
<term>Simulation model</term>
<term>Single host population</term>
<term>Smaller amplitude</term>
<term>Special case</term>
<term>Stability analysis</term>
<term>Strain model</term>
<term>Subtypes</term>
<term>Survivorship curve</term>
<term>Susceptibility</term>
<term>Threshold condition</term>
<term>Threshold quantity</term>
<term>Time approaches infinity</term>
<term>Time step</term>
<term>Transfer diagram</term>
<term>Transmission coefficient</term>
<term>Transmission coefficients</term>
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<front><div type="abstract" xml:lang="en">Abstract: 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.</div>
</front>
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