Threshold and stability results for an age-structured epidemic model
- 1 June 1990
- journal article
- research article
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 28 (4) , 411-434
- https://doi.org/10.1007/bf00178326
Abstract
We study a mathematical model for an epidemic spreading in an age-structured population with age-dependent transmission coefficient. We formulate the model as an abstract Cauchy problem on a Banach space and show the existence and uniqueness of solutions. Next we derive some conditions which guarantee the existence and uniqueness for non-trivial steady states of the model. Finally the local and global stability for the steady states are examined.This publication has 8 references indexed in Scilit:
- Epidemiological models with age structure, proportionate mixing, and cross-immunityJournal of Mathematical Biology, 1989
- Analytical threshold and stability results on age-structured epidemic models with vaccinationTheoretical Population Biology, 1988
- Analytical Results on the Stability of Age-Structured Recurrent Epidemic ModelsMathematical Medicine and Biology: A Journal of the IMA, 1987
- Proportionate mixing models for age-dependent infection transmissionJournal of Mathematical Biology, 1985
- Age-related changes in the rate of disease transmission: implications for the design of vaccination programmesEpidemiology and Infection, 1985
- An Age-Structured Model of Pre- and Post-Vaccination Measles TransmissionMathematical Medicine and Biology: A Journal of the IMA, 1984
- On the number of solutions of nonlinear equations in ordered Banach spacesJournal of Functional Analysis, 1972
- Applications of Mathematics to Medical ProblemsProceedings of the Edinburgh Mathematical Society, 1925