The effect of integral conditions in certain equations modelling epidemics and population growth
- 1 August 1980
- journal article
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 10 (1) , 13-32
- https://doi.org/10.1007/bf00276393
Abstract
Models of epidemics that lead to delay differential equations often have subsidiary integral conditions that are imposed by the interpretation of these models. The neglect of these conditions may lead to solutions that behave in a radically different manner from solutions restricted to obey them. Examples are given of such behavior, including cases where periodic solutions may occur off the natural set defined by these conditions but not on it. A complete stability analysis is also given of a new model of a disease propagated by a vector where these integral conditions play an important role.Keywords
This publication has 9 references indexed in Scilit:
- Stability analysis for a vector disease modelRocky Mountain Journal of Mathematics, 1979
- Periodic Solutions of a Periodic Nonlinear Delay Differential EquationSIAM Journal on Applied Mathematics, 1978
- Self-oscillations for epidemic modelsMathematical Biosciences, 1978
- Theory of Functional Differential EquationsPublished by Springer Nature ,1977
- Positively invariant closed sets for systems of delay differential equationsJournal of Differential Equations, 1976
- Mathematical Theories of PopulationsPublished by Society for Industrial & Applied Mathematics (SIAM) ,1975
- Behavior near constant solutions of functional differential equationsJournal of Differential Equations, 1974
- Some equations modelling growth processes and gonorrhea epidemicsMathematical Biosciences, 1973
- A problem in the theory of epidemicsMathematical Biosciences, 1970