Four SEI endemic models with periodicity and separatrices

Linda Q. Gao, JAIME JUAN FERNANDO MENA LORCA, Herbert W. Hethcote

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

Periodic solutions have been found for some infectious disease models of the SI and SEI types. Here four SEI models with either disease-reduced or uniform reproduction are examined to determine the model features that do and do not lead to periodic solutions. The two SEI models with the simple mass action incidence βXY can have periodic solutions for some parameter values, but the two SEI models with the standard mass action incidence λXY N do not have periodic solutions. For some intermediate values of λ in the SEI model with incidence λXY N and uniform reproduction, the interior equilibrium is a saddle whose stable manifold separates the attractive regions for the disease-free equilibrium and the susceptible-free equilibrium.

Original languageEnglish
Pages (from-to)157-184
Number of pages28
JournalMathematical Biosciences
Volume128
Issue number1-2
DOIs
StatePublished - 1995
Externally publishedYes

Fingerprint Dive into the research topics of 'Four SEI endemic models with periodicity and separatrices'. Together they form a unique fingerprint.

Cite this