Open AccessA CLASS OF VOLTERRA INTEGRAL EQUATIONS ARISING IN DELAYED‐RECRUITMENT POPULATION MODELS
Author(s) -
Brauer Fred
Publication year - 1987
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.1987.tb00038.x
Subject(s) - volterra integral equation , mathematics , volterra equations , class (philosophy) , differential equation , integral equation , population , differential (mechanical device) , mathematical analysis , physics , computer science , nonlinear system , thermodynamics , demography , quantum mechanics , artificial intelligence , sociology
We formulate a Volterra integral equation which contains as special cases the differential‐difference equation model of Blythe, Gurney and Nisbet for populations with delayed recruitment and a differential‐difference equation with two delays related to the epidemic model of Wilson and Burke. We establish upper and lower bounds for positive solutions and give a classification of equilibria with conditions to determine whether an equilibrium is stable for all delays (absolutely stable), unstable for all delays, or switches from stable to unstable as the delay increases.