Asymptotically periodic solutions to Volterra integral equations in epidemic models
type: Item
instance of: scholarly article
title: Asymptotically periodic solutions to Volterra integral equations in epidemic models
zbMATH Open document ID: 0589.92017
DOI: 10.1016/0022-247X(85)90310-5
author: Thomas L. Cromer
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The author studies the equation \[ x(t)=f(t)+\int^{t}_{0}a(s)P(t- s)g(x(s))ds \] which arises in models for SIS epidemics and he proves some results saying that if either f or a are periodic functions, then the solution x is asymptotically periodic. These results are applied to several models used in describing epidemics of gonorrhea and some numerical results are also given.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45M05
zbMATH DE Number: 3948068
zbMATH Keywords: scalar nonlinear Volterra integral equation
zbMATH Keywords: oscillations in
zbMATH Keywords: infective populations
zbMATH Keywords: asymptotically periodic solutions
zbMATH Keywords: SIS epidemics
zbMATH Keywords: epidemics of gonorrhea
zbMATH Keywords: numerical results
reviewed by: Gustaf Gripenberg
MaRDI profile type: Publication
cites work: On a Nonlinear Integral Equation for Population Growth Problems
cites work: Constant rate harvesting of populations governed by Volterra integral equations
cites work: A periodicity threshold theorem for epidemics and population growth
cites work: Q4402828
cites work: Asymptotic behavior in a deterministic epidemic model
cites work: Nonlinear Oscillations in Epidemic Models
cites work: On a nonlinear Volterra integral equation
cites work: Almost-periodic behavior of solutions of a nonlinear Volterra system.
cites work: Q5607581
cites work: Q3324449
cites work: A Periodicity Threshold Theorem for Some Nonlinear Integral Equations
cites work: On periodic solutions of a delay integral equation modelling epidemics
description: scientific article; zbMATH DE number 3948068