Prelude to Hopf bifurcation in an epidemic model: Analysis of a characteristic equation associated with a nonlinear Volterra integral equation

DOI10.1007/BF02154757zbMath0487.92023OpenAlexW1986142163WikidataQ52434779 ScholiaQ52434779MaRDI QIDQ1165801

R. Montijn, Odo Diekmann

Publication date: 1982

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02154757

zbMATH Keywords

periodic solutionsHopf bifurcationcharacteristic equationFourier coefficientsnonlinear Volterra equationepidemic modeltemporary immunity

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Volterra integral equations (45D05) Qualitative behavior of solutions to integral equations (45M99)

Related Items (13)

Stability analysis of age-structured population equations by pseudospectral differencing meth\-ods ⋮ An SIR epidemic model with partial temporary immunity modeled with delay ⋮ Models for diseases with exposed periods ⋮ The change of susceptibility following infection can induce failure to predict outbreak potential by \(\mathcal{R}_0 \) ⋮ Generality of endemic prevalence formulae ⋮ Threshold dynamics in an SEIRS model with latency and temporary immunity ⋮ On the formulation of epidemic models (an appraisal of Kermack and McKendrick) ⋮ Hopf bifurcation with constraints ⋮ Equivalent probability density moments determine equivalent epidemics in an SIRS model with temporary immunity ⋮ Analysis of an epidemiological model structured by time-since-last-infection ⋮ Numerical bifurcation analysis of renewal equations via pseudospectral approximation ⋮ Invariant manifolds for Volterra integral equations of convolution type ⋮ Stability of the endemic equilibrium in epidemic models with subpopulations

Cites Work

• Hopf bifurcation for functional equations
• Integral equation models for endemic infectious diseases
• Periodic solutions of an epidemic model
• Stability in a class of cyclic epidemic models with delay
• The effect of integral conditions in certain equations modelling epidemics and population growth
• Stability analysis for models of diseases without immunity
• Behavior near constant solutions of functional differential equations
• Nonlinear Oscillations in Epidemic Models
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