Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence

Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence

In this paper we analyze the dynamics of two families of epidemiological models which correspond to transitions from the SIR (susceptible-infectious-resistant) to the SIS (susceptible-infectious-susceptible) frameworks. In these models we assume that the force of infection is a nonlinear function of...

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Veröffentlicht in:Journal of mathematical biology 2005-10, Vol.51 (4), p.414-430
Hauptverfasser: Gomes, M G M, Margheri, A, Medley, G F, Rebelo, C
Format: Artikel
Sprache:eng
Schlagworte:
Communicable Diseases - epidemiology
Communicable Diseases - immunology
Communicable Diseases - transmission
Disease transmission
Epidemiologic Methods
Epidemiology - statistics & numerical data
Humans
Mathematics
Models, Biological
Models, Immunological
Models, Statistical
Nonlinear Dynamics
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Zusammenfassung:In this paper we analyze the dynamics of two families of epidemiological models which correspond to transitions from the SIR (susceptible-infectious-resistant) to the SIS (susceptible-infectious-susceptible) frameworks. In these models we assume that the force of infection is a nonlinear function of density of infectious individuals, I. Conditions for the existence of backwards bifurcations, oscillations and Bogdanov-Takens points are given.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-005-0331-9