Linked Life Data

15778334

Source:http://linkedlifedata.com/resource/pubmed/id/15778334

Statements in which the resource exists as a subject.
PredicateObject
rdf:type
lifeskim:mentions
pubmed:issue
2
pubmed:dateCreated
2005-6-29
pubmed:abstractText
In this paper we consider the impact of the form of the non-linearity of the infectious disease incidence rate on the dynamics of epidemiological models. We consider a very general form of the non-linear incidence rate (in fact, we assumed that the incidence rate is given by an arbitrary function f (S, I, N) constrained by a few biologically feasible conditions) and a variety of epidemiological models. We show that under the constant population size assumption, these models exhibit asymptotically stable steady states. Precisely, we demonstrate that the concavity of the incidence rate with respect to the number of infective individuals is a sufficient condition for stability. If the incidence rate is concave in the number of the infectives, the models we consider have either a unique and stable endemic equilibrium state or no endemic equilibrium state at all; in the latter case the infection-free equilibrium state is stable. For the incidence rate of the form g(I)h(S), we prove global stability, constructing a Lyapunov function and using the direct Lyapunov method. It is remarkable that the system dynamics is independent of how the incidence rate depends on the number of susceptible individuals. We demonstrate this result using a SIRS model and a SEIRS model as case studies. For other compartment epidemic models, the analysis is quite similar, and the same conclusion, namely stability of the equilibrium states, holds.
pubmed:language
eng
pubmed:journal
pubmed:citationSubset
IM
pubmed:status
MEDLINE
pubmed:month
Jun
pubmed:issn
1477-8599
pubmed:author
pubmed:issnType
Print
pubmed:volume
22
pubmed:owner
NLM
pubmed:authorsComplete
Y
pubmed:pagination
113-28
pubmed:dateRevised
2006-11-15
pubmed:meshHeading
pubmed:year
2005
pubmed:articleTitle
Non-linear incidence and stability of infectious disease models.
pubmed:affiliation
Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, UK. korobein@maths.ox.ac.uk
pubmed:publicationType
Journal Article, Research Support, Non-U.S. Gov't