On estimating the basic reproduction number in distinct stages of a contagious disease spreading

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dc.contributor.authorSchimit P.H.T.
dc.contributor.authorMonteiro L.H.A.
dc.date.accessioned2024-03-13T01:07:34Z
dc.date.available2024-03-13T01:07:34Z
dc.date.issued2012
dc.description.abstractIn epidemiology, the basic reproduction number R 0 is usually defined as the average number of new infections caused by a single infective individual introduced into a completely susceptible population. According to this definition, R 0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R 0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R 0>1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable; when R 0<1, the corresponding pathogen tends to naturally disappear because the disease-free stationary solution is asymptotically stable. Here we intend to answer the following question: Do these two different approaches for calculating R 0 give the same numerical values? In other words, is the number of secondary infections caused by a unique sick individual equal to the threshold obtained from stability analysis of steady states of ODE? For finding the answer, we use a susceptible-infective-recovered (SIR) model described in terms of ODE and also in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. The values of R 0 obtained from both approaches are compared, showing good agreement. © 2012 Elsevier B.V.
dc.description.firstpage156
dc.description.lastpage160
dc.description.volume240
dc.identifier.doi10.1016/j.ecolmodel.2012.04.026
dc.identifier.issn0304-3800
dc.identifier.urihttps://dspace.mackenzie.br/handle/10899/36780
dc.relation.ispartofEcological Modelling
dc.rightsAcesso Restrito
dc.subject.otherlanguageBasic reproduction number
dc.subject.otherlanguageComplex network
dc.subject.otherlanguageEpidemiology
dc.subject.otherlanguageOrdinary differential equations
dc.subject.otherlanguageProbabilistic cellular automata
dc.titleOn estimating the basic reproduction number in distinct stages of a contagious disease spreading
dc.typeArtigo
local.scopus.citations9
local.scopus.eid2-s2.0-84862249855
local.scopus.subjectAsymptotically stable
local.scopus.subjectAverage numbers
local.scopus.subjectBasic reproduction number
local.scopus.subjectBifurcation parameter
local.scopus.subjectComplex networks
local.scopus.subjectContagious disease
local.scopus.subjectEpidemiological models
local.scopus.subjectInitial stages
local.scopus.subjectNumerical values
local.scopus.subjectProbabilistic cellular automatons
local.scopus.subjectRandom network
local.scopus.subjectStability analysis
local.scopus.subjectStationary solutions
local.scopus.subjectSteady state
local.scopus.subjectSusceptible population
local.scopus.updated2024-05-01
local.scopus.urlhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84862249855&origin=inward
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