Global stability for infectious disease models that include immigration of infected individuals and delay in the incidence

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dc.contributor.authorUggenti, Chelsea
dc.contributor.authorMcCluskey, C. Connell
dc.date.accessioned2022-01-24T20:54:31Z
dc.date.available2022-01-24T20:54:31Z
dc.date.issued2018-03-07
dc.description.abstractWe begin with a detailed study of a delayed SI model of disease transmission with immigration into both classes. The incidence function allows for a nonlinear dependence on the infected population, including mass action and saturating incidence as special cases. Due to the immigration of infectives, there is no disease-free equilibrium and hence no basic reproduction number. We show there is a unique endemic equilibrium and that this equilibrium is globally asymptotically stable for all parameter values. The results include vector-style delay and latency-style delay. Next, we show that previous global stability results for an SEI model and an SVI model that include immigration of infectives and non-linear incidence but not delay can be extended to systems with vector-style delay and latency-style delay.
dc.description.departmentMathematics
dc.formatText
dc.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationUggenti, C., & McCluskey, C. C. (2018). Global stability for infectious disease models that include immigration of infected individuals and delay in the incidence. <i>Electronic Journal of Differential Equations, 2018</i>(64), pp. 1-14.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15206
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectGlobal stability
dc.subjectLyapunov function
dc.subjectEpidemiology
dc.subjectImmigration
dc.titleGlobal stability for infectious disease models that include immigration of infected individuals and delay in the incidenceen_US
dc.typeArticle

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