Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes | Zendy

C. Connell McCluskey | Zendy

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Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes

Author(s) -

C. Connell McCluskey

Publication year - 2012

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2012.9.819

Subject(s) - basic reproduction number , stability theory , smoothness , lyapunov function , epidemic model , exponential stability , mathematics , stability (learning theory) , infectious disease (medical specialty) , persistence (discontinuity) , tuberculosis , pure mathematics , disease , mathematical analysis , computer science , medicine , physics , population , environmental health , geotechnical engineering , pathology , nonlinear system , quantum mechanics , machine learning , engineering

We study a model of disease transmission with continuous age-structure for latently infected individuals and for infectious individuals. The model is very appropriate for tuberculosis. Key theorems, including asymptotic smoothness and uniform persistence, are proven by reformulating the system as a system of Volterra integral equations. The basic reproduction number R0 is calculated. For R0 < 1, the disease-free equilibrium is globally asymptotically stable. For R0 > 1, a Lyapunov functional is used to show that the endemic equilibrium is globally stable amongst solutions for which the disease is present. Finally, some special cases are considered.

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