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Title: Exact solution to a dynamic SIR model
Author: Bohner, Martin
Streipert, Sabrina
Torres, Delfim F. M.
Keywords: Dynamic equations on time scales
Deterministic epidemic model
Closed-form solution
Time-varying coefficients
Asymptotic behavior
Issue Date: May-2019
Publisher: Elsevier
Abstract: We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's approach. If the coefficients are constant, both solution methods yield the same result. After a brief introduction to time scales, we formulate the SIR (susceptible–infected–removed) model in the general time domain and derive its solution. In the discrete case, this provides the solution to a new discrete epidemic system, which exhibits the same behavior as the continuous model. The last part is dedicated to the analysis of the limiting behavior of susceptible, infected, and removed, which contains biological relevance.
Peer review: yes
DOI: 10.1016/j.nahs.2018.12.005
ISSN: 1751-570X
Publisher Version:
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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