Exact Solution to a Dynamic SIR Model
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.
Recommended Citation
M. Bohner et al., "Exact Solution to a Dynamic SIR Model," Nonlinear Analysis: Hybrid Systems, vol. 32, pp. 228 - 238, Elsevier, May 2019.
The definitive version is available at https://doi.org/10.1016/j.nahs.2018.12.005
Department(s)
Mathematics and Statistics
Keywords and Phrases
Continuous time systems; Epidemiology; Asymptotic behaviors; Closed form solutions; Deterministic epidemic models; Time-scales; Time-varying coefficients; Time domain analysis; Closed-form solution; Dynamic equations on time scales
International Standard Serial Number (ISSN)
1751-570X
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2019 Elsevier, All rights reserved.
Publication Date
01 May 2019
Comments
Torres has been partially supported by FCT within CIDMA, Portugal project UID/MAT/04106/2019, and by TOCCATA FCT, Portugal project PTDC/EEI-AUT/2933/2014 . The authors are very grateful to three anonymous reviewers for several constructive comments, questions and suggestions, which helped them to improve the paper.