Exact solution to a dynamic SIR model. (May 2019)

• Record Type: Journal Article
• Authors: Bohner, Martin; Streipert, Sabrina; Torres, Delfim F.M.
• Is Part Of: Nonlinear analysis. Volume 32(2019)
• Page Start: 228
• Page End: 238
• Publication Date: 2019-05
• Subjects: 92D25 -- 34N05; Dynamic equations on time scales -- Deterministic epidemic model -- Closed-form solution -- Time-varying coefficients -- Asymptotic behavior; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2018.12.005
• Languages: English
• ISSNs: 1751-570X

Abstract

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.