Exact Solution to a Dynamic SIR Model
arXiv:1812.09759 · doi:10.1016/j.nahs.2018.12.005
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.
This is a preprint of a paper whose final and definite form is with 'Nonlinear Analysis: Hybrid Systems', ISSN: 1751-570X. Submitted 16/May/2018; Revised 10/Oct/2018; Accepted for publication 18/Dec/2018
References in corpus (2)
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