On Exact Solutions to Epidemic Dynamic Models

Abstract

In this study, we address an SIR (susceptible-infected-recovered) model that is given as a system of first order differential equations and propose the SIR model on time scales which unifies and extends continuous and discrete models. More precisely, we derive the exact solution to the SIR model and discuss the asymptotic behavior of the number of susceptibles and infectives. Next, we introduce an SIS (susceptible-infected-susceptible) model on time scales and find the exact solution. We solve the models by using the Bernoulli equation on time scales which provides an alternative method to the existing methods. Having the models on time scales also leads to new discrete models. We illustrate our results with examples where the number of infectives in the population is obtained on different time scales.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Asymptotic; Behavior. Dynamic equations; Epidemic models; Time scales

International Standard Serial Number (ISSN)

2156-907X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Wilmington Scientific Publisher, All rights reserved.

Publication Date

01 Dec 2020

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