ON EXACT SOLUTIONS TO EPIDEMIC DYNAMIC MODELS

Elvan Akın; Gülșah Yeni

doi:10.11948/20190087

2020 Volume 10 Issue 6

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Elvan Akın, Gülșah Yeni. ON EXACT SOLUTIONS TO EPIDEMIC DYNAMIC MODELS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2299-2312. doi: 10.11948/20190087

Citation:

Elvan Akın, Gülșah Yeni. ON EXACT SOLUTIONS TO EPIDEMIC DYNAMIC MODELS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2299-2312. doi: 10.11948/20190087

ON EXACT SOLUTIONS TO EPIDEMIC DYNAMIC MODELS

Elvan Akın^1, ,,
Gülșah Yeni²

1.
Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 W 12th St, 65409 Rolla, MO, USA
2.
Department of Mathematics, Pennsylvania State University, 16802, University Park, PA, USA

Corresponding author: Email address: akine@mst.edu (E. Akın)

Abstract

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.
- Dynamic equations /
- time scales /
- epidemic models /
- asymptotic behavior
MSC: 34N05, 92D25, 34A34

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References

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