On Exact Solutions to Epidemic Dynamic Models
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.
E. Akin and G. Yeni, "On Exact Solutions to Epidemic Dynamic Models," Journal of Applied Analysis and Computation, vol. 10, no. 6, pp. 2299 - 2312, Wilmington Scientific Publisher, Dec 2020.
The definitive version is available at https://doi.org/10.11948/20190087
Mathematics and Statistics
Keywords and Phrases
Asymptotic; Behavior. Dynamic equations; Epidemic models; Time scales
International Standard Serial Number (ISSN)
Article - Journal
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01 Dec 2020