The SIR Model When S(t) is a Multi-Exponential Function.

Author

Teshome Mogessie Balkew, East Tennessee State University

Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

12-2010

Committee Chair or Co-Chairs

Jeff R. Knisley

Committee Members

Ariel Cintron-Arias, Frederick Norwood, Robert B. Gardner

Abstract

The SIR can be expressed either as a system of nonlinear ordinary differential equations or as a nonlinear Volterra integral equation. In general, neither of these can be solved in closed form. In this thesis, it is shown that if we assume S(t) is a finite multi-exponential, i.e. function of the form S(t) = a+ ∑ⁿ_k=1 r_ke^-σ_kt or a logistic function which is an infinite-multi-exponential, i.e. function of the form S(t) = c + a/b+e^wt, then we can have closed form solution. Also we will formulate a method to determine R₀ the basic reproductive rate of an infection.

Document Type

Thesis - unrestricted

Recommended Citation

Balkew, Teshome Mogessie, "The SIR Model When S(t) is a Multi-Exponential Function." (2010). Electronic Theses and Dissertations. Paper 1747. https://dc.etsu.edu/etd/1747

Copyright

Copyright by the authors.