East Tennessee State University
The SIR Model When S(t) is a Multi-Exponential Function.
Abstract
dc:description.abstract<p>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 <em>S</em>(<em>t</em>) is a finite multi-exponential, i.e. function of the form <em>S</em>(<em>t</em>) = <em>a</em>+ ∑<sup><em>n</em></sup><sub><em>k</em>=1</sub> <em>r<sub>k</sub>e</em><sup>-σ<em><sub>k</sub>t</em></sup> or a logistic function which is an infinite-multi-exponential, i.e. function of the form <em>S</em>(<em>t</em>) = <em>c</em> + <em>a</em>/<em>b</em>+<em>e<sup>wt</sup></em>, then we can have closed form solution. Also we will formulate a method to determine <em>R</em><sub>0</sub> the basic reproductive rate of an infection.</p>
Degree
thesis:*- Name thesis:degree_name
- MS (Master of Science)
- Level thesis:degree_level
- Thesis - unrestricted
- Discipline thesis:degree_discipline
- Mathematical Sciences
- Year dc:date.issued
- 2010
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Balkew, Teshome Mogessie
Subjects
dc:subject × 7Rights
dc:rights- Statement dc:rights
-
- Copyright by the authors.
Identifiers
dc:identifier.*- Repository record dc:identifier
- https://dc.etsu.edu/etd/1747
- OAI identifier oai:identifier
- oai:dc.etsu.edu:etd-3102