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+ ∑nk=1 rke-σkt or a logistic function which is an infinite-multi-exponential, i.e. function of the form S(t) = c + a/b+ewt, then we can have closed form solution. Also we will formulate a method to determine R0 the basic reproductive rate of an infection.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Balkew, Teshome Mogessie"],"institution":null,"degree_name":"MS (Master of Science)","degree_level":"Thesis - unrestricted","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-12-18T08:00:00Z","date_published":"2010-12-18T08:00:00Z","updated_at":"2026-07-24T02:20:55Z","subjects":["SIR model","Relative Removal Rate","Phase Plane Analysis","R0","Applied Mathematics","Non-linear Dynamics","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/1747","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Balkew, Teshome Mogessie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2010-12-18T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - unrestricted"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS (Master of Science)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["SIR model","Relative Removal Rate","Phase Plane Analysis","R0","Applied Mathematics","Non-linear Dynamics","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright by the authors."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.etsu.edu/context/etd/article/3102/viewcontent/BalkewT111610f.pdf","https://dc.etsu.edu/etd/1747"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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+ ∑nk=1 rke-σkt or a logistic function which is an infinite-multi-exponential, i.e. function of the form S(t) = c + a/b+ewt, then we can have closed form solution. Also we will formulate a method to determine R0 the basic reproductive rate of an infection.
"]},{"key":"dc:title","label":"Title","values":["The SIR Model When S(t) is a Multi-Exponential Function."]}]}],"canonical_facts":{"dc:creator":["Balkew, Teshome Mogessie"],"dc:date.issued":["2010-12-18T08:00:00Z"],"dc:description.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+ ∑nk=1 rke-σkt or a logistic function which is an infinite-multi-exponential, i.e. function of the form S(t) = c + a/b+ewt, then we can have closed form solution. Also we will formulate a method to determine R0 the basic reproductive rate of an infection.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/3102/viewcontent/BalkewT111610f.pdf","https://dc.etsu.edu/etd/1747"],"dc:rights":["Copyright by the authors."],"dc:subject":["SIR model","Relative Removal Rate","Phase Plane Analysis","R0","Applied Mathematics","Non-linear Dynamics","Physical Sciences and Mathematics"],"dc:title":["The SIR Model When S(t) is a Multi-Exponential Function."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:20:55Z"}