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Optimal Control of an SIR Epidemic Model with a Saturated Treatment
Stockholm University, Faculty of Science, Department of Mathematics. National University of Sciences and Technology, Pakistan.
2016 (English)In: Applied Mathematics & Information Sciences, ISSN 1935-0090, E-ISSN 2325-0399, Vol. 10, no 1, 185-191 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we formulate an optimal control problem for an SIR epidemic model with saturated incidence and saturated treatment. Two main efforts, namely treatment and vaccination are considered to limit the disease transmission. The impacts of vaccination and treatment on the disease transmission are discussed through the basic reproduction number. Then to achieve control of the disease, a control problem is formulated and the existence of the control is shown. Two control functions are used, one for vaccinating the susceptible and the other for treatment efforts for infectious individuals. Appropriate optimal control methods are used to characterize the optimal levels of the two controls. The effectiveness of the proposed control solution is shown by comparing the behavior of controlled and uncontrolled systems. Numerical results show the impacts of two controls in decreasing both susceptible and infectious members of the population.

Place, publisher, year, edition, pages
2016. Vol. 10, no 1, 185-191 p.
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-137087DOI: 10.18576/amis/100117OAI: oai:DiVA.org:su-137087DiVA: diva2:1059416
Available from: 2016-12-22 Created: 2016-12-22 Last updated: 2016-12-22Bibliographically approved

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Lashari, Abid Ali
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