Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period
Mathematics Letters
Volume 4, Issue 4, December 2018, Pages: 67-73
Received: Nov. 5, 2018; Accepted: Nov. 19, 2018; Published: Jan. 3, 2019
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Author
Prince Osei Affi, Department of Mathematics and Statistics, University of Ghana, Legon, Ghana
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Abstract
In this paper, the objective was to find out the influence of introducing treatment at the latent period of disease (infectious) transmission as a result the global dynamics of the SEIR epidemic model with the introduction of treatment at the latent period is explored. The basic reproduction number is estimated. Whenever the basic reproduction number is not larger than unity (R0≤1) then the disease – free equilibrium is globally stable and the disease dies out. But when the basic reproduction number is larger than unity (R0>1), then there exist the endemic equilibrium point which is stable and hence the disease will persist. This was demonstrated with a tuberculosis data obtained from Amansie west district health directorate in the Ashanti region of Ghana.In this instance the endemic equilibrium point was found to be stable. The sensitivity analysis also revealed that increasing the treatment rate introduced at the latent period will reduce the value of the basic reproduction number.
Keywords
Basic Reproduction Number, Disease – Free Equilibrium, Endemic Equilibrium Point
To cite this article
Prince Osei Affi, Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period, Mathematics Letters. Vol. 4, No. 4, 2018, pp. 67-73. doi: 10.11648/j.ml.20180404.12
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Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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