Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period

Prince Osei Affi

doi:doi:10.11648/j.ml.20180404.12

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Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period

Prince Osei Affi

Published in Mathematics Letters (Volume 4, Issue 4)

Received: 5 November 2018 Accepted: 19 November 2018 Published: 3 January 2019

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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.

Published in	Mathematics Letters (Volume 4, Issue 4)
DOI	10.11648/j.ml.20180404.12
Page(s)	67-73
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Basic Reproduction Number, Disease – Free Equilibrium, Endemic Equilibrium Point

References

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[7]	O. Diekmann, J. A. Heesterbeek, and J. A.Metz, “On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations,” Journal of Mathematical Biology, vol. 28, no. 4, pp. 365–382, 1990.
[8]	P. van den Driessche and J. Watmough (2002). Reproduction numbers and sub thresholdEndemic equilibria for compartmental models of disease transmission. Mathematical biosciences, 180, 29-48.
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[17]	J. M. Hyman and J. Li (1998). Modeling the effectiveness of isolation strategies in preventing STD epidemics. SIAM journal of applied mathematics, 58, 912.
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[19]	L. Wu and Z. Feng (2000). Homoclinic bifurcation in an SIQR model for childhooddiseases. Journal of differential equations, 168, 150.
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Prince Osei Affi. (2019). Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period. Mathematics Letters, 4(4), 67-73. https://doi.org/10.11648/j.ml.20180404.12

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ACS Style

Prince Osei Affi. Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period. Math. Lett. 2019, 4(4), 67-73. doi: 10.11648/j.ml.20180404.12

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AMA Style

Prince Osei Affi. Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period. Math Lett. 2019;4(4):67-73. doi: 10.11648/j.ml.20180404.12

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@article{10.11648/j.ml.20180404.12,
  author = {Prince Osei Affi},
  title = {Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period},
  journal = {Mathematics Letters},
  volume = {4},
  number = {4},
  pages = {67-73},
  doi = {10.11648/j.ml.20180404.12},
  url = {https://doi.org/10.11648/j.ml.20180404.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180404.12},
  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.},
 year = {2019}
}

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TY  - JOUR
T1  - Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period
AU  - Prince Osei Affi
Y1  - 2019/01/03
PY  - 2019
N1  - https://doi.org/10.11648/j.ml.20180404.12
DO  - 10.11648/j.ml.20180404.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
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EP  - 73
PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.ml.20180404.12
AB  - 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.
VL  - 4
IS  - 4
ER  -

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Author Information

Prince Osei Affi

Department of Mathematics and Statistics, University of Ghana, Legon, Ghana

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Prince Osei Affi. (2019). Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period. Mathematics Letters, 4(4), 67-73. https://doi.org/10.11648/j.ml.20180404.12

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ACS Style

Prince Osei Affi. Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period. Math. Lett. 2019, 4(4), 67-73. doi: 10.11648/j.ml.20180404.12

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AMA Style

Prince Osei Affi. Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period. Math Lett. 2019;4(4):67-73. doi: 10.11648/j.ml.20180404.12

Copy | Download

@article{10.11648/j.ml.20180404.12,
  author = {Prince Osei Affi},
  title = {Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period},
  journal = {Mathematics Letters},
  volume = {4},
  number = {4},
  pages = {67-73},
  doi = {10.11648/j.ml.20180404.12},
  url = {https://doi.org/10.11648/j.ml.20180404.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180404.12},
  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.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Global Stability Analysis of the SEIR Deterministic Model in the Presence of Treatment at the Latent Period
AU  - Prince Osei Affi
Y1  - 2019/01/03
PY  - 2019
N1  - https://doi.org/10.11648/j.ml.20180404.12
DO  - 10.11648/j.ml.20180404.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 67
EP  - 73
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20180404.12
AB  - 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.
VL  - 4
IS  - 4
ER  -

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