Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate

Sumit Kumar Banerjee; Boaz Andrews

doi:doi:10.11648/j.bsi.20230803.11

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Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate

Sumit Kumar Banerjee, Boaz Andrews

Published in Biomedical Statistics and Informatics (Volume 8, Issue 3)

Received: 13 February 2023 Accepted: 9 March 2023 Published: 18 September 2023

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Abstract

A passivity SEIR epidemic model with inconsistent incidence rate embedded with latency period for the imparting dynamics of epidemics is succeed and thoroughly inspected. The problem is constructed by a system of nonlinear ordinary differential equations analyzing the evaluation of susceptible, exposed, infected and removed individuals. The suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points have been discussed, namely, the disease free equilibrium, endemic equilibrium with respect to strain 1, endemic equilibrium with respect to strain 2 and the terminal endemic equilibrium with respect to both strains. By constructing the suitable stability analysis function the global stability of the disease free equilibrium is proved depending on the basic reproduction number. Furthermore by using other well-known functionals the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number and strain 2 reproduction number. Necessary numerical simulations are performed in order to confirm the theoretical results. Numerical comparison between the model results and clinical data was conducted. The findings of this research includes the model consistence of discordant compartments which are globally asymptotically stable aseptic equilibrium in state have an epidemiological threshold value (also known as basic reproduction rate) less than unity.

Published in	Biomedical Statistics and Informatics (Volume 8, Issue 3)
DOI	10.11648/j.bsi.20230803.11
Page(s)	37-41
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), 2024. Published by Science Publishing Group

Keywords

Epidemic, Incidence, Asymptotically, Threshold, Basic Reproduction Number

References

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[2]	E. Beretta and D. Breda (2018). An SEIR epidemic model with constant latency time and infectious period, Mathematical Biosciences and Engineering, Vol. 8, no. 4, PP. 931-952.
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[4]	K. Dietz (1975). Transmission and control of arbovirus disease, in Epidemiology, K. L. cooke, Ed., Philadelphia, USA, PP. 104-112.
[5]	L. D. Wang and J. Q. Li (2005). Global stability of an epidemic model with nonlinear incidence rate and differential infectivity, Applied Mathematics and computation, Vol. 161, no. 3, PP. 769-778.
[6]	R. M. Anderson and R. M. May (1991). Infectious diseases of humans dynamics and control, Oxford University press, New York, USA, PP. 28-38.
[7]	R. M. Anderson and R. M. Verlag (1982). Population Biology of infectious diseases, Springer, New York, USA, PP. 235-256.
[8]	Z. Feng and J. X. Velasco-Hernandez (1997). Competitive exclusion in a vector-host model for the dengue fever, Journal of Mathematical Biology, Vol. 35, no. 5, PP. 523-544.
[9]	R. M. Anderson and R. M. Verlag (1989). Competitive exclusion in a parasitic model Population Biology of infectious diseases, Springer, New York, USA, PP. 836-858.
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[12]	E. Hayeti and D. Breda (2017). An SIR epidemic model with inconsistent latency infectious period, Mathematical Biosciences and Engineering, Vol. 3, no. 3, PP. 654-676.
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[15]	N. Bacaer, H. W. Hethcote, D. Breda (2018). Wavering in seasonally forced epidemiological models, Journal of Mathematical Biology, Vol. 89, no. 8, PP. 118-148.

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APA Style

Sumit Kumar Banerjee, Boaz Andrews. (2023). Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate. Biomedical Statistics and Informatics, 8(3), 37-41. https://doi.org/10.11648/j.bsi.20230803.11

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ACS Style

Sumit Kumar Banerjee; Boaz Andrews. Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate. Biomed. Stat. Inform. 2023, 8(3), 37-41. doi: 10.11648/j.bsi.20230803.11

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AMA Style

Sumit Kumar Banerjee, Boaz Andrews. Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate. Biomed Stat Inform. 2023;8(3):37-41. doi: 10.11648/j.bsi.20230803.11

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@article{10.11648/j.bsi.20230803.11,
  author = {Sumit Kumar Banerjee and Boaz Andrews},
  title = {Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate},
  journal = {Biomedical Statistics and Informatics},
  volume = {8},
  number = {3},
  pages = {37-41},
  doi = {10.11648/j.bsi.20230803.11},
  url = {https://doi.org/10.11648/j.bsi.20230803.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20230803.11},
  abstract = {A passivity SEIR epidemic model with inconsistent incidence rate embedded with latency period for the imparting dynamics of epidemics is succeed and thoroughly inspected. The problem is constructed by a system of nonlinear ordinary differential equations analyzing the evaluation of susceptible, exposed, infected and removed individuals. The suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points have been discussed, namely, the disease free equilibrium, endemic equilibrium with respect to strain 1, endemic equilibrium with respect to strain 2 and the terminal endemic equilibrium with respect to both strains. By constructing the suitable stability analysis function the global stability of the disease free equilibrium is proved depending on the basic reproduction number. Furthermore by using other well-known functionals the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number and strain 2 reproduction number. Necessary numerical simulations are performed in order to confirm the theoretical results. Numerical comparison between the model results and clinical data was conducted. The findings of this research includes the model consistence of discordant compartments which are globally asymptotically stable aseptic equilibrium in state have an epidemiological threshold value (also known as basic reproduction rate) less than unity.},
 year = {2023}
}

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TY  - JOUR
T1  - Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate
AU  - Sumit Kumar Banerjee
AU  - Boaz Andrews
Y1  - 2023/09/18
PY  - 2023
N1  - https://doi.org/10.11648/j.bsi.20230803.11
DO  - 10.11648/j.bsi.20230803.11
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 37
EP  - 41
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20230803.11
AB  - A passivity SEIR epidemic model with inconsistent incidence rate embedded with latency period for the imparting dynamics of epidemics is succeed and thoroughly inspected. The problem is constructed by a system of nonlinear ordinary differential equations analyzing the evaluation of susceptible, exposed, infected and removed individuals. The suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points have been discussed, namely, the disease free equilibrium, endemic equilibrium with respect to strain 1, endemic equilibrium with respect to strain 2 and the terminal endemic equilibrium with respect to both strains. By constructing the suitable stability analysis function the global stability of the disease free equilibrium is proved depending on the basic reproduction number. Furthermore by using other well-known functionals the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number and strain 2 reproduction number. Necessary numerical simulations are performed in order to confirm the theoretical results. Numerical comparison between the model results and clinical data was conducted. The findings of this research includes the model consistence of discordant compartments which are globally asymptotically stable aseptic equilibrium in state have an epidemiological threshold value (also known as basic reproduction rate) less than unity.
VL  - 8
IS  - 3
ER  -

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Author Information

Sumit Kumar Banerjee

Department of Mathematics & Computer Science, PNG University of Technology, Lae, Papua New Guinea
Boaz Andrews

Department of Mathematics & Computer Science, PNG University of Technology, Lae, Papua New Guinea

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APA Style

Sumit Kumar Banerjee, Boaz Andrews. (2023). Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate. Biomedical Statistics and Informatics, 8(3), 37-41. https://doi.org/10.11648/j.bsi.20230803.11

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ACS Style

Sumit Kumar Banerjee; Boaz Andrews. Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate. Biomed. Stat. Inform. 2023, 8(3), 37-41. doi: 10.11648/j.bsi.20230803.11

Copy | Download

AMA Style

Sumit Kumar Banerjee, Boaz Andrews. Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate. Biomed Stat Inform. 2023;8(3):37-41. doi: 10.11648/j.bsi.20230803.11

Copy | Download

@article{10.11648/j.bsi.20230803.11,
  author = {Sumit Kumar Banerjee and Boaz Andrews},
  title = {Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate},
  journal = {Biomedical Statistics and Informatics},
  volume = {8},
  number = {3},
  pages = {37-41},
  doi = {10.11648/j.bsi.20230803.11},
  url = {https://doi.org/10.11648/j.bsi.20230803.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20230803.11},
  abstract = {A passivity SEIR epidemic model with inconsistent incidence rate embedded with latency period for the imparting dynamics of epidemics is succeed and thoroughly inspected. The problem is constructed by a system of nonlinear ordinary differential equations analyzing the evaluation of susceptible, exposed, infected and removed individuals. The suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points have been discussed, namely, the disease free equilibrium, endemic equilibrium with respect to strain 1, endemic equilibrium with respect to strain 2 and the terminal endemic equilibrium with respect to both strains. By constructing the suitable stability analysis function the global stability of the disease free equilibrium is proved depending on the basic reproduction number. Furthermore by using other well-known functionals the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number and strain 2 reproduction number. Necessary numerical simulations are performed in order to confirm the theoretical results. Numerical comparison between the model results and clinical data was conducted. The findings of this research includes the model consistence of discordant compartments which are globally asymptotically stable aseptic equilibrium in state have an epidemiological threshold value (also known as basic reproduction rate) less than unity.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate
AU  - Sumit Kumar Banerjee
AU  - Boaz Andrews
Y1  - 2023/09/18
PY  - 2023
N1  - https://doi.org/10.11648/j.bsi.20230803.11
DO  - 10.11648/j.bsi.20230803.11
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 37
EP  - 41
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20230803.11
AB  - A passivity SEIR epidemic model with inconsistent incidence rate embedded with latency period for the imparting dynamics of epidemics is succeed and thoroughly inspected. The problem is constructed by a system of nonlinear ordinary differential equations analyzing the evaluation of susceptible, exposed, infected and removed individuals. The suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points have been discussed, namely, the disease free equilibrium, endemic equilibrium with respect to strain 1, endemic equilibrium with respect to strain 2 and the terminal endemic equilibrium with respect to both strains. By constructing the suitable stability analysis function the global stability of the disease free equilibrium is proved depending on the basic reproduction number. Furthermore by using other well-known functionals the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number and strain 2 reproduction number. Necessary numerical simulations are performed in order to confirm the theoretical results. Numerical comparison between the model results and clinical data was conducted. The findings of this research includes the model consistence of discordant compartments which are globally asymptotically stable aseptic equilibrium in state have an epidemiological threshold value (also known as basic reproduction rate) less than unity.
VL  - 8
IS  - 3
ER  -

Copy | Download