Biomedical Statistics and Informatics

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Analysis of SEIR Epidemic Model Engraft with Incompatible Incidence Rate

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.

DOI 10.11648/j.bsi.20230803.11
Published in Biomedical Statistics and Informatics (Volume 8, Issue 3, September 2023)
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
[1] C. Rebelo, A. Margheri and N. Bacaer (2012). Persistence in seasonally forced epidemiological models, Journal of Mathematical Biology, Vol. 64, no. 6, PP. 933-949.
[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.
[3] H. W. Hethcote (2015). Mathematics of infectious diseases, SIAM review, Vol. 42, no. 4, PP. 599-653.
[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.
[10] H. W. Hethcote, D. Breda (2017). Mathematics of epidemiological stabalities, SIAM review, Vol. 8, no. 1, PP. 217-235.
[11] J. Q. Li and H. W. Hethcote (2014). Global stability of an epidemic model with linear incidence rate and differential infectivity, Applied Mathematics and computation, Vol. 138, no. 7, PP. 869-878.
[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.
[13] A. Margheri and P. Helderson (2016). Nonlinear seasonally forced epidemiological models, Journal of Mathematical Biology, Vol. 52, no. 4, PP. 833-862.
[14] H. W. Hethcote and L. D. Wang (2017). Mathematics of inconsistent incidence rate of infectious diseases, SIAM review, Vol. 48, no. 7, PP. 233-287.
[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
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    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
  • Department of Mathematics & Computer Science, PNG University of Technology, Lae, Papua New Guinea

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

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