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QUALITATIVE ANALYSIS OF SEIRS ENDEMIC MODEL BOTH FROM PDEs AND ODEs PERSPECTIVE

Author

Listed:
  • LEI ZHANG

    (School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, P. R. China)

  • TAREQ SAEED

    (��Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia)

  • MIAO-KUN WANG

    (��Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China§Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China)

  • NUDRAT AAMIR

    (�Department of Basic Sciences and Humanities, CECOS University of IT and Emerging Sciences, Peshawar, Pakistan)

  • MUHAMMAD IBRAHIM

    (��Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia¶Department of Basic Sciences and Humanities, CECOS University of IT and Emerging Sciences, Peshawar, Pakistan)

Abstract

An age-structured susceptible–exposed–infected–recovered–susceptible (SEIRS) endemic model is proposed in this analysis utilizing the tools of partial differential equations. Because of different outflows and inflows that are lopsided by migration and demographics factors, the population is supposed to be not constant. To demonstrate that the model is well-posed, an abstract Cauchy problem is developed from the proposed system. The simple reproduction number R0 is used to analyze the local and global behavior of the disease-free equilibrium. The disease present equilibrium point is shown to exist and be stable locally under appropriate assumptions and conditions. We consider the age-free parameters and the problem is converted into an ordinary differential equations (ODEs) model. The ODEs model is investigated for disease-free and endemic equilibria and the global stability of each equilibrium is presented therein. A few simulations are carried out and discussed at the end of the paper to explain the central theorem of the study.

Suggested Citation

  • Lei Zhang & Tareq Saeed & Miao-Kun Wang & Nudrat Aamir & Muhammad Ibrahim, 2022. "QUALITATIVE ANALYSIS OF SEIRS ENDEMIC MODEL BOTH FROM PDEs AND ODEs PERSPECTIVE," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-17, August.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401326
    DOI: 10.1142/S0218348X22401326
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