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Global dynamics of an epidemic model with standard incidence rate and vaccination strategy

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  • Parsamanesh, Mahmood
  • Erfanian, Majid

Abstract

We study an SIS epidemic model with a constant recruitment. The disease-related death is included in the model and total population size is variable. A vaccination program also affects both new members and susceptible individuals. Two equilibria of the model; the disease-free equilibrium (DFE) and the endemic equilibrium (EE), and the basic reproduction number R0, are obtained. It is shown that DFE is locally and also globally asymptotically stable if R0<1. Furthermore, it is proven that EE is locally asymptotically stable when R0>1. In addition, in this case some conditions for global asymptotic stability of EE are found by using Lyapunov’s direct method. Finally, some numerical simulations are presented to verify obtained theoretical results.

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  • Parsamanesh, Mahmood & Erfanian, Majid, 2018. "Global dynamics of an epidemic model with standard incidence rate and vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 192-199.
    • Handle: RePEc:eee:chsofr:v:117:y:2018:i:c:p:192-199
    DOI: 10.1016/j.chaos.2018.10.022
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    References listed on IDEAS

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    1. Dawei Zhao & Lianhai Wang & Shudong Li & Zhen Wang & Lin Wang & Bo Gao, 2014. "Immunization of Epidemics in Multiplex Networks," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-5, November.
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    3. Rahman Farnoosh & Mahmood Parsamanesh, 2017. "Stochastic differential equation systems for an SIS epidemic model with vaccination and immigration," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8723-8736, September.
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    Cited by:

    1. Parsamanesh, Mahmood & Erfanian, Majid, 2021. "Stability and bifurcations in a discrete-time SIVS model with saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Hossain, Mainul & Pal, Nikhil & Samanta, Sudip, 2020. "Impact of fear on an eco-epidemiological model," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Das, Tanuja & Srivastava, Prashant K., 2023. "Effect of a novel generalized incidence rate function in SIR model: Stability switches and bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Khan, Tahir & Ullah, Zakir & Ali, Nigar & Zaman, Gul, 2019. "Modeling and control of the hepatitis B virus spreading using an epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 1-9.
    5. Jorge E. Macías-Díaz & Nauman Ahmed & Muhammad Rafiq, 2019. "Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model," Mathematics, MDPI, vol. 7(12), pages 1-16, December.

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