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Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate

Muhammad Altaf Khan

Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan

E-mail Address: altafdir@gmail.com

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Yasir Khan

Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia

E-mail Address: yasirmath@yahoo.com

Corresponding author.

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Sehra Khan

Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan

E-mail Address: sehrakhan@yahoo.com

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, and

Saeed Islam

Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan

E-mail Address: saeedislam@wkum.edu.pk

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https://doi.org/10.1142/S1793524516500686Cited by:10 (Source: Crossref)

Abstract

This study considers SEIVR epidemic model with generalized nonlinear saturated incidence rate in the host population horizontally to estimate local and global equilibriums. By using the Routh–Hurwitz criteria, it is shown that if the basic reproduction number $ℛ_{0} < 1$ , the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if $ℛ_{0} < 1$ . The geometric approach is used to present the global stability of the endemic equilibrium. For $ℛ_{0} > 1$ , the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.

Keywords:

AMSC: 92D25, 93D20, 34D23

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