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Design of intelligent computing solver with Morlet wavelet neural networks for nonlinear predator–prey model. Appl Soft Comput 2022. [DOI: 10.1016/j.asoc.2022.109975] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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Umar M, Sabir Z, Raja MAZ. Intelligent computing for numerical treatment of nonlinear prey–predator models. Appl Soft Comput 2019. [DOI: 10.1016/j.asoc.2019.04.022] [Citation(s) in RCA: 75] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Khan MA, Khan Y, Badshah Q, Islam S. Global stability of SEIVR epidemic model with generalized incidence and preventive vaccination. INT J BIOMATH 2015. [DOI: 10.1142/s1793524515500825] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, an SEIVR epidemic model with generalized incidence and preventive vaccination is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number [Formula: see text]. If the basic reproduction number [Formula: see text], the disease-free equilibrium is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number [Formula: see text], the disease is uniformly persistent and the unique endemic equilibrium of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.
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Affiliation(s)
- Muhammad Altaf Khan
- Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan
| | - Yasir Khan
- Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia
| | - Qaiser Badshah
- Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan
| | - Saeed Islam
- Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan
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