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Dynamical Analysis and Simulation of a General Two-Strain SEIR Epidemic Model with Caputo Fractional Derivative and Vaccination |
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PP: 311-332 |
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doi:10.18576/pfda/110207
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Author(s) |
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Manal M. Hikal,
Tamer E. M. Atteya,
Hamed M. Hemeda,
Assem Elshenawy,
Waheed K. Zahra,
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Abstract |
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| In this study, the dynamical behavior of a two-strain SEIR epidemic model with fractional order of differentiation and having general non-linear incidence rates. The mathematical representation of the epidemic model is given and the constant solution is evaluated according to the reproduction number of the two strains. The boundedness and uniqueness of the solution are studied. The stability of the model has been investigated by examining the stability of each constant solution of the system. Constructing appropriate Lyapunov functions helps to investigate the global stability of the system’s constant solutions. A new numerical technique based on approximating the Caputo fractional order derivative by difference schemes of a high-order approximation of the L2 type. This scheme is called ”The Non-uniform L2 Fractional differentiation numerical scheme (NU L2 FDNS)” which is used to verify the analytically proven results and also clarify the effect of system transactions on the control of the disease. Especially the vaccination rate controls the disease very well.
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