| Citation: |
I. Masti, K. Sayevand, H. Jafari. ON EPIDEMIOLOGICAL TRANSITION MODEL OF THE EBOLA VIRUS IN FRACTIONAL SENSE[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1625-1647. doi: 10.11948/20230319
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ON EPIDEMIOLOGICAL TRANSITION MODEL OF THE EBOLA VIRUS IN FRACTIONAL SENSE
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Abstract
Recently, many researchers have focused on modeling and analyzing various problems in biological phenomena and life sciences such as viruses and nervous system. One of these cases can be seen in the modeling of the Ebola virus. In this paper, we present an efficient method based on properties of Bernstein's operational matrices as well as dual Bernstein for the system of nonlinear equations of Ebola virus in the Caputo fractional sense. The operational matrix of the fractional derivative of order v is obtained based on the dual Bernstein. The proposed dual Bernstein method reduces the solution of the Ebola virus in fractional sense to the solution of a system of nonlinear algebraic equations. The unknown coefficients are obtained by solving the final system of nonlinear equations using the Newton-Raphson method. Another feature of this method is that a reasonable approximate solution can be found with a small number of bases. Moreover, some numerical treatments of fractional models of Ebola Virus are examined. The existence, uniqueness and stability of the suggested methodologies are discussed and proven. Numerical simulations are reported for various fractional orders and by using comparisons between the simulated and measured data, we find the best value of the fractional order. Finally, we will use the data provided by the World Health Organization (WHO) and we compare the fractional Mellin transform, real data, Caputo's derivative, and the classical model. According to the obtained results, the ordinary derivative is less accurate than the fractional order model. In other words, the results showed that fractional order derivatives are superior to classical orders, more reliable and effective in describing biological processes.
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References
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I. Masti, K. Sayevand, H. Jafari. ON EPIDEMIOLOGICAL TRANSITION MODEL OF THE EBOLA VIRUS IN FRACTIONAL SENSE[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1625-1647. doi: 10.11948/20230319
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Figure 1.
Ebola virus [45].
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Figure 2.
Snapshots of the changing shadow of changing fence for
$ I_{t}^{v} $ $ v = 0.75 $ $ S(t) = \frac{1}{2}\sin(t)+t $ $ \Delta t=0.5 $ -
Figure 3.
The fence and its shadows
$ I_{t}^{1} $ $ I_{t}^{v} $ $ v = 0.75 $ $ S(t) = \frac{1}{2}\sin(t)+t $ -
Figure 4.
The process of change of the fence basis shape for
$ I_{t}^{v} $ $ v = 0.75 $ -
Figure 5.
Comparison of real data and approximate method for number of infected people (
$ S_{2}(t) $ -
Figure 6.
Comparison of real data and suggested method for number of infected people (
$ S_{2}(t) $ -
Figure 7.
Comparison of real data and solution of the classic model and the solution of the fractional model.
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Figure 8.
Comparison of real data and suggested method for number of infected people (
$ S_{2}(t) $ $ m=4 $ -
Figure 9.
Comparison of fractional Mellin transform, real data, Caputo derivative and classic model for presented example in Section 6.