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- MakaleAçık Erişim2022Scopus SJRQ3A MODIFICATION OF APPROXIMATE RANDOM CHARACTERISTICS FOR A MODEL OF ZIKA VIRUS TRANSMISSION
Bekiryazici, Zafer; Kesemen, Tulay; Merdan, Mehmet; Khaniyev, Tahir
In this study, a theoretical model of Zika virus transmission is investigated with random parameters. The parameters of a deterministic model are transformed to random variables to obtain a system of random differential equations. The approximate solutions of the model are analyzed with modified random differential transformation method. It is seen that modified random differential transformation method performs better than random differential transformation method on long time intervals
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İncele - MakaleAçık Erişim2022Scopus SJRQ4Transmission of Cholera Disease with Laplacian and Triangular Parameters
Merdan, Mehmet; Bekiryazici, Zafer; Kesemen, Tulay; Khaniyev, Tahir
A mathematical model has been introduced for the transmission dynamics of cholera disease by GQ Sun et al. recently. In this study, we add Laplacian and Triangular random effects to this model and analyze the variation of results for both cases. The expectations and co-efficients of variation are compared for the random models and the results are used to comment on the differences and similarities between the effects of these probability distributions. The randomness of the model itself is also investigated through comparison of the random and deterministic outcomes.
AtıfOpenAlex1İncele - MakaleAçık Erişim2018Scopus SJRQ3ANALYZING THE DYNAMICS OF EBOLA TRANSMISSION WITH RANDOM EFFECTS
Merdan, Mehmet; Bekiryazici, Zafer; Kesemen, Tulay; Khaniyev, Tahir
In this study, a deterministic mathematical model of Ebola transmission is analyzed under random ef-fects. A recent compartmental model of Berge et al. incorporates both direct and indirect transmission in the model. We assume the parameters of this model are normally distributed random variables to investigate the random behavior of disease transmission. Random differential transformation method is used to obtain the ap-proximate expectation of disease recovery. Furthermore, the approximation for expected recovery is modified by using Laplace-Padé method. Comparison of results indicate that the Laplace-Padé modification provides a better approximation. We also interpret the long term random behavior of the disease dynamics using simulation results.
AtıfScopus3WoS2OpenAlex3İncele - MakaleAçık Erişim2017Scopus SJRQ1Deterministic stability and random behavior of a Hepatitis C model
Merdan, Mehmet; Bekiryazici, Zafer; Kesemen, Tulay; Khaniyev, Tahir
The deterministic stability of a model of Hepatitis C which includes a term defining the effect of immune system is studied on both local and global scales. Random effect is added to the model to investigate the random behavior of the model. The numerical characteristics such as the expectation, variance and confidence interval are calculated for random effects with two different distributions from the results of numerical simulations. In addition, the compliance of the random behavior of the model and the deterministic stability results is examined.
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İncele - MakaleAçık Erişim2017Scopus SJRQ2Comparison of stochastic and random models for bacterial resistance
Merdan, Mehmet; Bekiryazici, Zafer; Kesemen, Tulay; Khaniyev, Tahir
In this study, a mathematical model of bacterial resistance considering the immune system response and antibiotic therapy is examined under random conditions. A random model consisting of random differential equations is obtained by using the existing deterministic model. Similarly, stochastic effect terms are added to the deterministic model to form a stochastic model consisting of stochastic differential equations. The results from the random and stochastic models are also compared with the results of the deterministic model to investigate the behavior of the model components under random conditions.
AtıfScopus25WoS25OpenAlex25İncele - MakaleAçık Erişim2016Scopus SJRQ4On the fractional Riccati differential equation
Khaniyev, Tahir; Merdan, Mehmet
In this paper, We tried to find an analytical solution of nonlinear Riccati conformable fractional differential equation. Fractional derivatives are described in the conformable derivative. The behavior of the solutions and the effects of different values of fractional order α are presented graphically and table. The results obtained by the CFD(conformable fractional derivative) are compared with homotopy perturbation method(HPM), fractional variational iteration method(FVIM).
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