Sürdürülebilir Kalkınma Amaçları
Yayınlar
- MakaleAçık Erişim2022A 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
- MakaleAçık Erişim2022Homotopy Perturbation Elzaki Transform Method for Obtaining the Approximate Solutions of the Random Partial Differential Equations
Anac, Halil; Merdan, Mehmet; Kesemen, Tulay
The series solutions of the random nonlinear partial differential equations have been examined by a hybrid method. The random nonlinear partial differential equations are studied by both normal and uniform distributions. Two initial-value problems are indicated to exemplify the influence of the solutions acquired by the hybrid method. Also, the functions for the first and second moments of the approximate solutions of random nonlinear partial differential equations are acquired in the MAPLE software. The hybrid method is implemented to analyze the solutions of the random nonlinear partial differential equations. MAPLE software is used to find the solutions. Besides, MAPLE software is used for the drawing the figures.
- MakaleAçık Erişim2022Transmission 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.
- MakaleYalnız künye2021Modification of the random differential transformation method and its applications to compartmental models
Bekiryazici, Zafer; Merdan, Mehmet; Kesemen, Tulay
In this study, a modification of the random differential transformation method is given by using Laplace-Padé method. The modification, which has previously been introduced for the deterministic differential transformation method (DTM), is used to obtain improved approximate expected values, variances, and confidence intervals for systems of random differential equations. Comparison of approximate results obtained from the random differential transformation method and the modified method are given to underline the improvement of the approximations. Epidemiological compartmental models of type SIR and SIIR are used to implement the modified method and demonstrate its advantages. Simulations and deterministic counterparts of the models are also investigated to confirm the suitability of the results of the approximations.
- MakaleAçık Erişim2018ANALYZING 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.
- BildiriYalnız künye2018Generalized beta parameters for a SVEIR-type random model of Polio transmission
Bekiryazici, Zafer; Merdan, Mehmet; Kesemen, Tulay; Tosun, M.
In this study, a SVEIR-type compartmental model of Poliomyelitis transmission is examined under random effects. We introduce Generalized Beta and normal distributed random parameters into the equation system to investigate the random dynamics of the disease. The approximate analytical solution of the model under random effects is obtained by using Random Differential Transformation Method (RDTM). Results from simulations and RDTM are analyzed to comment on the randomness of the compartments and disease transmission. It is seen that the random model successfully provides similar results that can be obtained through the deterministic model while providing additional information on the random behavior of the disease, such as the standard deviations and the variation coefficients.
- MakaleAçık Erişim2017Deterministic 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.
- MakaleAçık Erişim2017Comparison 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.