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- 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.
- 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.