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- MakaleYalnız künye2023Scopus SJRQ4MODELING DISEASE TRANSMISSION DYNAMICS WITH RANDOM DATA AND HEAVY TAILED RANDOM EFFECTS: THE ZIKA CASE
Bekiryazici, Z.; Kesemen, T.; Merdan, M.; Khaniyev, T.
In this study, we investigate a compartmental model of Zika Virus transmission under random effects. Random effects enable the analysis of random numerical characteristics of transmission, which cannot be modeled through deterministic equations. Data obtained from Zika studies in the literature are used along with heavy tailed random effects to obtain new random variables for the parameters of the deterministic model. Finally, simulations of the model are carried out to analyze the random dynamics of Zika Virus transmission. Deterministic results are compared with results from the simulations of the random system to underline the advantages of a random modeling approach. It is shown that the random model provides additional results for disease transmission dynamics such as results for standard deviation and coefficients of variation, making it a valuable alternative to deterministic modeling. Random results suggest around 90% - 120% coefficient of variation for the random model underlining the fact that the randomness should not be ignored for the transmission of this disease.
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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 - MakaleYalnız künye2021Scopus SJRQ3Modification 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.
AtıfScopus14WoS12OpenAlex19İncele - 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 - 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.
AtıfScopus1WoS1İncele - 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.
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