GLOBAL STABILITY IN A PATHOGEN-SPECIFIC CD8 IMMUNE RESPONSE PREDICTION MODEL

Bekiryazici, Zafer/0000-0001-5671-9995WOS: 000522760300008In this study, a system of ordinary differential equations used for modeling pathogen-specific CD8 cell immune response is studied. the positivity and the limitation of the model solutions are proven. the equilibrium points in the cases with the presence and the absence of the pathogen are determined and their stabilities are investigated. Furthermore, the essential reproduction number is obtained for the system. the conditions of the reproduction number for the stability of the equilibrium are shown and numerical examples are given for supporting the analytical results.Gumushane University Scientific Research Project [17, F5121.02.01]This work was supported by the Gumushane University Scientific Research Project under the Grant No. 17.F5121.02.0

Generalized Beta Parameters for a SVEIR-Type Random Model of Polio Transmission

7th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA) -- AUG 28-31, 2018 -- Kyiv, UKRAINEBekiryazici, Zafer/0000-0001-5671-9995WOS: 000469338300004In 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

Modification of the random differential transformation method and its applications to compartmental models

Bekiryazici, Zafer/0000-0001-5671-9995WOS: 000508292800001In this study, a modification of the random differential transformation method is given by using Laplace-Pade 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

Modelling of Cohesive -Sediment Depositional Areas Carried by the Solakh River to the Eastern Black-Sea

Bekiryazici, Zafer/0000-0001-5671-9995WOS: 000433524500026In this study, cohesive sediment depositional areas carried by the Solakh River to the Eastern Black-Sea are examined in the marine environment. Effects of changes in the amount of cohesive sediment entering the sea from Solakh River, sediment drift velocity, direction and magnitude of wind-stream components are observed. For high sediment drift velocity, it is found that the affects of wind-stream components on deposition areas of cohesive sediment are very little. According to the results of the study, entrance angle of the stream mouth effects the deposition areas of sediment in the marine environment. Cohesive sediment depositional areas are examined on the charts by changing one of the parameters in the sediment transport model while keeping others constant.European UnionEuropean Union (EU) [TR9CI.01-02/298]This study was supported by the European Union under project number TR9CI.01-02/298. the title of the project is "Integrated coastal monitoring of environmental problems in the port sea region and the ways of their solution-ICME

Modelling of Cohesive –Sediment Depositional Areas Carried by the Solaklı River to the Eastern Black-Sea

721-728In this study, cohesive sediment depositional areas carried by the Solaklı River to the Eastern Black-Sea are examined in the marine environment. Effects of changes in the amount of cohesive sediment entering the sea from Solaklı River, sediment drift velocity, direction and magnitude of wind-stream components are observed. For high sediment drift velocity, it is found that the affects of wind-stream components on deposition areas of cohesive sediment are very little. According to the results of the study, entrance angle of the stream mouth effects the deposition areas of sediment in the marine environment. Cohesive sediment depositional areas are examined on the charts by changing one of the parameters in the sediment transport model while keeping others constant

A modification of approximate random characteristics for a model of Zika virus transmission

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

ANALYZING THE DYNAMICS OF EBOLA TRANSMISSION WITH RANDOM EFFECTS

Bekiryazici, Zafer/0000-0001-5671-9995WOS: 000493447400006In this study, a deterministic mathematical model of Ebola transmission is analyzed under random effects. 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 approximate expectation of disease recovery. Furthermore, the approximation for expected recovery is modified by using Laplace-Pade method. Comparison of results indicate that the Laplace-Pade modification provides a better approximation. We also interpret the long term random behavior of the disease dynamics using simulation results

Values and descriptions of the parameters of the model [7].

<p>Values and descriptions of the parameters of the model [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181571#pone.0181571.ref007" target="_blank">7</a>].</p

Variances of <i>T</i>(<i>t</i>), <i>I</i>(<i>t</i>) and <i>V</i>(<i>t</i>).

<p>Variances of <i>T</i>(<i>t</i>), <i>I</i>(<i>t</i>) and <i>V</i>(<i>t</i>).</p

Confidence intervals of <i>T</i>(<i>t</i>), <i>I</i>(<i>t</i>) and <i>V</i>(<i>t</i>).

<p>Confidence intervals of <i>T</i>(<i>t</i>), <i>I</i>(<i>t</i>) and <i>V</i>(<i>t</i>).</p