Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Arshad, SadiaScopus Q: search.filters.scopusQuartile.Q1

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  • Article
    Citation - WoS: 174
    Citation - Scopus: 199
    A New Fractional Modelling and Control Strategy for the Outbreak of Dengue Fever
    (Elsevier, 2019) Arshad, Sadia; Baleanu, Dumitru; Jajarmi, Amin
    This paper deals with a new mathematical model for a dengue fever outbreak based on a system of fractional differential equations. The equilibrium points and stability of the new system are studied. To simulate this model, a new and efficient numerical method is provided and its stability and convergence are proved. According to a real outbreak on the Cape Verde Islands occurred in year 2009, the new model is examined for a period of three months by using singular or nonsingular kernels in the definition of derivative operator. Simulation results show that the proposed formalism with exponential kernel agrees well with the real data in the early stage of the epidemic while the Mittag-Leffler kernel fits the reality for the later part of the time interval. Hence, the new framework in a hybrid manner can properly simulate the dynamics of the disease in the whole of the time interval. In order to stabilize the disease-free equilibrium point of the system under investigation, two control strategies are suggested. Numerical simulations verify that the proposed stabilizing controllers are efficient and provide significantly remarkable results. (C) 2019 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 39
    Citation - Scopus: 42
    A Second Order Accurate Approximation for Fractional Derivatives With Singular and Non-Singular Kernel Applied To a Hiv Model
    (Elsevier Science inc, 2020) Baleanu, Dumitru; Arshad, Sadia; Defterli, Ozlem
    In this manuscript we examine the CD4(+) T cells model of HIV infection under the consideration of two different fractional differentiation operators namely Caputo and Caputo-Fabrizio (CF). Moreover, the generalized HIV model is investigated by considering Reverse Transcriptase (RT) inhibitors as a drug treatment for HIV. The threshold values for the stability of the equilibrium point belonging to non-infected case are calculated for both models with and without treatment. For the numerical solutions of the studied model, we construct trapezoidal approximation schemes having second order accuracy for the approximation of fractional operators with singular and non-singular kernel. The stability and convergence of the proposed schemes are analyzed analytically. To illustrate the dynamics given by these two fractional operators, we perform numerical simulations of the HIV model for different biological scenarios with and without drug concentration. The studied biological cases are identified by considering different values of the parameters such as infection rate, growth rate of CD4(+) T cells, clearance rate of virus particles and also the order of the fractional derivative. (C) 2020 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 28
    Citation - Scopus: 34
    Optimal Chemotherapy and Immunotherapy Schedules for a Cancer-Obesity Model With Caputo Time Fractional Derivative
    (Wiley, 2018) Arshad, Sadia; Baleanu, Dumitru; Akman Yildiz, Tugba
    This work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy and immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population and minimize the drug dose over a finite time interval. The constraint is a model including tumor cells, immune cells, fat cells, and chemotherapeutic and immunotherapeutic drug concentrations with the Caputo time fractional derivative. We investigate the existence and stability of the equilibrium points, namely, tumor-free equilibrium and coexisting equilibrium, analytically. We discretize the cancer-obesity model using the L1 method. Simulation results of the proposed model are presented to compare three different treatment strategies: chemotherapy, immunotherapy, and their combination. In addition, we investigate the effect of the differentiation order alpha and the value of the decay rate of the amount of chemotherapeutic drug to the value of the cost functional. We find out the optimal treatment schedule in case of chemotherapy and immunotherapy.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 28
    New Observations on Optimal Cancer Treatments for a Fractional Tumor Growth Model With and Without Singular Kernel
    (Pergamon-elsevier Science Ltd, 2018) Arshad, Sadia; Baleanu, Dumitru; Akman Yildiz, Tugba
    The aim of this study is to examine a fractional optimal control problem (FOCP) governed by a cancer-obesity model with and without singular kernel, separately. We propose a new model including the population of immune cells, tumor cells, normal cells, fat cells, chemotherapeutic and immunotherapeutic drug concentrations. Existence and stability of the tumor free equilibrium point and coexisting equilibrium point are investigated analytically. We obtain the numerical solution of the fractional cancer-obesity model using L1 formula. The aim behind the FOCP is to find the optimal doses of chemotherapeutic and immunotherapeutic drugs which minimize the difference between the number of tumor cells and normal cells. To do so, we insert some weight constants as the coefficients of tumor and normal cells in the cost functional so that normal cell population is larger compared to tumor burden. On the other hand, we investigate the effect of obesity to the choice and schedules of treatment strategies in case of low and high caloric diets. Moreover, we discuss the choice of the differentiation operator, namely operators with and without singular kernel. Lastly, some illustrative examples are shown to examine the impact of the fractional derivatives of different orders on cancer-obesity model and we observe the contribution of the cost functional to eradicate tumor burden and regenerate normal cell population. Our model predicts the negative effect of obesity on the health of patient and we show that the most efficient treatment choice to eradicate the tumor is to apply combined therapy together with low caloric diet. (C) 2018 Elsevier Ltd. All rights reserved.