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, SadiaCOAR Access Rights: search.filters.coarAccessRights.open access

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Now showing 1 - 4 of 4
  • 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: 32
    Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations With Riesz Derivative
    (Mdpi, 2018) Baleanu, Dumitru; Huang, Jianfei; Al Qurashi, Maysaa Mohamed; Tang, Yifa; Zhao, Yue; Arshad, Sadia
    In this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space derivative is approximated by the second-order fractional weighted and shifted Grunwald-Letnikov formula. Based on the equivalence between the fractional differential equation and the integral equation, we have transformed the fractional differential equation into an equivalent integral equation. Then, the integral is approximated by the trapezoidal formula. Further, the stability and convergence analysis are discussed rigorously. The resulting scheme is formally proved with the second order accuracy both in space and time. Numerical experiments are also presented to verify the theoretical analysis.
  • Article
    Citation - WoS: 39
    Citation - Scopus: 52
    Effects of Hiv Infection on Cd4<sup>+</Sup> T-Cell Population Based on a Fractional-Order Model
    (Springeropen, 2017) Baleanu, Dumitru; Bu, Weiping; Tang, Yifa; Arshad, Sadia
    In this paper, we study the HIV infection model based on fractional derivative with particular focus on the degree of T-cell depletion that can be caused by viral cytopathicity. The arbitrary order of the fractional derivatives gives an additional degree of freedom to fit more realistic levels of CD4(+) cell depletion seen in many AIDS patients. We propose an implicit numerical scheme for the fractional-order HIV model using a finite difference approximation of the Caputo derivative. The fractional system has two equilibrium points, namely the uninfected equilibrium point and the infected equilibrium point. We investigate the stability of both equilibrium points. Further we examine the dynamical behavior of the system by finding a bifurcation point based on the viral death rate and the number of new virions produced by infected CD4(+) T-cells to investigate the influence of the fractional derivative on the HIV dynamics. Finally numerical simulations are carried out to illustrate the analytical results.
  • Article
    Citation - WoS: 48
    Citation - Scopus: 58
    Dynamical Analysis of Fractional Order Model of Immunogenic Tumors
    (Sage Publications Ltd, 2016) Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Al Qurashi, Maysaa Mohamed; Arshad, Sadia
    In this article, we examine the fractional order model of the cytotoxic T lymphocyte response to a growing tumor cell population. We investigate the long-term behavior of tumor growth and explore the conditions of tumor elimination analytically. We establish the conditions for the tumor-free equilibrium and tumor-infection equilibrium to be asymptotically stable and provide the expression of the basic reproduction number. Existence of physical significant tumor-infection equilibrium points is investigated analytically. We show that tumor growth rate, source rate of immune cells, and death rate of immune cells play vital role in tumor dynamics and system undergoes saddle-node and transcritical bifurcation based on these parameters. Furthermore, the effect of cancer treatment is discussed by varying the values of relevant parameters. Numerical simulations are presented to illustrate the analytical results.