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		题名	作者	年代	出处	被引量
	1	Fractional-Order Model of the Disease Psoriasis:A Control Based Mathematical Approach显示文摘Autoimmune diseases are generated through irregular immune response of the human body.Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epidermal Keratinocytes.Dendritic Cells and CD8^+T-Cells have a significant role for the occurrence of this disease.In this paper,the authors have developed a mathematical model of Psoriasis involving CD4^+T-Cells,Dendritic Cells,CD8^+T-Cells and Keratinocyte cell populations using the fractional differential equations with the effect of Cytokine release to observe the impact of memory on the cell-biological system.Using fractional calculus,the authors try to explore the suppressed memory,associated with the cell-biological system and to locate the position of Keratinocyte cell population as fractional derivative possess non-local property.Thus,the dynamics of Psoriasis can be predicted in a better way using fractional differential equations rather than its corresponding integer order model.Finally,the authors introduce drug into the system to obstruct the interaction between CD4^+T-Cells and Keratinocytes to restrict the disease Psoriasis.The authors derive the Euler-Lagrange conditions for the optimality of the drug induced system.Numerical simulations are made through Matlab by developing iterative schemes.	CAO Xianbing DATTA Abhirup AL BASIR Fahad ROY Priti Kumar	2016	Journal of Systems Science & Complexity2016，29，6：	3
	2	Role of antibiotic therapy in bacterial disease:A mathematical study显示文摘	Priti Kumar Roy Yanhui Zhang Priyanka Ghosh Joydeep Pals Fahad Al Basir	2018	International Journal of Biomathematics2018，11，3：	0
	3	A multi-delay model for pest control with awareness induced interventions — Hopf bifurcation and optimal control analysis显示文摘Farming awareness is an important measure for pest controlling in agricultural practice.Time delay in controlling pest may affect the system.Time delay occurs in organizing awareness campaigns,also time delay may takes place in becoming aware of the control strategies or implementing suitable controlling methods informed through social media.Thus we have derived a mathematical model incorporating two time delays into the system and Holling type-II functional response.The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays.Stability changes occur through Hopf-bifurcation when time delays cross the critical values.Optimal control theory has been applied for cost-effectiveness of the delayed system.Numerical simulations are carried out to justify the analytical results.This study shows that optimal farming awareness through radio,TV etc.can control the delay induced bifurcation in a cost-effective way.	Fahad Al Basir	2020	International Journal of Biomathematics2020，13，6：	0

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