Jatropha Curcas Linnaeous(Jatropha Curcas L)is a wonder plant with a variety of applications and enormous economic potential.Biodiesel,an alternative fuel from non edible vegetable oil of Jatropha Curcas plant,has the...Jatropha Curcas Linnaeous(Jatropha Curcas L)is a wonder plant with a variety of applications and enormous economic potential.Biodiesel,an alternative fuel from non edible vegetable oil of Jatropha Curcas plant,has the requisite potential of providing a promising and commercially viable alternative to diesel oil since it has the desirable physicochemical and performance characteristics comparable to diesel.This alternative fuel is eco-friendly,cost effective and has the huge potentiality for the future generations throughout the world.For effective cultivation of this plant, protection from different viral diseases is essential.In this paper,we describe the eco-epidemiological model of the plant Jatropha Curcas L for understanding the disease dynamics which helps to control the viral infection of the Jatropha Curcas plant cell.By this approach,this plant can grow ideally for the renewable green fuel of the future world.展开更多
Due to the unpredictable growth of tumor cells,the tumor-immune interactive dynamics continues to draw attention from both applied mathematicians and oncologists.Math-ematical modeling is a powerful tool to improve ou...Due to the unpredictable growth of tumor cells,the tumor-immune interactive dynamics continues to draw attention from both applied mathematicians and oncologists.Math-ematical modeling is a powerful tool to improve our understanding of the complicated biological system for tumor growth.With this goal,we report a mathematical model which describes how turmor cells evolve and survive the brief encounter with the immune system mediated by immune effector cells and host cells which includes discrete time delay.We analyze the basic mathematical properties of the considered model such as positivity of the system and the boundedness of the solutions.By analyzing the distri-bution of eigenvalucs,local stability analysis of the biologically feasible equilibria and the existence of Hopf bifurcation are obtained in which discrete time delay is used as a bifurcation parameter.Based on the normal form theory and center manifold theorem,we obtain explicit expressions to determine the direction of Hopf bifurcation and the stability of Hopf bifurcating periodic solutions.Numerical simulations are carried out to illustrate the rich dynamical behavior of the delayed tumor model.Our model simula-tions demonstrate that the delayed tumor model exhibits regular and irregular periodic oscillations or chaotic behaviors,which indicate the scenario of long-term tumor relapse.展开更多
基金supported by the Department of Mathematics,Jadavpur University,PURSE DST, Government of India
文摘Jatropha Curcas Linnaeous(Jatropha Curcas L)is a wonder plant with a variety of applications and enormous economic potential.Biodiesel,an alternative fuel from non edible vegetable oil of Jatropha Curcas plant,has the requisite potential of providing a promising and commercially viable alternative to diesel oil since it has the desirable physicochemical and performance characteristics comparable to diesel.This alternative fuel is eco-friendly,cost effective and has the huge potentiality for the future generations throughout the world.For effective cultivation of this plant, protection from different viral diseases is essential.In this paper,we describe the eco-epidemiological model of the plant Jatropha Curcas L for understanding the disease dynamics which helps to control the viral infection of the Jatropha Curcas plant cell.By this approach,this plant can grow ideally for the renewable green fuel of the future world.
基金the Indo-French Centre for Applied Mathe-matics(IFCAM)(Grant No.MA/IFCAM/18/50).
文摘Due to the unpredictable growth of tumor cells,the tumor-immune interactive dynamics continues to draw attention from both applied mathematicians and oncologists.Math-ematical modeling is a powerful tool to improve our understanding of the complicated biological system for tumor growth.With this goal,we report a mathematical model which describes how turmor cells evolve and survive the brief encounter with the immune system mediated by immune effector cells and host cells which includes discrete time delay.We analyze the basic mathematical properties of the considered model such as positivity of the system and the boundedness of the solutions.By analyzing the distri-bution of eigenvalucs,local stability analysis of the biologically feasible equilibria and the existence of Hopf bifurcation are obtained in which discrete time delay is used as a bifurcation parameter.Based on the normal form theory and center manifold theorem,we obtain explicit expressions to determine the direction of Hopf bifurcation and the stability of Hopf bifurcating periodic solutions.Numerical simulations are carried out to illustrate the rich dynamical behavior of the delayed tumor model.Our model simula-tions demonstrate that the delayed tumor model exhibits regular and irregular periodic oscillations or chaotic behaviors,which indicate the scenario of long-term tumor relapse.
