For drugs obeying parallel first-order and Michaelis-Menten elimination kinetics,mathematical analysis concerning the optimum dosage regimen of intravenous infusion is conducted and following equations are derived:whe...For drugs obeying parallel first-order and Michaelis-Menten elimination kinetics,mathematical analysis concerning the optimum dosage regimen of intravenous infusion is conducted and following equations are derived:where Xo is the intravenous loading dose,Cb the plasma concentration level desired in clinical therapy,V the apparent distribution volume,k0 the rate constant of intravenouns infusion,K the first－order elimination rate constant,Vm the theoretical maximum rate of the Michaelis－Menten elimination process,Km the Michaelis constant.From this dosage regimen,plasma level maintains a constant Cb during the administration period.When K=0 the dosage regimen above is also suitable for drugs obeying Michaelis-Menten elimination kinetics.展开更多
This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation contain...This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.展开更多
In this paper, we investigated stability and bifurcation behaviors of a predator-prey model with Michaelis-Menten type prey harvesting. Sufficient conditions for local and global asymptotically stability of the interi...In this paper, we investigated stability and bifurcation behaviors of a predator-prey model with Michaelis-Menten type prey harvesting. Sufficient conditions for local and global asymptotically stability of the interior equilibrium point were established. Some critical threshold conditions for transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation were explored analytically. Furthermore, It should be stressed that the fear factor could not only reduce the predator density, but also affect the prey growth rate. Finally, these theoretical results revealed that nonlinear Michaelis-Menten type prey harvesting has played an important role in the dynamic relationship, which also in turn proved the validity of theoretical derivation.展开更多
Traditional May type cooperative model incorporating Michaelis-Menten type harvesting is proposed and studied in this paper. Sufficient conditions which ensure the extinction of the first species and the existence of ...Traditional May type cooperative model incorporating Michaelis-Menten type harvesting is proposed and studied in this paper. Sufficient conditions which ensure the extinction of the first species and the existence of a unique globally attractive positive equilibrium are obtained, respectively. Numeric simulations are carried out to show the feasibility of the main results.展开更多
文摘For drugs obeying parallel first-order and Michaelis-Menten elimination kinetics,mathematical analysis concerning the optimum dosage regimen of intravenous infusion is conducted and following equations are derived:where Xo is the intravenous loading dose,Cb the plasma concentration level desired in clinical therapy,V the apparent distribution volume,k0 the rate constant of intravenouns infusion,K the first－order elimination rate constant,Vm the theoretical maximum rate of the Michaelis－Menten elimination process,Km the Michaelis constant.From this dosage regimen,plasma level maintains a constant Cb during the administration period.When K=0 the dosage regimen above is also suitable for drugs obeying Michaelis-Menten elimination kinetics.
文摘This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.
文摘In this paper, we investigated stability and bifurcation behaviors of a predator-prey model with Michaelis-Menten type prey harvesting. Sufficient conditions for local and global asymptotically stability of the interior equilibrium point were established. Some critical threshold conditions for transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation were explored analytically. Furthermore, It should be stressed that the fear factor could not only reduce the predator density, but also affect the prey growth rate. Finally, these theoretical results revealed that nonlinear Michaelis-Menten type prey harvesting has played an important role in the dynamic relationship, which also in turn proved the validity of theoretical derivation.
基金supported by the National Natural Science Foundation of China under Grant(11601085)the Natural Science Foundation of Fujian Province(2019J01783)
文摘Traditional May type cooperative model incorporating Michaelis-Menten type harvesting is proposed and studied in this paper. Sufficient conditions which ensure the extinction of the first species and the existence of a unique globally attractive positive equilibrium are obtained, respectively. Numeric simulations are carried out to show the feasibility of the main results.
