In this paper, we introduced nonstandard finite difference scheme (NSFD) for solving the continuos model with Michaelis-Menten harvesting rate. We have seen that proposed preserve local stability and positivity. Stability analysis of each fixed point discrete time has been proven. Also, numerical comparisons were made between method other methods.

Understanding the mechanism of brain glucose transport across the blood-brain barrier is of importance to understanding brain energy metabolism. The specific kinetics of glucose transport have been generally described using standard Michaelis-Menten kinetics. These models predict that the steady-state glucose concentration approaches an upper limit in the human brain when the plasma glucose lev...

Catalytic isomerization of glucose to fructose by immobilized glucose isomerase in an aqueous-ethanol medium was studied. Using Michaelis-Menten equation and Haldane relationship, the main kinetic parameters were determined: Kmf, Vmf, Kmr, Vmr. By comparing the aqueous-ethanol medium with an aqueous solution, the measured values of Kmr and Kmf were increased in the aqueous-ethanol solution, whi...

OBJECTIVES To test the validity of a Michaelis-Menten-like kinetic model of pulmonary clearance of insoluble dusts. METHODS Data were investigated from studies of pulmonary clearance in F344 rats exposed to antimony trioxide (Sb2O3), photocopy test toner, polyvinyl chloride powder (PVC), and diesel exhaust particles. The Michaelis-Menten-like model was used to develop a relation in which the ...

Quantitative biology relies on the construction of accurate mathematical models, yet the e↵ectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis-Menten approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, due to the ubiq...

The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical pitchfork are identified; then Hopf bifurcation, relaxation oscillation, together transition from bifurcation to oscillation discussed.

We consider the basic SIR epidemiological model with the Michaelis-Menten formulation of the contact rate. From the study of Michaelis-Menten basic enzymatic reaction, we design two types of Nonstandard Finite Difference (NSFD) schemes for the SIR model: Exact-related schemes based on the Lambert W function and schemes obtained by using Mickens’s rules of more complex denominator functions for ...

For the Michaelis-Menten model we determine designs which maximize the minimum of the D-eÆciencies over a certain interval for the non-linear parameter. The best two point designs can be found explicitly and a characterization is given, when these designs are optimal within the class of all designs. In most cases of practical interest the determined designs are highly eÆcient and robust with re...