We propose two novel mathematical models with impulsive injection of insulin or its analogues for type 1 and 2 diabetes mellitus. One model incorporates the periodic insulin. analytically show existence uniqueness a positive globally asymptotically stable solution diabetes, which implies that perturbation caused by will not disturb homeostasis but amend glucose from pathological level toward healthier level. also system is uniformly permanent is, concentration bounded above below. The other...

In the last three decades, several models on interaction of glucose and insulin have appeared in literature, mostly used one is generally known as "minimal model" which was first published 1979 modified 1986. Recently, this minimal model has been questioned by De Gaetano Arino [4] from both physiological modeling aspects. Instead, they proposed a new mathematically more reasonable model, called "dynamic model". Their makes use certain simple specific functions introduces time delay...

Insulin signaling is essential for -cell survival and proliferation in vivo. also has potent mitogenic anti-apoptotic actions on cultured -cells, with maximum effect the high picomolar range diminishing at nanomolar doses. In order to understand whether these effects of insulin are constitutive or can be subjected physiological modulation, it estimate extracellular concentration monomeric within an intact islet. Unfortunately, vivo monomers islet cannot measured directly current technology....

In the last three decades, several models relevant to subcutaneous injection of insulin analogues have appeared in literature. Most them model absorption depot and then compute plasma concentration. The most recent systemic directly simulate dynamics. These been and/or can be applied technology pump or coming closed-loop systems, also known as artificial pancreas. this paper, we selectively review these detail at point out that provide key building blocks for some important endeavors into...

It is well known that Michaelis–Menten kinetics suitable for the response function in chemical reaction, when reaction rate does not increase indefinitely an excess of resource available. However, existing models insulin therapies assume clearance proportional to concentration. In this paper, we propose a new model therapy both type 1 and 2 diabetes mellitus, which degradation assumes kinetics. Our analysis shows it possible mimic pancreatic secretion by exogenous infusions, our numerical...

We continue our attempt of modeling the open-loop control glucose level by impulsive insulin injections. Several time delays exist in system. The include needed for from injection depot to transport interstitial compartment, slow inhibition hepatic production (HGP), and secretion caused elevated concentration remaining functional pancreatic $\beta$-cells. None them are negligible. model proposed this paper incorporates these delays. Our analytical studies show that all solutions permanent, a...

Type 1 diabetics must inject exogenous insulin or analogues one more times daily. The timing and dosage of administration have been a critical research area since the invention analogues. Several pharmacokinetical models proposed, some are applied clinically in modeling various therapies. However, their plasma concentration be computed separately from models' output. Furthermore, minimal analytical study was performed these existing models. We propose two systemic simplified ordinary...

Type 2 diabetes mellitus (T2DM) has become prevalent pandemic disease in view of the modern life style. Both diabetic population and health expenses grow rapidly according to American Diabetes Association. Detecting potential onset T2DM is an essential focal point research mellitus. The intravenous glucose tolerance test (IVGTT) effective protocol determine insulin sensitivity, effectiveness, pancreatic β-cell functionality, through analysis parameter estimation a proper differential...

The entire genomic DNA sequence of Arabidopsis will be available by the end this year. As has been case for a number prokaryotic and eukaryotic species whose sequences have completed, many open reading frames in genome encode proteins unknown

State-to-state rotational relaxation processes play a critical role in predicting nonequilibrium, which can significantly affect total laser power and spectral distribution. In this paper, the state-to-state rate coefficients for pumping reaction of F + H2, energy transfer HF(υ, j = 0–10) HF(υ′, j′ H2 are calculated. Subsequently, detailed chemical kinetic mechanism is constructed including 61 species 124,482 elementary reactions HF lasers. All these have been expressed with Arrhenius-like...

We consider the one-dimensional shallow water problem with capillary surfaces and moving contact {lines}. An energy-based model is derived from two-dimensional wave equations, where we explicitly discuss case of a stationary force balance at line highlight necessary changes to dynamic angles. The becomes our free boundary level depth degenerates near boundary, which causes singularities for derivatives degeneracy viscosity. This similar physical vacuum compressible flows in literature....

Maintenance of adequate physical and functional pancreatic $\beta$-cell mass is critical for the prevention or delay diabetes mellitus. It well established that insulin potently activates mitogenic anti-apoptotic signaling cascades in cultured $\beta$-cells. Loss receptors sufficient to induce type 2 mice. However, it remains unclear whether {\em vitro} effect human islets vivo} effects mice can be applied physiology. The major obstacle a complete understanding insulin's feedback pancreas...

This paper concerns the Dirichlet problem of three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity. When viscosity coefficient $\mu(\rho)$ is a power function density ($\mu(\rho)=\mu\rho^\alpha$ $\alpha>1$), it proved that system will admit unique global strong solution as long initial data are sufficiently large. first result concerning existence large for in three dimensions.

This paper concerns the initial boundary value problem of three-dimensional inhomogeneous incompressible liquid crystal flows with density-dependent viscosity. When viscosity coefficient $\mu(\rho)$ is a power function density larger than $1$, that $\mu(\rho)=\mu\rho^\alpha$ $\alpha>1$, it proved system exists unique global strong solution as long sufficiently large and $L^3$-norm derivative director small. first result concerning for without smallness velocity.

In this paper, we consider the Cauchy problem for three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering system as an elliptic-dominated structure and defining suitable energy functionals, after elaborate index analysis, establish global existence of strong solutions long initial data is large enough. This a big contrast to classical results where small perturbation some resting states.