The SEIR model with nonlinear incidence rates in epidemiology is studied. Global stability of the endemic equilibrium is proved using a general criterion for the orbital stability of periodic orbits associated with higher-dimensional nonlinear autonomous systems as well as the theory of competitive systems of differential equations.
In this paper we establish some new oscillation criteria for the third-order nonlinear dynamic equation (c(t) (a(t)x ∆ (t)) ∆ γ) ∆ + f (t, x(t)) = 0, t ∈ [a, ∞) T on time scales, where γ ≥ 1 is a quotient of odd integers. Our results not only unify the oscillation theory for third-order nonlinear differential and difference equations but also are new for… (More)
For the Nicholson's blowflies equation with a distributed delay ˙ N (t) = −δN (t) + p Z t h(t) N (s)e −aN (s) dsR(t, s), t ≥ 0, we obtain existence, positiveness and permanence results for solutions with positive initial conditions. We prove that all nonoscillatory about the positive equilibrium N * solutions tend to N *. In the case δ < p < δe there are no… (More)
OBJECTIVE Drug eluting stents (DES) reduce the incidence of restenosis after coronary angioplasty. Enthusiasm has been tempered by a possible increased risk of in-stent thrombosis. We examined the effects of paclitaxel and rapamycin on the endothelial transcriptome to identify alterations in gene expression associated with thrombosis. METHODS AND RESULTS… (More)
To test the hypothesis that NO contributes to effects of angiotensin-converting enzyme inhibitors on fibrinolysis, fibrinolytic balance was assessed in 17 normal subjects during placebo and after randomized, double-blind 4-week treatment with the NO precursor L-arginine (3 g TID), ramipril (10 mg QD), or L-arginine+ramipril. Neither L-arginine nor ramipril… (More)
Host community composition and biodiversity can limit and regulate tick abundance which can have profound impacts on the incidence and severity of tick-borne diseases. Our understanding of the relationship between host community composition and tick abundance is still very limited. Here, we present a novel mathematical model of a stage-structured tick… (More)