In order to investigate the impact of awareness programs and time delays on the cholera outbreaks, we propose a cholera epidemic model, incorporating awareness programs by media as a separate class and two time‐delay factors. The bifurcation theory is applied to explore the variety of dynamics of this model for various combinations of the delays when R0>1. Moreover, we analyze the direction, stability, and period of the bifurcating periodic solutions arising through Hopf bifurcation by using the normal form concept and the center manifold theory. Finally, we present numerical simulations to verify the main theoretical results. 相似文献
The oracle property of model selection procedures has attracted a large volume of favorable publications in the literature, but also faced criticisms of being ineffective and misleading in applications. Such criticisms, however, have appeared to be largely ignored by the majority of the popular statistical literature, despite their serious impact. In this paper, we present a new type of Hodges’ estimators that can easily produce model selection procedures with the oracle and some other desired properties, but can be readily seen to perform poorly in parts of the parameter spaces that are fixed and independent of sample sizes. Consequently, the merits of the oracle property for model selection as extensively advocated in the literature are questionable and possibly overstated. In particular, because the mathematics employed in this paper are at an elementary level, this finding leads to new discoveries on the merits of the oracle property and exposes some overlooked crucial facts on model selection procedures.
Toward Lions' open question in Lions(1996) concerning the propagation of regularity for density patch, we prove that the boundary regularity of the 3-D density patch persists by time evolution for inhomogeneous incompressible viscous flows, with the initial density given by(1-η)1_(?_0)+ 1_(?_0~c )for some small enough constant η and some W~(k+2p),domain ?_0, p ∈]3, ∞[, and with the initial velocity satisfying some smallness condition and appropriate conormal regularities. 相似文献
In this paper, we consider the existence and uniqueness of stationary solution to the bipolar quantum hydrodynamic model in one dimensional space with general non-constant doping profile. The existence of the stationary solution is proved by Leray-Schauder fixed-point theorem and a crucial truncation technique is used to derive the positive upper and lower bounds of the stationary solution. The uniqueness of the stationary solution is shown by a delicate energy estimate. 相似文献
In this paper, a nonautonomous Predator-prey model with functional response and impulses is studied. By using comparison theorem and the mono-tonicity, some sufficient conditions which guarantee the permanence and asymptotic behavior of this system are obtained. 相似文献
In this paper we prove the existence of global weak solutions of the p-harmonic flow with potential between Riemannian manifolds M and N for arbitrary initial data having finite p-energy in the case when the target N is a homogeneous space with a left invariant metric.
Received March 17, 1999, Revised September 22, 1999, Accepted October 15, 1999 相似文献