A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate

Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>1.This approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using that.In addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)<1 and linearly stable if R_(c)=1;while V^(0)is unstable if R_(c)>1.

A Note on Equilibrium of Eventually Strongly Monotone Skew-product Semiflows

In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on Ec （the set consisting of continuous equilibria of τ） implies the strong one.

Square-mean Almost Automorphic Solutions to Some Stochastic Evolution Equations I: Autonomous Case

This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear functional integro-differential stochastic evolution equations in real separable Hilbert spaces. Under some suitable assumptions, the existence, uniqueness and asymptotic stability of the square-mean almost automorphic mild solution to some stochastic differential equations are established. As an application, we analyze the almost automorphic mild solution to some stochastic partial functional differential equation which turns out to be in good agreement with our abstract results.

Grazing-induced legacy effects enhance plant adaption to drought by larger root allocation plasticity

Aims To explore whether grazing-induced legacy effects on plants could benefit plants adaptation to drought.Methods A water-controlled experiment was conducted in the greenhouse,which with Agropyron cristatum and Carex korshinskyi collected from free-grazing and enclosed plots on a typical grassland in Inner Mongolia.Important Findings We found that A.cristatum and C.korshinskyi collected from the free-grazing plot were less affected by drought in terms of ramet biomass,ramet number and total biomass than those collected from the enclosed plot.The enhanced adaptation to drought for plants collected from the free-grazing plot should partly be ascribed to the larger root biomass allocation plasticity under drought treatment.Our findings suggest that grazing management can be used to improve the adaptation of grassland plants to climate change.