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 Mathematical Model of the Photosynthetic Carbon Metabolism Has Multiple Steady States Under the Same Parameter Conditions

This paper analyzes a mathematical model of the photosynthetic carbon metabolism, which incorporates not only the Calvin-Benson cycle, but also another two important metabolic pathways： starch synthesis and photorespiratory pathway. Theoretically, the paper shows the existence of steady states, stability and instability of the steady states, the effects of CO2 concentration on steady states. Especially, a critical point is found, the system has only one steady state with C02 concentration in the left neighborhood of the critical point, but has two with C02 concentration in the right neighborhood. In addition, the paper also explores the influence of C02 concentration on the efficiency of photosynthesis. These theoretical results not only provide insight to the kinetic behaviors of the photosynthetic carbon metabolism, but also can be used to help improving the efficiency of photosynthesis in plants.

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.

Almost Periodic Solutions by the Harmonic Balance Method

We consider non-autonomous ordinary differential equations in two cases.One is the one-dimensional case that admits a condition of hyperbolicity,and the other one is the higher-dimensional case that admits an exponential dichotomy.For differential equations of this kind,we give a rigorous treatment of the Harmonic Balance Method to look for almost periodic solutions.

Analysis of Topological Structure in Transiently Chaotic Neural Networks

Under the condition that the damping factor is between zero and one, chaotic dynamics is proved to exist in one-dimensional transiently chaotic neural networks by Li-Misiurewicz theorem. This result extends the previous result which is done under the condition that the damping factor is zero. Because the value of damping factor affects the speed of dynamical process of transiently chaotic neural networks, this result provides more complete theoretical basis for applications. Finally, two examples by numerical simulation are given to reinforce and illustrate this result.