Stability Analysis of SIQS Epidemic Model with Saturated Incidence Rate

A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac’s criterion respectively.

Erbium-Doped Zirconia-Alumina Silica Glass-Based Fiber as a Saturable Absorber for High Repetition Rate Q-Switched All-Fiber Laser Generation

We propose and demonstrate a Q-switched erbium-doped fiber laser （EDFL） using an erbium-doped zirconia-alumina silica glass-based fiber （Zr-EDF） as a saturable absorber. As a 16-cm-long Zr-EDF is incorporated into a ring EDFL cavity, a stable Q-switching pulse train operating at 1565？nm wavelength is successfully obtained. The repetition rate is tunable from 33.97？kHz to 71.23？kHz by increasing the pump power from the threshold of 26？mW to the maximum of 74？mW. The highest pulse energy of 26.67？nJ is obtained at the maximum pump power.

Isola in a linear one-degree-of-freedom feedback system with actuator rate saturation

This short communication uses numerical continuation to highlight the existence of an isola in a simple one-degree-of-freedom harmonically forced feedback system with actuator rate limiting as its only nonlinear element.It was found that the isola(1)contains only rate-limited responses,(2)merges with the main branch when the forcing amplitude is sufficiently large,and(3)includes stable solutions that create a second attractor in regions where rate limiting is not expected.Furthermore,the isola is composed of two solutions for a given forcing frequency.These solutions have the same amplitudes in the state(pitch rate)projection;however,they have distinct phases,and their amplitudes are also distinct when projected onto the integrator state in the controller.The rich dynamics observed in such a simple example underlines the impact of rate limiting on feedback systems.Specifically,the combination of feedback and rate limiting can create detrimental dynamics that is hard to predict and requires careful analysis.

Bifurcation analysis of an SIS epidemic model with a generalized non-monotonic and saturated incidence rate

In this paper,a new generalized non-monotonic and saturated incidence rate was introduced into a susceptible-infected-susceptible(SIS)epidemic model to account for inhibitory effect and crowding effect.The dynamic properties of the model were studied by qualitative theory and bifurcation theory.It is shown that when the infuence of psychological factors is large,the model has only disease-free equilibrium point,and this disease-free equilibrium point is globally asymptotically stable;when the influence of psychological factors is small,for some parameter conditions,the model has a unique endemic equilibrium point,which is a cusp point of co-dimension two,and for other parameter conditions the model has two endemic equilibrium points,one of which could be weak focus or center.In addition,the results of the model undergoing saddle-node bifurcation,Hopf bifurcation and Bogdanov-Takens bifurcation as the parameters vary were also proved.These results shed light on the impact of psychological behavior of susceptible people on the disease transmission.

Influence of soil organic matter contents on soil water characteristics of forests on east slope of Gongga Mountain

By testing soil organic matter （SOM） contents, soil water contents （SWC） within low suctions, and saturated infiltration rates of samples taken from east slope of Gongga Mountain of China, the enhancive effects of SOM contents on SWC within low suctions and saturated infiltration rates were quantified. The simulated functions might be applied on regional experience forest-hydrology model. The improving function of protecting forest floor and increasing SOM contents on forest ecosystem hydrological effects were also embodied.

Global Dynamics of a New Huanglongbing Transmission Model with Quarantine Measures

Incorporating plant-dependent saturated reproduction function, chemical insecticide, and its resistance, a plant-vector-virus model which describes the spread of infection throughout the plant by the insect is investigated in this paper. First of all, the basic reproduction number R0 is obtained by using the method of the next generation matrix, and the existence of disease-free equilibrium and endemic equilibrium is examined. Then we show that the disease-free steady state is globally asymptotically stable if R0 1, the system is uniformly persistent and the endemic equilibrium is local stability. Finally, numerical simulation is carried out to illustrate our theoretical results. Our result implies that insecticide resistance has a vital impact on the control of plant diseases.

Dynamical behavior of a stochastic multigroup staged-progression HIV model with saturated incidence rate and higher-order perturbations

In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic Lyapunovfunction.In addition,we make up adequate conditions for complete eradication and wip-ing out the infectious disease.In a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long term.Finally,examples and numerical simulations are introduced to validate our theoretical results.