STABILITY OF AN SEIS EPIDEMIC MODEL WITH CONSTANT RECRUITMENT AND A VARYING TOTAL POPULATION SIZE

This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium O is globally stable. If R〉1, there is a unique endemic equilibrium and O is unstable. For two important special cases of bilinear and standard incidence ,sufficient conditions for the global stability of this endemic equilibrium are given. The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period. Some existing results are extended and improved.

Stability analysis of long hydrodynamic journal bearings based on the journal center trajectory

In this study,we observe that there are two threshold speeds(stability threshold speed and second threshold speed)for the long journal bearing,which is different for the short bearing.When the rotating speed is below the stability threshold speed,the stability boundary nearly coincides with the clearance circle,and the journal center gradually returns to the equilibrium point after being released at an initial point.If the rotating speed is between the stability threshold speed and the second threshold speed,after being released at an initial point,the journal center converges to a contour containing the equilibrium point.In this situation,for a higher rotating speed,the corresponding contour is also larger.When the rotating speed exceeds the second threshold speed,the journal gradually moves towards the bearing surface after being released at an initial point.

Comparison of surface water extraction performances of different classic water indices using OLI and TM imageries in different situations

Recently,water extraction based on the indices method has been documented in many studies using various remote sensing data sources.Among them,Landsat satellites data have certain advantages in spatial resolution and cost.After the successful launch of Landsat 8,the Operational Land Imager(OLI)data from the satellite are getting more and more attention because of its new improvements.In this study,we used the OLI imagery data source to study the water extraction performance based on the Normalized Difference Vegetation Index,Normalized Difference Water Index,Modified Normalized Water Index(MNDWI),and Automated Water Extraction Index(AWEI)and compared the results with the Thematic Mapper(TM)imagery data.Two test sites in Tianjin City of north China were selected as the study area to verify the applicability of OLI data and demonstrate its advantages over TM data.We found that the results of surface water extraction based on OLI data are slightly better than that based on TM in the two test sites,especially in the city site.The AWEI and MNDWI indices performs better than the other two indices,and the thresholds of water indices show more stability when using the OLI data.So,it is suitable to combine OLI imagery with other Landsat sensor data to study water changes for long periods of time.

ASYMPTOTICAL ANALYSIS OF A REACTIONDIFFUSION EQUATIONS D-SIS EPIDEMIC MODEL

By monotone methods and invariant region theory, a reaction-diffusion equations D-SIS epidemic model with bilinear rate is studied. The existence and uniqueness of the solution of the model are proved. The basic reproductive number which determines whether the disease is extinct or not is found. The globally asymptotical stability of the disease-free equilibrium and the endemic equilibrium are obtained. Some results of the ordinary differential equations model are extended to the present partial differential equations model.