stability of foundations near slopes is one of the important and complicated problems in geotechnical engineering, which has been investigated by various methods such as limit equilibrium, limit analysis, slip-line, finite element and discrete element. the complexity of this problem is resulted from the combination of two probable failures: foundation failure and overall slope failure. the curr...

this paper is concerned with global analysis of a delay sveir epidemiological model in a population of varying size. by using lyapunov stability method and lasalle’s invariance principle for delay systems, we prove that when there is no endemic equilibrium, the disease free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally stable.

In  this  paper a  non-linear  model  with  fractional  order  is  presented  for  analyzing  and  controlling the  spread  of  HIV virus.  Both  the  disease-free  equilibrium and the endemic equilibrium are  found  and  their  stability is  discussed. The basic reproduction number , which is a function of the constant parameters in the model, plays an essential  role in the stability of  the ...

In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...