We propose a seasonal forcing iSIR (indirectly transmitted SIR) model with a modified incidence function, due to the fact that the seasonal fluctuations can be the main culprit for cholera outbreaks. For this nonautonomous system, we provide a sufficient condition for the persistence and the existence of a periodic solution. Furthermore, we provide a sufficient condition for the global stabilit...

<p style='text-indent:20px;'>In this paper, we investigate a class of stochastic recurrent neural networks with discrete and distributed delays for both biological mathematical interests. We do not assume any Lipschitz condition on the nonlinear term, just continuity assumption together growth conditions so that uniqueness Cauchy problem fails to be true. Moreover, existence pullback attr...

Let (E,h1,∞) be a nonautonomous discrete dynamical system (briefly, N.D.D.S.) that is defined by sequence (hj)j=1∞ of continuous maps hj:E→E over nontrivial metric space (E,d). This paper defines and discusses some forms ergodicity sensitivity for the upper density, lower positive integers. Under conditions, if rate convergence at which converges to limit map h “fast enough” with respect intege...

In this paper, we obtain sufficient conditions for the permanence of a family nonautonomous systems delay differential equations. This includes structured models from mathematical biology, with either discrete or distributed delays in both linear and nonlinear terms, where typically terms are nonmonotone. Applications to generalized Nicholson Mackey-Glass given.