Threshold Dynamics of a Stochastic S

A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control

Global stability of a delayed mosquito-transmitted disease model with stage structure

This article presents a new eco-epidemiological deterministic delay differential equation model considering a biological controlling approach on mosquitoes, for endemic dengue disease with variable host (human) and variable vector (Aedes aegypti) populations, and stage structure for mosquitoes. In this model, predator-prey interaction is considered by using larvae as prey and mosquito-fish as predator. We give a complete classification of equilibria of the model, and sufficient conditions for global stability/global attractivity of some equilibria are given by constructing suitable Lyapunov functionals and using Lyapunov-LaSalle invariance principle. Also, numerical simulations are presented to show the validity of our results

Necessary and sufficient conditions for oscillation of neutral delay differential equations

In this article, we concerned with oscillation of the neutral delay differential equation $[x(t)-px(t-\tau)]'+qx(t-\sigma)=0$ with constant coefficients. By constructing several suitable auxiliary functions, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the aforementioned equation for the cases $0<p<1$ and $p>1$