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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.

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 $01$.