This article proposes a mathematical model based on ordinary nonlinear differential equations that describes the dynamics of population growth of the mosquito Aedes aegypti throughout its life cycle. Then, a modification is made to the model by implementing a time delay, initially constant and then distributed over time. In addition, h, the population growth threshold, is established, the equilibrium points (trivial equilibrium, coexistence equilibrium) of the population are found and an analysis of local stability of the coexistence equilibrium is performed. If \(h>1\), this results in the population of adult aquatic mosquitoes persisting in the environment, approaching a equilibrium of coexistence, regardless of whether the time delay is considered or not. Finally, numerical simulations are carried out using Matlab software using the functions ode45 and dde23, with a value of \( h>1 \), which allow the solutions of the initial model of ordinary differential equations to be compared to the solutions when the delay is implemented.

本文提出了一个基于普通非线性微分方程的数学模型，该模型描述了埃及伊蚊在其整个生命周期中的种群增长动态。然后，通过实现时间延迟（最初是恒定的，然后随时间分布）来对模型进行修改。此外，建立了人口增长阈值h，找到了人口的均衡点（平凡均衡，共存均衡），并对共存均衡的局部稳定性进行了分析。如果\（h> 1 \），无论是否考虑了时间延迟，这都会导致成年水生蚊子在环境中持续存在，并趋于平衡。最后，使用函数ode45和dde23使用Matlab软件进行数值模拟，数值为\（h> 1 \），这可以将常微分方程初始模型的解与延迟时的解进行比较。被实施。