A new model that describes the life cycle of mosquitoes of the species Aedes aegypti, main carriers of vector-borne diseases, is proposed. The novelty is to include in the model the coexistence of two independent diffusion processes, one fast which obeys the constitutive Fick’s law, the other slow which satisfies the Cattaneo evolution equation. The analysis of the corresponding ODE model shows the overall stability of the Mosquitoes-Free Equilibrium (MFE), together with the local stability of the other equilibrium point admitted by the system. Traveling wave type solutions have been investigated, providing an estimate of the minimal speed for which there are monotone waves that connect the homogeneous equilibria allowed by the system. A special section is dedicated to the analysis of the hyperbolic model obtained neglecting the fast diffusive contribution. This particular case is suitable to describe the biological process as it overcomes the paradox of infinite speed propagation, typical of parabolic systems. Several numerical simulations compare the existing models in the literature with those presented in this discussion, showing that although the generalized model is parabolic, the associated wave velocity admits upper bound represented by the speed of the waves linked to the classic parabolic model present in the published literature, so the presence of a slow flux together with a fast one slows down the speed with which a population spreads.

中文翻译：

---

埃及伊蚊生命周期中快慢扩散过程并存

提出了一种描述媒介传播疾病主要携带者埃及伊蚊生命周期的新模型。新颖之处在于模型中包含两个独立扩散过程的共存，一个快速的遵循本构 Fick 定律，另一个满足 Cattaneo 演化方程的慢速。对相应 ODE 模型的分析显示了无蚊子平衡 (MFE) 的整体稳定性，以及系统允许的其他平衡点的局部稳定性。已经研究了行波型解决方案，提供了对连接系统允许的均匀平衡的单调波的最小速度的估计。一个专门的部分专门用于分析忽略快速扩散贡献而获得的双曲线模型。这种特殊情况适合描述生物过程，因为它克服了抛物线系统典型的无限速度传播悖论。几个数值模拟将文献中的现有模型与本讨论中提出的模型进行了比较，表明尽管广义模型是抛物线的，但相关的波速允许由与已发表的经典抛物线模型相关的波速表示的上限文学，所以一个缓慢的流动和一个快速的流动一起减慢了人口传播的速度。这种特殊情况适合描述生物过程，因为它克服了抛物线系统典型的无限速度传播悖论。几个数值模拟将文献中的现有模型与本讨论中提出的模型进行了比较，表明尽管广义模型是抛物线的，但相关的波速允许由与已发表的经典抛物线模型相关的波速表示的上限文学，所以一个缓慢的流动和一个快速的流动一起减慢了人口传播的速度。这种特殊情况适合描述生物过程，因为它克服了抛物线系统典型的无限速度传播悖论。几个数值模拟将文献中的现有模型与本讨论中提出的模型进行了比较，表明尽管广义模型是抛物线的，但相关的波速允许由与已发表的经典抛物线模型相关的波速表示的上限文学，所以一个缓慢的流动和一个快速的流动一起减慢了人口传播的速度。