The assessment and the management of the risks linked to insect pests can be supported by the use of physiologically-based demographic models. These models are useful in population ecology to simulate the dynamics of stage-structured populations, by means of functions (e.g., development, mortality and fecundity rate functions) realistically representing the nonlinear individuals physiological responses to environmental forcing variables. Since density-dependent responses are important regulating factors in population dynamics, we propose a nonlinear physiologically-based Kolmogorov model describing the dynamics of a stage-structured population in which a time-dependent mortality rate is coupled with a nonlocal density-dependent term. We prove existence and uniqueness of the solution for this resulting highly nonlinear partial differential equation. Then, the equation is discretized by finite volumes in space and semi-implicit backward Euler scheme in time. The model is applied for simulating the population dynamics of the fall armyworm moth (Spodoptera frugiperda), a highly invasive pest threatening agriculture worldwide.

使用基于生理的人口统计模型可以支持对与害虫相关的风险的评估和管理。这些模型在种群生态学中可用于模拟阶段结构种群的动态，通过函数（例如，发育、死亡率和繁殖率函数）真实地表示非线性个体对环境强迫变量的生理反应。由于密度相关反应是人口动态中的重要调节因素，我们提出了一种基于非线性生理学的 Kolmogorov 模型，该模型描述了阶段结构人口的动态，其中时间相关死亡率与非局部密度相关项相结合。我们证明了这个高度非线性偏微分方程的解的存在性和唯一性。然后，通过空间上的有限体积和时间上的半隐式后向欧拉格式将方程离散化。该模型用于模拟秋粘虫蛾的种群动态（Spodoptera frugiperda），一种威胁全球农业的高度入侵性害虫。