Modeling age-structured population density with time and spatial noises based on uncertain partial differential equation

How to model migration population with age structure has always been one of the most concerned topics in demography. Meanwhile, stability analysis is to study whether the demographic models can remain stable under perturbation, and it takes up an important position in actual applications. In view of this, a novel model, namely an uncertain age-structured population density equation with time and spatial noises (UASPE-TS), is proposed in this paper. UASPE-TS is an important class of uncertain partial differential equations driven by two independent Liu processes. Furthermore, UASPE-TS can be applied to depicting the change laws of population dynamics due to migration disturbance. To begin with, this paper provides a detailed derivation of UASPE-TS based on demographic principle and gives the analytic expression of its solution. Next, inverse uncertainty distribution of UASPE-TS is studied. Moreover, stability analysis is also considered for UASPE-TS. Then uncertain moment estimation according to residuals is put forward to infer unknown parameters of UASPE-TS. Finally, an empirical case is presented to illustrate the applicability of the proposed method. This will provide a new idea and methodology for the stability research of population migration system.