Age-structured population model under uncertain environment

In this work, we present an age-structured population model with uncertain external inflow. Based on the comparison principle for the population model, we apply the mathematical tools from uncertainty theory to prove an inverse distribution theorem, which relates the inverse uncertainty distribution of the solution of the given model to the corresponding θ -path. As an application of this theorem, we derive formulas to compute the expected values of a monotone function of population density and total population density. In addition, we introduce a finite difference method to solve the θ -path. A numerical experiment is provided to show the effectiveness of the theoretical results.