Global weak solution for a multi-stage physiologically structured population model with resource interaction

Bouchra Aylaj (1) , Ahmed Noussair (1, 2)

1 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics
2 IMB - Institut de Mathématiques de Bordeaux

We construct a multistage kinetic model of a physiologically structured insect population whose life history consists of fourth stages of development termed eggs, larval, pupal and adult moth (male and female). The model is a system of weakly coupled hyperbolic partial differential equations with nonlocal boundary conditions. The vital rates depend on the resource which satisfy an ordinary differential equation. We discretize the physiological space and formulate an implicit scheme and we prove the existence and uniqueness of the solution. The numerical simulation provides an analytical tool to improve the understanding of the moth's biology

Keywords: Population dynamics; Kinetic models; Age structured population; Fully implicit scheme; Stability; Helly-compactness

Domains: Computation [stat.CO]; Numerical Analysis [math.NA]

Bouchra Aylaj, Ahmed Noussair. Global weak solution for a multi-stage physiologically structured population model with resource interaction. Nonlinear Analysis: Real World Applications, 2009, in press. ⟨10.1016/j.nonrwa.2009.03.021⟩. ⟨hal-00391753⟩