[SS07] Dynamic system and applications to mathematical biology

[SS07-05] Application of Lyapunov functionals in discrete diffusion infectious diseases on 2-D lattice

*RAN ZHANG¹ (1. Heilongjiang University (China))

Keywords:

Lattice system,Infectious diseases model,Lyapunov functional,Traveling wave solution,Diffusive model

This report mainly focuses on the traveling wave solution problem of discrete diffusion infectious disease models, especially models on two-dimensional lattice. The classic methods of upper and lower solutions with fixed point theories can solve the existence problem of traveling wave solutions in such models. As is well known, Lyapunov functionals are crucial in proving the asymptotic behavior of traveling wave solutions in diffusion infectious disease models. We are committed to constructing Lyapumov functional that can solve the asymptotic behavior of traveling wave solutions in disease models on two-dimensional lattice.