Preview of Beiyang Mathematics Lecture丨Mathematics for propagation and spreading of species

Propagation is a phenomenon observed in the real world with different forms; for example, it occurs in ecological invasion where an invading species is expanding its territory, and it happens in an epidemic when the disease is spreading to new areas. Mathematics, more precisely a class of simple partial differential equation models, has been used to successfully reveal some key features of propagation. In the first part of this talk, I will briefly recall this success story. In the second part, I will discuss some inadequacies of these classical models and look at several new developments on the mathematical modeling of propagation. Some numerical simulation results will be used to illustrate the mathematical findings.