| Abstract: |
| I will talk about
an epidemic reaction-diffusion system with nonlinear incidence mechanism of the form $S^qI^p\,(p,\,q>0)$. The coefficients of the system are spatially heterogeneous and time dependent (particularly time periodic).
We first establish the $L^\infty$-bounds of the solutions of a class of systems. Based on such estimates,
we then study the long-time behavior of the solutions of the system.
Our results reveal the delicate effect of the infection mechanism, transmission rate, recovery rate
and disease-induced mortality rate on the infection dynamics.
Our analysis can be adapted to models with some other types of infection incidence mechanisms. |
|