Talk 1 Title:

 

Basic Reproduction Ratios for Periodic Compartmental Models with Time Delay

 

Abstract:

 

In this talk, I will report our recent research on basic reproduction ratios for a large class of time-delayed compartmental population models in a periodic environment. It is proved that this ratio serves as a threshold value for the stability of the zero solution of the associated periodic linear systems. As an illustrative example, we also apply the developed theory to a periodic SEIR model with an incubation period and obtain a threshold result on its global dynamics in terms of the basic reproduction ratio.

 

 

Talk 2 Title:

 

Spatial Invasion Threshold of Lyme Disease

 

Abstract:

 

A mathematical model of Lyme disease is formulated to incorporate the spatially heterogenous structures. The basic reproduction number R0 of the disease and its computation formulae are established. It is shown that R0 serves a threshold value between the extinction and the persistence of Lyme disease evolution. Numerical simulations indicate that the spatial heterogeneity of disease transmission coefficient increases the basic reproduction number, but the spatial heterogeneity of carrying capacity of mice alleviates the value of R0. Moreover, influences of host population sizes, destruction of tick habitats and deployment of vaccinations are studied to give insights into optimal control of the disease.