**Financial support through the following projects:**

UID/MAT/00297/2019

UID/MAT/00297/2013

PEst-OE/MAT/UI0297/2014

PEst-OE/MAT/UI0297/2011

Carlota Rebelo, CMAFCIO/FC/UL

**Data:** 26/2/2018

**Hora:** 14h00

**Local:** Sala 1.19- Edifício VII, FCT-UNL

**Abstract:**

Mathematical analysis is a useful tool to give insights in very different mathematical biology problems.

In this talk we will present two examples of this fact. First of all we consider a simple epidemiological model with heterogeneity and discuss the relation between variance in the susceptibility of the individuals and prevalence of infection.Then we consider predator-prey models. Using the notion of basic reproduction number $R_0$, given by Nicolas Baca\"er in the case of periodic models, we prove uniform persistence when $R_0 >1$. We will give some examples such as models including competition among predators, prey- mesopredator-superpredator models and Leslie-Gower systems.

This talk is based in joint works with N. Baca\"er, M. Garrione, M.G.M. Gomes and A. Margheri.