Applied Mathematics Seminar: Hao Kang
This is a past event.
Thursday, October 10, 2019 at 2:00pm to 3:00pm
DM - Deuxieme Maison, 409A
11200 SW 8th ST 33199, Deuxieme Maison, Miami, Florida 33199
The Applied Math Seminar incorporates not only topics in applied math but also connections with various other disciplines and areas.
Dynamics of Population Models with Two Physiological Structures
Speaker: Hao Kang, Bio-Math, University of Miami
Abstract: It is well-known for a long time that the age-structure of a population affects the nonlinear dynamics of the species in ecology and the transmission dynamics of infectious diseases in epidemiology. In modeling specific diseases, the age could be chronological age (the age of the population), infection age (the time elapsed since infection), recovery age (the time elapsed sine the last infection), class age (the length of time in the present group), etc. Other physiological conditions or physical characteristics such as size, location, status, and movement have also been taken in consideration in population dynamical models.
Recently there are some studies taking into account the combined effects of two physiological characteristics (such as age-age, age-size, age-maturation, age-stage), however there are very few theoretical studies on such models.
In this paper, we consider a scalar population model with two physiological structures and study its fundamental properties and dynamical behaviors. First, the semigroup will be defined based on the solutions and its infinitesimal generator will be determined; then the compactness of the solution trajectories will be analyzed; next spectrum theory will be employed to investigate stability of the zero steady state; when the zero steady state is unstable asynchronous growth of the solutions will be studied; finally we will apply theory of integral semigroup and non-densely defined operators to nonlinear models to establish the principle of linearized stability.