Virginia Tech
Nonsmooth Bifurcations and the Role of Density Dependence in a Chaotic Infectious Disease Model
Abstract
dc:description.abstractDiscrete dynamical systems can exhibit rich and interesting dynamics at lower dimensions (and co-dimensions) than that of ODE models. Classically, the minimal dimension to observe chaotic behavior in an ODE model is three; whereas it can be achieved in a one-dimensional discrete map. It is often the choice of mathematical biologists to use discrete systems as it fills many roles such as sparse data, incorporation of life cycle stages and noisy measurements. This work is analyzes a discrete time model of an infected salmon population. It provides an in-depth analysis of non-smooth bifurcations for alternate functional forms for density dependence in the growth function of a given model. These demonstrate interesting structures and chaotic behaviors with biologically feasible interpretations such as intrinsic growth rate and probability of death. The choice of density dependence function, as well as parameterization, leads to whether chaos occurs or not.
Degree
thesis:*- Name thesis:degree_name
- Master of Science
- Level thesis:degree_level
- masters
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2020
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Hughes, Ryan Patrick
- Chair dc:contributor.committeechair
-
- Childs, Lauren M.
- Committee members dc:contributor.committeemember
-
- Blackwood, Julie C.
- Ciupe, Stanca M.
Subjects
dc:subject × 3Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:23713
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/96567