Evolutionary Dynamics in an Individual Spatial and a Mean Field Differential Equation Host-Pathogen Model
Abstract
We examine a host-pathogen model in which three types of species exist: empty sites,
healthy hosts, and infected hosts. In this model six different transitions can occur:
empty sites can be colonized by healthy hosts, healthy hosts can be infected, and
infected hosts can either recover or die. We implement this general model in both
a spatial context with discrete time and in a homogeneously mixing model in continuous
time. We then explore evolution for pairs of parameters, calculating viable regions
in the ODE model and and evolutionary vector fields in both models. Our results show
that results from the spatial model do not always converge to our ODE model results,
that stochasticity in the spatial evolutionary vector field can be used as a measure
of the magnitude of evolutionary pressure and as an indicator of non-viable parameters,
and that the evolutionary pressures on different parameters are not necessarily independent.
For example, a lower transmissibility greatly lowers the magnitude of evolutionary
pressure for all parameters associated with transitions from infected hosts.
Description
Mathematics Undergraduate Honors Thesis
Type
Honors thesisDepartment
MathematicsPermalink
https://hdl.handle.net/10161/6966Citation
Zhang, William (2013). Evolutionary Dynamics in an Individual Spatial and a Mean Field Differential Equation
Host-Pathogen Model. Honors thesis, Duke University. Retrieved from https://hdl.handle.net/10161/6966.Collections
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