Holly Gaff
Mathematical modeling of tick-borne diseases
Abstract
Recent increases in reported outbreaks of vector-borne diseases
throughout the world have led to increased interest in understanding and
controlling epidemics involving transmission vectors. Ticks have very
unique life histories that create epidemics that differ from other
vector-borne diseases. The differential equations underlying our tick-borne
disease model are designed for the lone star tick (Amblyomma americanum)
and the spread of human monocytic ehrlichiosis (Ehrlichia chaffeensis).
Analytical results show that under certain criteria for the parameters, the
epidemic would be locally stable. The system was then expanded to multiple
patches to evaluate the effect of spatial heterogeneity on the spread of
the disease. The use of control measures was added, and it was found that
the relative success of disease eradication was dependent upon the patch
structure and location of control application. Results from simulations
using a twelve patch system are compared with field data from an outbreak
of ehrlichiosis in eastern Tennessee, USA. Finally, optimal control
techniques are used to evaluate the location and amount of control needed
to eliminate the disease from different patch scenarios. There remain many
open questions that can be addressed by using this model that we have just
begun to explore.
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