  Borrelia burgdorferi sensu stricto is a bacterial spirochete prevalent in the
Northeastern United States that causes Lyme disease. Lyme disease is the most
common arthropod-borne disease in the United States; affecting mice, deer,
humans and other mammals. The disease is spread by Ixodes Scapularis, a species
of tick whose primary food source are deer and mice. Reducing the population of
ticks feeding on both large and small mammals below some critical threshold can
decrease the prevalence of Lyme disease among humans. A simplified,
six-dimensional Susceptible-Infected, SI, model is used to capture the
mice-deer-tick dynamics while considering the impact of varying
population-specific death rates on infected population size. We analyzed the
stability of the models two equilibria, the unstable disease free equilibrium
and the endemic equilibrium. Static forward sensitivity analysis is conducted
on the basic reproduction number and the endemic equilibrium. A dynamic
approach was explored to observe change in the sensitivity of the death rates
over time. These analyses were conducted to determine the efficacy of changing
death rates in order to reduce prevalence of Lyme disease.
