Ticks, Deer, Mice, and a Touch of Sensitivity: A Recipe for Controlling Lyme Disease

TL;DR

This paper models the dynamics of Lyme disease transmission involving ticks, mice, and deer, analyzing how altering death rates of these populations can control disease prevalence.

Contribution

It introduces a six-dimensional SI model for Lyme disease that incorporates population-specific death rates and analyzes their impact on disease control strategies.

Findings

Reducing tick populations can lower Lyme disease prevalence.

Sensitivity analysis identifies key populations affecting disease spread.

Dynamic sensitivity analysis shows how intervention timing influences effectiveness.

Abstract

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.