Mathematical Models of Lyme Disease: An Overview

Lyme disease is the most common vector-borne disease in the United States. It is caused by bacteria Borrelia burgdorferi and transmitted to humans by blacklegged ticks. The transmission is a complex process that involves several different non-human host species, including small mammals such as mice and large mammals such as deer. Due to this complexity, mathematical modeling has proved invaluable to understanding the spread of Lyme disease.

There are about 100 models focused specifically on Lyme disease and many more applicable to generic tick-born diseases. We provide an overview of the existing literature. We discuss different models addressing major topics such as tick population growth, host biodiversity and Lyme disease risk dilution, spatial invasion of ticks, and models for Lyme disease in humans. One interesting feature of many models not typically found in other epidemiological models is the existence of two reproduction numbers—one for the ticks and one for the Lyme disease. We believe that there is a need for more models addressing co-infection with other tick-born diseases, as well as models explaining the discrepancy between tick and disease prevalence.