Modeling the Dynamics and Control of Lyme Disease in a Tick-Mouse System Subject to Vaccination of Mice Populations

Lyme disease is one of the most prevalent and the fastest growing vector-borne bacterial illnesses in the United States, with over 25,000 new confirmed cases every year. Lyme disease cases have more than doubled in recent years, and the Centers for Disease Control and Prevention estimates that those numbers could be significantly underrepresented. Humans contract the bacteria, Borrelia burgdorferi, through the bite of Ixodes scapularis, commonly known as the deer tick or Eastern blacklegged tick. The tick can receive the bacterium from a variety of small mammal and bird species but Peromyscus leucopus, commonly known as white-footed mice, are the primary reservoirs in the northeastern United States, especially near human settlement. The life cycle and behavior of the ticks depends greatly on the season, with different stages of tick biting at different times. Reducing the infection in mice populations and the overall tick population may greatly reduce the number of humans affected by this disease in some parts of the affected region. However, research on the effects of various mouse-targeted interventions is limited. One particularly promising method is the administration of vaccine pellets to white-footed mice through special bait boxes. In this study, we develop and analyze a mathematical model consisting of a system of non-linear difference equations to understand the complex transmission dynamics and vector demographics in both tick and mice populations. Later, we evaluate to what extent vaccination of white-footed mice can affect the population of infected I. scapularis and under which conditions this method is a cost-effective preventative measure against Lyme disease. We find that vaccination can eliminate mouse=tick transmission of B. burgdorferi while saving money when instituted in areas with high human risk.