A Mathematical Model for Tick Transmission of Lyme Disease: Does Questing Style Impact the Competition Between Two Strains of Infection?

Abstract

Borrelia burgdorferi is the bacteria responsible for Lyme disease and there are multiple strains of B. burgdorferi that exist. There is a perception that all ticks carry Lyme disease and all bacteria responsible for the disease are equal. Each strain of B. burgdorferi can be characterised by varying persistence in a host. By investigating the questing behaviours of ticks, an analysis is conducted to explore the conditions conducive to different strains. A model is constructed to reproduce the dynamics of the life cycle of the tick and the relationship with hosts to replicate natural interactions between the tick and a host species. The model construction captures the intra-seasonal dynamics using differential equations and inter-seasonal dynamics using a set of discrete recursions. Using an invasion analysis, the conditions that allow for mutant invasion and environmental factors that favour invasion are investigated. The questing styles, both synchronous and asynchronous, are replicated using mathematical techniques. It is found that the relative fitness of competing strains is not impacted by questing style but rather the absolute fitness of a strain is impacted. A conclusion can be drawn that chronic infection is predominantly found in asynchronous systems and with the worsening state of climate change, the persistence of acute infection is less likely.