Borrelia burgdorferi (Bb) and Babesia microti (Bm) are vector-borne zoonotic pathogens commonly found co-circulating in Ixodes scapularis and Peromyscus leucopus populations. The restricted distribution and lower prevalence of Bm has been historically attributed to lower host-to-tick transmission efficiency and limited host ranges. We hypothesized that prevalence patterns are driven by coinfection dynamics and vertical transmission. We use a multi-year, multiple-location, longitudinal dataset with mathematical modelling to elucidate coinfection dynamics between Bb and Bm in natural populations of P. leucopus, the most competent reservoir host for both pathogens in the eastern USA. Our analysis indicates that, in the absence of vertical transmission, Bb is viable at lower tick numbers than Bm. However, with vertical transmission, Bm is viable at lower tick numbers than Bb. Vertical transmission has a particularly strong effect on Bm prevalence early in the active season while coinfection has an increasing role during the nymphal peak. Our analyses indicate that coinfection processes, such as facilitation of Bm infection by Bb, have relatively little influence on the persistence of either parasite. We suggest future work examines the sensitivity of Bm vertical transmission and other key processes to local environmental conditions to inform surveillance and control of tick-borne pathogens.

Study animals and sample preparation: Mice and ticks were sampled on a biweekly basis from grids established at three sites in both Block Island, RI (BI) and Connecticut (CT) from May-August for three years (2014–2016). Tissue, blood, and attached ticks were collected from P. leucopus which were tagged and released at the site of capture. Questing I. scapularis nymphs were collected in each grid. Pathogen prevalence in each animal (mice and ticks) was assessed via standard qPCR [64, 65]. Data from this study and from the literature were used to estimate model parameters (Supp Table S1, S2). 

Multi-state Markov Model: We used the program Mark via the RMark interface to fit a multi-state Markov model (MSM) to the mark-recapture mouse infection state data collected from the field. For each location (BI and CT) we used records of mice sampled at two or more of the seven sample points in a given year to estimate the relative intensities of transitions between infection states: uninfected (0), Bb infected (1), Bm infected (2), or coinfected (12). Not all mice were observed at all sample points; therefore, the model also allows for mice to be alive but unobserved, or dead. The MSM model is based on the parsimonious assumption that infection states were observed without error. We did not collect data on the observation error in our study, but the qPCR assays we used are known to be highly sensitive, specific, and accurate for Bb and Bm. See the Supplementary Text for details. 

Mechanistic mathematical model: We developed a mechanistic eco-epidemiological model to examine how interactions between Bb and Bm, combined with vertical transmission of Bm in hosts, drive the epidemiological dynamics of both pathogens (see Supplementary Text). The underlying framework is similar to existing models for Borrelia eco-epidemiology. However, in contrast to most existing models, we use a semi-discrete-time formulation to capture the complex seasonality and epidemiological dynamics of the system. In the active season of each year (spring to autumn), the system is modelled in continuous time using ordinary differential equations. In the dormant season (winter), all demographic and epidemiological processes except mortality and recovery cease and the model progresses to the beginning of the next active season in a single time-step.

The ecological component of the model describes the population dynamics of mice and ticks. Mice grow logistically throughout the active season. A specified proportion of the population present at the end of the active season survive the dormant season and form the initial population for the next cycle. The tick population is divided into larvae and nymphs. A fixed number of eggs are present at the beginning of each active season. Modelling a constant number of eggs at the beginning of each year simplifies and stabilizes the ecological dynamics and provides a single control parameter (Omega) that summarizes the suitability of the environment for the tick population. Starting on a specified day of the active season, larvae emerge from these eggs at a constant rate and quest for a host. Hosts may be mice or another unspecified host type that is not competent for Bb or Bm transmission. After encountering hosts, larvae become inactive for the remainder of the season, and a proportion molt to nymphs and survive the dormant season to emerge as nymphs the following year. Larvae that do not successfully find a host by the end of the active season overwinter and a proportion survive to re-emerge the following year and continue questing. Starting on a specified day of the active season, nymphs emerge from overwinter diapause at a constant rate and quest for a host. After nymphs encounter a host, or at the end of the active season, they are removed from the model. We do not include adult ticks in the model because they are not involved in the enzootic transmission cycle of Bb or Bm (adults feed on white-tailed deer which are not competent for either pathogen).

The epidemiological component of the model describes the transmission dynamics of Bb and Bm in the mouse and tick populations (Supp Table S3). An encounter between a tick and a mouse may result in transmission if either party is infected. The probability of transmission is modified by interactions between Bb and Bm based on empirical observations: A mouse with an existing Bm infection has increased susceptibility to Bb; a coinfected mouse has an increased probability of transmitting Bm to larvae but a reduced probability of transmitting Bb to larvae. Evidence for these interactions comes from previous research. Bm may also be transmitted vertically from an infected mouse to her offspring. No evidence for vertical transmission of Bb in P. leucopus mice has been documented.

In the model, mice recover from Bb infection at a constant rate throughout the active and dormant seasons and become susceptible again, coinfection does not affect the recovery rate, and mice do not recover from Bm. Although some evidence exists that recovery occurs at a low rate, life-long chronic infection is a reasonable approximation as Bm infection can persist on average for 9 months, and the life expectancy of wild P. leucopus is less than 6 months. We are not aware of any evidence regarding the effect of coinfection on Bm recovery. Therefore, in the interests of parsimony, in the model, we assume that coinfection does not affect the recovery rate. Ticks do not recover from infection with either pathogen.

Parameter estimation: We used Approximate Bayesian Computation (ABC) to estimate model parameters by fitting model trajectories for the mouse population, tick burden, Bb and Bm prevalence in mice and ticks to three years of field data at each location. We held the parameter values constant across all three years and let the model reach approximate steady-state before comparing trajectories. Where published or our own empirical information about parameter values was available, we incorporated this into the prior distributions (Supp Tables S1, S2). 

Viability threshold: We examined how key parameters of the model affect the viability of Bb and Bm. We define the viability threshold of each pathogen to be the minimum tick egg density required at the beginning of each season for long-term persistence. The initial tick egg density is a strong determinant of larval and nymph population densities, and we interpret it as an indicator of the quality of the local environment. We take a pathogen to be persistent if the model initialized at demographic steady-state with very low prevalence of both pathogens converges to an asymptotic state where that pathogen is present. All code used in this study is available at https://github.com/cowparsley/borrelia-babesia-eco-epi.