DOI: 10.5061/dryad.573n5tbd3
title: Ecological interactions driving population dynamics of two tick-borne pathogens, Borrelia burgdorferi and Babesia microti

description: 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.
description: <em>Study animals and sample preparation:</em> 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 <em>P</em>. <em>leucopus</em> which
 were tagged and released at the site of capture. Questing
 <em>I</em>. <em>scapularis</em> 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).  <em>Multi-state Markov Model:</em> 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), <em>Bb</em> infected (1),
 <em>Bm</em> 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 <em>Bb</em> and <em>Bm</em>. See the
 Supplementary Text for details.  <em>Mechanistic
 mathematical model: </em>We developed a mechanistic
 eco-epidemiological model to examine how interactions between
 <em>Bb</em> and <em>Bm</em>, combined with
 vertical transmission of <em>Bm</em> in hosts, drive the
 epidemiological dynamics of both pathogens (see Supplementary Text). The
 underlying framework is similar to existing models for
 <em>Borrelia</em> 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 <em>Bb</em> or <em>Bm</em>
 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
 <em>Bb</em> or <em>Bm</em> (adults feed on
 white-tailed deer which are not competent for either pathogen).
 The epidemiological component of the model describes the
 transmission dynamics of <em>Bb</em> and
 <em>Bm</em> 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 <em>Bb</em> and <em>Bm</em>
 based on empirical observations: A mouse with an existing
 <em>Bm</em> infection has increased susceptibility to
 <em>Bb</em>; a coinfected mouse has an increased probability
 of transmitting Bm to larvae but a reduced probability of transmitting
 <em>Bb</em> to larvae. Evidence for these interactions comes
 from previous research. <em>Bm</em> may also be transmitted
 vertically from an infected mouse to her offspring. No evidence for
 vertical transmission of <em>Bb</em> in <em>P.
 leucopus</em> mice has been documented. In the
 model, mice recover from <em>Bb</em> 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 <em>Bm</em>. Although some evidence exists that
 recovery occurs at a low rate, life-long chronic infection is a reasonable
 approximation as <em>Bm</em> infection can persist on average
 for 9 months, and the life expectancy of wild <em>P.
 leucopus</em> is less than 6 months. We are not aware of any
 evidence regarding the effect of coinfection on <em>Bm</em>
 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.
 <em>Parameter estimation:</em> We used Approximate
 Bayesian Computation (ABC) to estimate model parameters by fitting model
 trajectories for the mouse population, tick burden,
 <em>Bb</em> and <em>Bm prevalence</em> 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).  <em>Viability threshold:</em> We
 examined how key parameters of the model affect the viability of
 <em>Bb</em> and <em>Bm</em>. 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.