Table 1.

Model parameters and symbology used in model. Estimate indicates value used in initial model trial; values in parentheses represent range of value used in sensitivity analysis.

Symbol	Description	Estimate	Range used in sensitivity analysis	Reference	Notes
${\beta }_{Larva}$	Probability larva will acquire pathogen from infected dog	0.11	0.05–0.30	Piranda et al. (2011)
${\beta }_{Nymph}$	Probability nymph will acquire pathogen from infected dog	0.35	0.1–0.7	Piranda et al. (2011)
${\beta }_{Adult}$	Probability adult will acquire pathogen from infected dog	0	0–0.25	Piranda et al. (2011)	Female ticks that are not infected until they are adults do not pass the infection on to offspring.
${\beta }_{Dog}$	Probability that a dog will become infected if fed on by infected tick	0.5	0.1–0.9	Binder et al. (2021)
$ToT$	Filial Transmission	0.37	0.05–0.75	Piranda et al. (2011)
$\gamma$	Recovery Rate	1/7	1/15-1/3	(Levin et al., 2014; Piranda et al., 2008, 2011)	Average duration of rickettsemia is 7 days
$\omega$	Loss of immunity	No loss of immunity	1/180-1/4000	Levin et al. (2014)
$\mu$	Daily per capita dog birth/death rate	0.001	0.0001–0.005	(Garcia et al., 2018; López-Pérez et al., 2020; Villatoro et al., 2016), others
$M_{Larva}$	Tick acquisition rate	25	7.25–100	(J. Foley et al., 2019; Tinoco-Gracia et al., 2009)	Maximum number of new ticks of each life stage feeding on a dog per day at highest point in season
$M_{Nymph}$		5	1.25–20
$M_{Adult}$		1	0.25–4
Time lag (Interstadial time)	Time (days) for ticks to move from one stage to the next	60	30–120	Louly et al. (2007)	Time it takes for tick to transition from one instar to next