Table 1.

Model parameters and their respective values. Time is measured in days for all parameters

Parameter	Description	Value
$t_{\bullet 0}$	start of activity period for tick life stage $\bullet$	varies
$t_{\bullet f}$	end of emergence period for tick life stage $\bullet$	varies
$l_{\bullet }$	length of emergence period for tick life stage $\bullet$	varies
$\widehat{L}$	size of emerging larval population	varies
${\widehat{N}}_i$	size of emerging infected nymphal population	varies
${\widehat{N}}_u$	size of emerging uninfected nymphal population	varies
${\gamma }_l$	density-dependent contact rate between larvae and mice	0.004 (Randolph 1999a)
${\gamma }_n$	density-dependent contact rate between nymphs and mice	0.008 (Randolph 1999a)
${\beta }_{\mathit{nm}}$	transmission probability from nymphs to mice	0.83 (Davis and Bent 2011)
${\beta }_{\mathit{ml}}$	transmission probability from mice to larvae	0.6 (Davis and Bent 2011)
${\mu }_l$	larval death rate	0.015 (Ogden et al. 2005a)
${\mu }_n$	nymphal death rate	0.015 (Ogden et al. 2005a)
${\mu }_m$	mouse death rate	0.01 (Schug et al. 1991)
b	mouse birth rate	0.1 (Schug et al. 1991)
k	mouse carrying capacity	varies (Ostfeld et al. 1996b)
${\sigma }_l$	larval overwintering survival probability	0.21 (Davis and Bent 2011)
${\sigma }_n$	compound fecundity and survival parameter	10 (Davis and Bent 2011)
$\alpha$	density dependence parameter	0.0045
$\tau$	season length	210 (Ogden et al. 2018)