Table 2 Definitions and corresponding values of the model parameter with the daily timescale

μ _E

mortality rate of eggs

(0.0025, [1])

μ _QL

mortality rate of questing larvae

(0.006, [1])

μ _QN

mortality rate of questing nymphs

(0.006, [1])

μ _QA

mortality rate of questing adults

(0.006, [1])

μ _FL

natural mortality rate of feeding larvae

(0.038, A)

μ _FN

natural mortality rate of feeding nymphs

(0.028, A)

μ _FA

natural mortality rate of feeding adults

(0.018, A)

H ₁

the number of white-footed mice

(200, [1])

${\beta }_{H_{1}L}$

transmission probability from H₁ to larvae

(0.6, [13])

${\beta }_{N{H}_1}$

transmission probability from nymphs to H₁

(1, [13])

${\mu }_{H_1}$

death rate of the white-footed mice

(0.012, [13])

H ₂

the number of alternative host H₂

(variable)

${\beta }_{H_{2}L}$

transmission probability from H₂ to larvae

(variable, [36])

${\beta }_{N{H}_2}$

transmission probability from nymphs to H₂

(variable, [36])

${\mu }_{H_2}$

death rate of the alternative host H₂

(variable)

D

the number of deer

(20, [1])

p

the maximum number of eggs produced

(3000, [1])

p ₁

larval biting bias for host H₂

(variable, [37])

p ₂

nymphal biting bias for host H₂

(variable, [37])

b(t)

birth rate of eggs produced

(see subsection ‘Time-dependent parameters’)

d _E (t)

development rate of eggs

(see subsection ‘Time-dependent parameters’)

d _L (t)

development rate of larvae

(see subsection ‘Time-dependent parameters’)

d _N (t)

development rate of nymphs

(see subsection ‘Time-dependent parameters’)

F _L (t)

feeding rate of larvae

(see subsection ‘Time-dependent parameters’)

F _N (t)

feeding rate of nymphs

(see subsection ‘Time-dependent parameters’)

F _A (t)

feeding rate of adults

(see subsection ‘Time-dependent parameters’)

D _L

density-dependent mortality rate of feeding larvae

($\frac{0.001084}{H_1+p_1{H}_2}$, E)

D _N

density-dependent mortality rate of feeding nymphs

($\frac{0.001084}{H_1+p_2{H}_2}$, E)

D _A

density-dependent mortality rate of feeding adults

($\frac{0.001084}{D}$, E)