Table 1 Model parameter description and disease input ranges used with supportive references

ι _i ^I

infectivity of species i in stage I

0.00000023

N/A

[12]

ι _i ^L

infectivity of species i in stage L (subclinical)

0.000000115

N/A

[8]

ι _i ^C

infectivity of species i in stage C (carrier infectivity)

0.000000115

N/A

[12]

s ₄ ^s

susceptibility of susceptible stage feedlot cattle

5.0

N/A

[19–21]

s _i ^s

susceptibility of animals besides feedlot in stage S

22.5

N/A

[21]

r(X)

1/measure of density of animals in county

N/A

USDA [1]

a

constant of proportion for contact rate

5

N/A

N/A

β _ij ^mn

transmission rate from type j in stage n to type i in stage m

N/A

[6, 17, 18, 21]

r _Vs

reduced susceptibility of vaccinated susceptible animals

0.5

N/A

[22–24]

r _Ve

reduced infectivity of vaccinated quiescent infected animals

0.5

N/A

[24, 25]

λ _L

rate of progression from latent to infectious stage (1/residency time in stage)

1/4.5 days

3-6

[26, 27]

λ _C

rate of progression from carrier to recovered

1/698.75 days

120-1277.5

[28]

λ _I

rate of progression from infectious to recovered

1/6 days

4-8

[8, 28]