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Table 1 Definitions of parameters and variables, and parameter values used for the age-structured US model.*

From: The United States and Canada as a coupled epidemiological system: An example from hepatitis A

Variable/Parameter

Definition

Values

Reference

S i U S MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaem4uam1aa0baaSqaaiabdMgaPbqaaiabdwfavjabdofatbaaaaa@30EE@

Number of susceptible individuals in the United States at a given time t in age class i

N/A (not applicable)

N/A

E i U S MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyrau0aa0baaSqaaiabdMgaPbqaaiabdwfavjabdofatbaaaaa@30D2@

Number of exposed (infected but not yet infectious) individuals in the United States at a given time t in age class i

N/A

N/A

I i U S MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemysaK0aa0baaSqaaiabdMgaPbqaaiabdwfavjabdofatbaaaaa@30DA@

Number of infectious individuals in the United States at a given time t in age class i

N/A

N/A

R i U S MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemOuai1aa0baaSqaaiabdMgaPbqaaiabdwfavjabdofatbaaaaa@30EC@

Number of recovered individuals in the United States at a given time t in age class i

N/A

N/A

V i U S MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemOvay1aa0baaSqaaiabdMgaPbqaaiabdwfavjabdofatbaaaaa@30F4@

Number of vaccinated individuals in the United States at a given time t in age class i

N/A

N/A

γ i

Mean duration of infectious period

3.5, 3.0, 2.5, 2.5, 2.5, 2.5, 2.5 weeks

[27,28]

δ

Mean duration of latent period

2 weeks

[27,29]

f

Rate of waning vaccine-derived immunity

0.58% per year

[24]

a i

Rate at which an individual in age class i ages (enters age class i+1)

0.2, 0.2, 0.1, 0.1, 0.1, 0.05, 0 per year for age classes 1, 2, ... 7

N/A

b US

Birth rate

0.015 per year

[30]

d i U S MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemizaq2aa0baaSqaaiabdMgaPbqaaiabdwfavjabdofatbaaaaa@3110@

Rate at which an individual in age class i dies

0, 0, 0, 0, 0, 0.0167, 0.0750 per year

[30]

Ï„ i , e n d U S MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeqiXdq3aa0baaSqaaiabdMgaPjabcYcaSiabdwgaLjabd6gaUjabdsgaKbqaaiabdwfavjabdofatbaaaaa@366D@

Rate at which a susceptible individual in age class i becomes exposed due to travel in endemic countries

1.90 × 10-3, 8.06 × 10-4, 1.42 × 10-4, 8.89 × 10-5, 5.94 × 10-5, 1.76 × 10-5, 1.80 × 10-5 per year

[8,13]

β i j U S MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeqOSdi2aa0baaSqaaiabdMgaPjabdQgaQbqaaiabdwfavjabdofatbaaaaa@32BD@

Rate at which an infectious person in age class j infects a susceptible person in age class i (domestic transmission)

See Appendix

See Appendix; [8,13]

g i U S MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaem4zaC2aa0baaSqaaiabdMgaPbqaaiabdwfavjabdofatbaaaaa@3116@

Rate at which a susceptible individual in age class i becomes vaccinated

Varies according to scenario

N/a

N i U S MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemOta40aa0baaSqaaiabdMgaPbqaaiabdwfavjabdofatbaaaaa@30E4@

Population size of age class i

20, 20, 40, 40, 40, 60, 40 (millions)

[30]

  1. * The superscript 'US' denotes that the parameter values is speific to the US. Lack of superscript indicates that the same value is used for Canada and the US.
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BMC Infectious Diseases

ISSN: 1471-2334

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