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Table 1 Summary and definition of symbols used in epidemiological models

From: A genetic epidemiological model to describe resistance to an endemic bacterial disease in livestock: application to footrot in sheep

Symbol

Definition

S

The number of susceptible animals

E

The number of infectious doses in the environment

L

The number of latently infected animals

I

The number of diseased and infectious animals in SELIRS model

D

The number of diseased and infectious animals in SELDCRS model

C

The number of infectious carriers in the SELDCRS model

N

The total number of host animals in the population

R

The number of recovered animals

ν

The rate at which latently infected animals develop clinical signs and become infectious

μ

The rate at which infectious doses (bacteria) die in the environment, other than by host animals

ω

The rate at which infectious doses (bacteria) are physically removed by each host animal in the population

χ

The total rate at which infectious doses (bacteria) are removed from the environment, calculated as μ + ω N

γ

The rate at which diseased and infectious animals stop showing clinical signs and are no longer infectious, in the SELIRS model

κ

The rate at which diseased animals stop showing clinical signs, while continuing to be infectious in the SELDCRS model

α

The rate at which infectious animals that no longer show clinical signs of the disease stop being infectious in the SELDCRS model

λ

The rate at which recovered animals lose resistance and become susceptible

ξ

The rate at which susceptible animals become infected by 1 unit of infectious dose in the environment

φ

The rate at which an infectious animal sheds infectious doses in the environment

p

The prevalence of the disease as observed from clinical signs

R'

The notional reproductive rate of the infectious disease