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Applying Network Theory to Epidemics: Control Measures for *Mycoplasma pneumoniae* Outbreaks

Lauren Ancel Meyers*†

, M.E.J. Newman*‡, Michael Martin§, and Stephanie Schrag§

Author affiliations: *Santa Fe Institute, Santa Fe, New Mexico, USA; †University of Texas at Austin, Austin, Texas, USA; ‡University of Michigan, Ann Arbor, Michigan, USA; §Centers for Disease Control and Prevention, Atlanta, Georgia, USA

Main Article

## Table

Notation for epidemiologic interaction network model

Notation |
Definition |

*W* |
Number of wards in the facility |

*C* |
Number of caregivers working in the facility |

*μ*_{w} |
Average no. of caregivers working in a ward |

*μ*_{c} |
Average no. of wards in which a caregiver works |

*r* |
Probability that a given caregiver works in a given ward |

*Ρ*_{χ} |
Probability that a caregiver works in *k* wards |

*q*_{χ} |
Probability that a ward has *k* caregivers working in it |

ƒ_{0}(*x*) |
Probability generating function (pgf) for the degree distribution of caregivers |

g_{0}(*x*) |
pgf for the degree distribution of wards |

ƒ_{1}(*x*) |
First select a random ward, and then select a random caregiver working there. This expression represents the pgf for the number of other wards in which that caregiver works. |

g_{1}(*x*) |
First select a random caregiver, and then select a random ward associated with that caregiver. This expression represents the pgf for the number of other caregivers working in that ward. |

*τ*_{w} |
Probability of transmission from a ward to a caregiver |

*τ*_{c} |
Probability of transmission from a caregiver to a ward |

Ф_{0}(x) |
pgf for the number of wards affected by transmission from a random caregiver |

Ф_{1}(x) |
First select a random ward and assume that it is affected by the bacterium, then select a random caregiver working there. This expression represents the pgf for the number of other wards affected by that caregiver. |

Γ_{0}(*x*) |
pgf for the number of caregivers affected by transmission from a random ward |

Γ_{1}(*x*) |
First select a random caregiver and assume he/she is infected, then select a random ward in which that caregiver works. This expression represents the pgf for the number of other caregivers infected by individuals working/living in that ward. |

_{} |
Average number of wards affected in an outbreak |

1 - *Ѕ*_{c} |
The size of the caregiver giant component—the largest set of infected caregivers that are all connected through work in common wards |

*2- Ѕ*_{w} |
The size of the ward giant component—the largest set of affected wards that are all connected through common caregivers |

β_{w}(*x*) |
pgf for the number of patients in affected ward *w* who contract the bacterium |

*Β*(*x*) |
pgf for the total number of patients in the facility who are infected during an epidemic |

Main Article

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