From: Theory of reactive interventions in the elimination and control of malaria

Symbol | Parameter | Assumed value or limits | Source |
---|---|---|---|

\(I_{t}\) |
Number of infectious individuals at time t
| \(0 \le I_{t} \le 10000\) | |

\(N\) | Total human population | \(N = 10,000\) | Approximate population of Zambian health centre catchment |

\(\beta\) | Transmission parameter, i.e. the potential number of new infections per infected individual at the next time step | \(\beta > 0\) | |

\(\gamma\) | Proportion of infectious population that remains infectious at next time step (which includes the removal of infections through passive detection) | \(0 < \gamma < 1\) | |

\(\varphi_{t}\) |
Number of infections detected (and treated) at time t
| \(\varphi_{t} > 0\) | |

\(\varepsilon_{t}\) |
Escape probability: the proportion of infections that escape treatment at time t
| \(0 < \varepsilon_{t} < 1\) | |

\(p\) | Proportion of population that is (patently) infected | \(0 < p < 1\) | |

\(\upiota\) | Number of index cases investigated per unit time | \(\upiota > 0\) | |

\(\upnu\) | Number of neighbours of passively-detected index cases investigated | \(0 < \nu < N\) | Fixed property of programme |

\(\uptau\) | Targeting ratio: ratio of the size of a random sample that would be need to be tested and treated, to the number actually treated, in order to achieve the same number of effective treatments. This is a measure of clustering of malaria infections | \(\uptau \ge 1\) | Estimated from cross-sectional survey data |