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# Table 1 Parameter values

From: Optimal control of visceral, cutaneous and post kala-azar leishmaniasis

Parameter | Definition | Value | Source |
---|---|---|---|

\(\Gamma _{h}\) | Human birth rate |
0.0015875 day^{−1}
| [17, 18] |

\(\Gamma _{r}\) | Dog birth rate |
0.073 day^{−1}
| [19] |

\(\Gamma _{v}\) | Sandfly birth rate |
0.299 day^{−1}
| [20] |

\(\mu _{h}\) | Human natural mortality rate |
0.00004 day^{−1}
| [20] |

\(\mu _{r}\) | Dog natural death rate |
0.000181 day^{−1}
| [21] |

\(\mu _{v}\) | Natural mortality rate of sandflies |
0.0714 day^{−1}
| [22] |

\(k_{1}\) | Inverse of \(C_{l}\)’s latent period |
0.0157871 day^{−1}
| [6] |

\(k_{2}\) | Inverse of \(V_{l}\)’s latent period |
0.007789 day^{−1}
| [2] |

\(k_{3}\) | Inverse of \(C_{l}\)’s latent period after \(V_{l}\) recovery |
0.011111 day^{−1}
| [6] |

\(k_{4}\) | Inverse of \(V_{l}\)’s latent period after \(C_{l}\) recovery |
0.005111 day^{−1}
| [2] |

\(k_{6}\) | Inverse of dormant period before the development of PKDL | 0.0049259 | [2] |

a
| Biting rate of sandflies |
0.125 day^{−1}
| [23] |

\(\gamma _{4}\) | Recovery rate from \(C_{l}\), after being recovered from \(V_{l}\) |
0.008 day^{−1}
| [14] |

\(\gamma _{5}\) | \(V_{l}\)’s treatment rate for \(C_{l}\)’s recovered |
0.03 day^{−1}
| Free to choose |

\(\delta _{1}\) | \(V_{l}\)-induced expiry in humans |
0.011 day^{−1}
| [24] |

\(\delta _{2}\) | \(V_{l}\)-induced expiry in humans for \(C_{l}\) recovered humans |
0.006 day^{−1}
| [14, 24] |

\(c_{1}\) | Trans. prob. of \(C_{l}\) in sandflies |
0.22 day^{−1}
| assumed |

\(b_{1}\) | Trans. prob. of \(C_{l}\) in humans |
0.0714 day^{−1}
| assumed |

\(c_{2}\) | Trans. prob. of \(V_{l}\) in sandflies |
0.22 day^{−1}
| [25] |

\(b_{2}\) | Trans. prob. of \(V_{l}\) in humans |
0.0714 day^{−1}
| [26] |

c
| Trans. prob. of either strain in a fly from reservoir |
0.22 day^{−1}
| [25] |

b
| Trans. prob. of either strain in dogs from a fly |
0.0714 day^{−1}
| [26] |

\(\gamma _{1}\) | Per capita rate of recovery from \(C_{l}\) |
0.0056 day^{−1}
| [14] |

\(\gamma _{2} \) | \(V_{l}\)’s treatment rate |
0.03 day^{−1}
| Free to choose |

\(\delta _{3}\) | PKDL-induced expiry rate in humans |
0.0006 day^{−1}
| [27] |

\(\alpha _{d}\) | Rate of \(V_{l}\)-induced expiry in dogs |
0.00181 day^{−1}
| [23] |

\(\tau _{d}\) | Natural recovery of dogs |
0.000274 day^{−1}
| [23] |

\(\beta _{2}\) | PKDL’s natural healing for \(C_{l}\)’s recovered human |
0.01 day^{−1}
| [14, 28] |

\(\varrho _{v}\) | Inverse vectors’s incubation period |
0.1428 day^{−1}
| [22] |

\(\omega _{d}\) | Rate of immunity loss in dogs |
0.00274 day^{−1}
| [23] |

k
| Rate of immunity loss in humans |
0.000548 day^{−1}
| [23] |

\(\beta _{1}\) | PKDL’s natural healing in humans |
0.00556 day^{−1}
| [28] |

ρ
| Cross-immunity between \(C_{l}\) and \(V_{l}\) | (0,1) | [14] |