Theory and Modern Applications
From: Optimal control of visceral, cutaneous and post kala-azar leishmaniasis
Parameter | Definition | Value | Source |
---|---|---|---|
\(\Gamma _{h}\) | Human birth rate | 0.0015875 day−1 | |
\(\Gamma _{r}\) | 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 | |
\(c_{1}\) | 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 | |
\(\varrho _{v}\) | 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] |