Table 1 Parameters of model (0.2) and (0.3) with default values
From: Dynamic modeling and optimal control of cystic echinococcosis
Parameters | Biological definition | Value (range) | Source |
|---|---|---|---|
\({A}_{h}\) | Annual recruitment rate of human population | \(7.482\times {10}^{4}\) | [35] |
\(p\) | Influence coefficient of publicity measures | 0.1 (0–1) | Set |
\(\mu\) | Recovery rate of humans who are received surgery | 0.75 | [13] |
\({d}_{h}\) | Natural death rate of humans | 1/76.5 | [35] |
\(m\) | The mortality rate induced by CE | 0.022 | [36] |
\({\beta }_{1}\) | Prevailing infection pressure between parasite eggs and humans | \(1.004\times {10}^{-12}\) | Esti |
\(\nu\) | Transition rate from exposed humans to infectious humans | 1/14 | [13] |
\({A}_{l}\) | Annual recruitment rate of sheep | \(6.88\times {10}^{5}\) | [35] |
\({\beta }_{2}\) | Prevailing infection pressure between parasite eggs and sheep | \(1.08\times {10}^{-9}\) | Esti |
\(\epsilon\) | Fraction of annual slaughtered sheep | 0.2 (0.16–0.667) | Assumption |
\(\omega\) | Vaccination rate of sheep | 0.4 (0.2–1) | Set |
\(\delta\) | Invalid sheep vaccination rate | 0.67 (0.5–2) | Assumption |
\({d}_{l}\) | Natural death rate of sheep | 0.152 | [35] |
\({A}_{d1}\) | Annual recruitment rate of domestic dogs | \(2\times {10}^{5}\) | [35] |
\(q\) | The proportion of domestic dogs intake the livers of sheep | 0.3 (0–1) | Set |
\({\beta }_{3}\) | Prevailing infection pressure between infectious sheep and domestic dogs | \(7.1\times {10}^{-9}\) | Esti |
\(\gamma\) | Deworming recovery rate of infectious domestic dogs | 0.4 (0.1–0.9) | Set |
\(d\) | Natural death rate of dog | 0.08 | [37] |
\({b}_{d2}\) | Birth rate of stray dog | 2 | Assumption |
\({K}_{d2}\) | The food resources of stray dogs in the environment | 8.5 × 107 (6.5–10.5) × 107 | Assumption |
\({\beta }_{4}\) | Prevailing infection pressure between infectious sheep and stray dogs | \(5\times {10}^{-8}\) | Esti |
\(\theta\) | Disposing rate of stray dogs | 0.4 (0.1–0.9) | Set |
\(\phi\) | Egg released rate of one worm unit time | 42 | [38] |
\(h\) | Worm produced rate per dog per year | 560 | [14] |
\(\eta\) | Parasite eggs mortality rate in the dogs body | 12/5 | [14] |
\({t}_{1} ({t}_{2})\) | The average lifespan of domestic dogs (stray dogs) | 6 (4) | [14] |
\({\eta }_{1}\) | Parasite eggs natural mortality in the environment | 10.42 | [37] |