Table 1 Model parameters and their biological definitions
Biological definition | Symbol | Units | Baseline value | Source |
|---|---|---|---|---|
Mortality rate for humans | \(b_h\) | \(\frac{1}{50\times 365}\) | Day\(^{-1}\)s | Ndondo et al. 2016 |
Cattle mortality rate | \(b_c\) | \(\frac{1}{10\times 365}\) | Day\(^{-1}\) | Ndondo et al. 2016 |
Wildlife mortality rate | \(b_w\) | \(\frac{1}{15\times 365}\) | Day\(^{-1}\) | Ndondo et al. 2016 |
Tsetse fly mortality rate | \(b_v\) | \(\frac{1}{30} (\frac{1}{33}-\frac{1}{30})\) | Day\(^{-1}\) | Ndondo et al. 2016 |
Ratio of tsetse flies to humans | \(\theta _{vh}\) | \(3 (1-10)\) | Dimensionless | Assumed |
Ratio of tsetse flies to cattle | \(\theta _{vc}\) | \(8(1-10)\) | Dimensionless | Assumed |
Ratio of tsetse flies to wildlife | \(\theta _{vw}\) | \(10(1-15)\) | Dimensionless | Assumed |
Incubation rate of vectors | \(q_v\) | \(\frac{1}{25}( \frac{1}{30}-\frac{1}{25})\) | Day\(^{-1}\) | Ndondo et al. 2016 |
Incubation rate of humans, cattle, wildlife | \(q_h,q_c,q_w\) | \(\frac{1}{12}(\frac{1}{14}-\frac{1}{10})\) | Day\(^{-1}\) | Ndondo et al. 2016 |
Vector biting rate | a | \(\frac{1}{3}(\frac{1}{10}-\frac{1}{3})\) | Day\(^{-1}\) | Ndondo et al. 2016 |
Proportion of blood-meal on human | \(p_h\) | 0.09 | Dimensionless | Rock et al. 2015b |
Proportion of blood-meal on cattle, wildlife | \(p_c,p_w\) | Varied (0-1) | Dimensionless | Â |
Probability that an infectious fly infects a human, cattle,wildlife | b, u | \(0.62 (0-1)\) | Dimensionless | Ndondo et al. 2016 |
Probability that a fly becomes infected after biting an infectious human, cattle, wildlife | c, v | \(0.01 (0-1)\) | Dimensionless | Ndondo et al. 2016 |
Rate of progression from stage I to stage II for humans | \(\gamma _h\) | \(\frac{1}{30}\) | Day\(^{-1}\) | Ndondo et al. 2016 |
Rate of progression from stage I to stage II for cattle | \(\gamma _c\) | \(\frac{1}{25}\) | Day\(^{-1}\) | Ndondo et al. 2016 |
Rate of progression from stage I to stage II for wildlife | \(\gamma _w\) | \(\frac{1}{25}\) | Day\(^{-1}\) | Ndondo et al. 2016 |
Rate of progression from stage II to recovery and loss of temporary immunity for untreated humans | \(\kappa _h\) | \(\frac{1}{90}\) | Day\(^{-1}\) | Ndondo et al. 2016 |
Rate of progression from stage II to recovery and loss of temporary immunity for untreated cattle, wildlife | \(\kappa _c, \kappa _w\) | \(\frac{1}{75}\) | Day\(^{-1}\) | Ndondo et al. 2016 |