Theory and Modern Applications
Table 1 Parameters of SIR-SI model (1)
From: Optimal control in a malaria model: intervention of fumigation and bed nets
No | Par | Description | Condition | Dimension |
|---|---|---|---|---|
1 | \(A_{{h}}\) | Daily human birth rate | \(A_{{h}}>0\) | person × day−1 |
2 | \(A_{{v}}\) | Daily mosquito birth rate | \(A_{{v}}>0\) | mosquito × day−1 |
3 | \(\mu_{{h}}\) | Natural death rate of humans | \(\mu_{ {h}}>0\) | day−1 |
4 | \(\mu_{{v}}\) | Natural death rate of mosquitos | \(\mu_{ {v}}>0\) | day−1 |
5 | γ | Recovery rate of humans | γ>0 | day−1 |
6 | δ | Rate of transition back to vulnerable humans due to the end of the immunity period | δ>0 | day−1 |
7 | \(c_{{h}}\) | Successful infection probability from infectious mosquitos to susceptible humans | \(c_{{h}}>0\) | \((\text{mosquito}\times\text{day})^{-1}\) |
8 | \(c_{{v}}\) | Successful infection probability from susceptible mosquitos to infectious humans | \(c_{{v}}>0\) | \((\text{mosquito}\times\text{day})^{-1}\) |
9 | \(\beta_{{h}}\) | Biting rate | \(\beta_{{h}}\geq1\) | \(\frac{\text{person}}{\text{mosquito} \times \text{day}}\) |
10 | \(\beta_{{v}}\) | Biting rate | \(\beta_{{v}}\geq1\) | day−1 |
11 | u | Fumigation rate | u ≥ 0 | day−1 |
12 | k | Bed net proportion | 0 ≤ k ≤ 1 | – |
13 | η | Bed net quality | 0<η<1 | – |