Table 1. Description of parameters and variables in model (5).
| Parameters | Value | Unit | Comments | resource |
|---|---|---|---|---|
| Am(t) | week−1 | The immigration number of migratory bird | ||
| Am1 | [3 × 106, 1 × 107] | year−1 | The immigration number of migratory bird | Assumed |
| Aw1 | [5 × 1010/520, 5 × 109/520] | week−1 | The average birth number of resident bird. | Assumed |
| Ap | (1.0438 × 109)/8 | week−1 | The birth number of domestic fowl. | [a] |
| Ah | (2.269741 × 108)/70/52 | week−1 | The birth number of human. | 24 |
| dm(t) | week−1 | The emigration rate of migratory bird. | ||
| dw | 1/520 | week−1 | The natural mortality rate of resident bird. | [b] |
| dp | 1/8 | week−1 | The sale rate of domestic fowl. | [c] |
| dh | 1/70/52 | week−1 | The natural death rate of human. | [d] |
| βmm | week−1 | Im(t)-to-Sm(t) transmission rate. | ||
| βm | week−1 | Vm(t)-to-Sm(t) transmission rate. | ||
| βwm | week−1 | Vw(t)-to-Sm(t) transmission rate. | ||
| βww | week−1 | Iw(t)-to-Sw(t) transmission rate. | ||
| βw | week−1 | Vw(t)-to-Sw(t) transmission rate. | ||
| βmw | week−1 | Vm(t)-to-Sw(t) transmission rate. | ||
| βpw | week−1 | Vp(t)-to-Sw(t) transmission rate. | ||
| βpp | week−1 | Ip(t)-to-Sp(t) transmission rate. | ||
| βp | week−1 | Vp(t)-to-Sp(t) transmission rate. | ||
| βwp | week−1 | Vw(t)-to-Sp(t) transmission rate. | ||
| βph | week−1 | Ip(t)-to-Sh(t) transmission rate. | ||
| βh | week−1 | Vp(t)-to-Sh(t) transmission rate. | ||
| p | week−1 | Confirmed rate of the infected population. | ||
| rm | [1, 10] | week−1 | The discharging quantity of H7N9 virus by Im. | Assumed |
| rw | [1, 10] | week−1 | The discharging quantity of H7N9 virus by Iw. | Assumed |
| rp | [1, 10] | week−1 | The discharging quantity of H7N9 virus by Ip. | Assumed |
| δ(T(t)) | week−1 | The natural mortality rate of virus. | ||
| q | 0.8 × 7 | week−1 | The effective disinfection rate. | [e] |
| σh | 7/3.3 | week−1 | The reciprocal of the incubation period. | 21 |
| μh | 0.36 | week−1 | The mortality rate of human caused by H7N9. | 21 |
| φm | [1/4, 2] | week−1 | The recovery rate of migrant birds. | Assumed |
| φw | [1/4, 2] | week−1 | The recovery rate of resident birds. | Assumed |
| φp | [1/4, 2] | week−1 | The recovery rate of domestic poultry. | Assumed |
| φh | week−1 | The recovery rate of human. | ||
| Sm(0) | Am1 | individual | The initial number of the susceptible migratory bird. | |
| Im(0) | individual | The initial number of the infective migratory bird. | ||
| Sw(0) | Aw1/dw | individual | The initial number of the susceptible resident bird. | |
| Iw(0) | individual | The initial number of the infective resident bird. | ||
| Sp(0) | 1.0483 × 109 | individual | The initial number of the susceptible domestic fowl. | [a] |
| Ip(0) | individual | The initial number of the infective domestic fowl. | ||
| Sh(0) | 2.269741 × 108 | IU | The initial number of the susceptible human. | 25 |
| Eh(0) | 0 | individual | The initial number of the exposed human. | |
| Ih(0) | 0 | individual | The initial number of the infected human. | |
| Vm(0) | 0 | individual | The initial quantity of H7N9 virus in environment discharged by migrant birds. | |
| Vw(0) | 0 | individual | The initial quantity of H7N9 virus in environment discharged by resident bird. | |
| Vp(0) | 0 | individual | The initial quantity of H7N9 virus in environment discharged by poultry. |
[a]The Laboratory of Animal Epidemiological Surveillance, China Animal Health & Epidemiology Center, Qingdao, Shandong, People's Republic of China.
[b]The lifetime of passerine birds, which will mature earlier, is only three or four years old. Large birds, such as eagle, eagle, etc., will need 8 to 11 years to arrive sexual maturity. In this paper, the average lifetime of resident birds is taken as 10 years.
[c]When domestic poultry grow to 8 weeks, they are the most flesh and will be sold by farmers. So, the sale coefficient is .
[d]dh is the reciprocal of the lifetime of human and the lifetime of human is taken as 70 years.
[e]Assuming the effective disinfection rate in every disinfection is 80% and trading markets are disinfected every day, the disinfection rate every week is 7 × 0.8.