ASF (Pen-Level) Decoding Infection and Transmission Dynamics
Within-pen infection, spillover to adjacent pens, and control via isolation, culling, and pen evacuation.
Model Architecture
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Differential Equations
$$
\frac{dS_{18}}{dt} = b_{18} -
\Big[
\beta_1 \frac{I_{18}}{N_{18}} S_{18}
+ \beta_2 \frac{P I_{17}}{N_{17}} S_{18}
+ \beta_3 \frac{F I_{17}}{N_{17}} S_{18}
\Big] f_T f_H f_{pH}
- \mu_{18} S_{18}
$$
$$
\frac{dE_{18}}{dt} =
\Big[
\beta_1 \frac{I_{18}}{N_{18}} S_{18}
+ \beta_2 \frac{P I_{17}}{N_{17}} S_{18}
+ \beta_3 \frac{F I_{17}}{N_{17}} S_{18}
\Big] f_T f_H f_{pH}
- \sigma_{18} E_{18} - \mu_{18} E_{18}
$$
$$
\frac{dI_{18}}{dt} = \sigma_{18} E_{18} - C_{18} I_{18}
$$
$$
\frac{dS_{17}}{dt} = b_{17} -
\Big[
\beta_4 \frac{I_{17}}{N_{17}} S_{17}
+ \beta_5 \frac{P I_{18}}{N_{18}} S_{17}
+ \beta_6 \frac{F I_{18}}{N_{18}} S_{17}
\Big] f_T f_H f_{pH}
- \mu_{17} S_{17}
$$
$$
\frac{dE_{17}}{dt} =
\Big[
\beta_4 \frac{I_{17}}{N_{17}} S_{17}
+ \beta_5 \frac{P I_{18}}{N_{18}} S_{17}
+ \beta_6 \frac{F I_{18}}{N_{18}} S_{17}
\Big] f_T f_H f_{pH}
- \rho_{17} E_{17} - \mu_{17} E_{17}
$$
$$
\frac{dI_{17}}{dt} = \rho_{17} E_{17} - \phi_{17} I_{17} - d_{17} I_{17}
$$
$$
\frac{dQ_{17}}{dt} = \phi_{17} I_{17} - d_{17} Q_{17} - \gamma_{17} Q_{17}
$$
$$
\frac{dR_{17}}{dt} = \gamma_{17} Q_{17} - \mu_{17} R_{17}
$$
$$
\frac{dS_{16}}{dt} = b_{16} - \mu_{16} S_{16} - \upsilon_{16} S_{16}
$$
$$
\frac{dR_{16}}{dt} = \upsilon_{16} S_{16} - \mu_{16} R_{16}
$$
Model Parameters
| # | Parameter | Description |
|---|---|---|
| 1 | S_i, S_j, S_k | Susceptible pigs in ith pen (i=1…18), adjacent (j=i±1), neighbor (k=i±2) |
| 2 | E_i, E_j | Exposed pigs in ith / jth pen |
| 3 | I_i, I_j | Infectious pigs in ith / jth pen |
| 4 | R_j, R_k | Recovered pigs in adjacent / neighbor pens |
| 5 | Q_j | Isolation compartment for infected pigs |
| 6 | b_i | Recruitment (new pigs introduced) into ith pen |
| 7 | β₁, β₄ | Pig-to-pig transmission rate |
| 8 | β₂, β₅ | Transmission via personnel movement |
| 9 | β₃, β₆ | Transmission via contaminated feed |
| 10 | μ_i | Natural mortality rate of pigs |
| 11 | σ_i, ρ_i | Rate exposed → infected |
| 12 | φ_i | Isolation rate of infected pigs |
| 13 | γ_i | Recovery rate from isolation |
| 14 | C_i | Culling rate in infected pen |
| 15 | d_i | Disease-induced mortality rate |
| 16 | υ_i | Vacating rate of whole pen |
| 17 | P | Movement of personnel index |
| 18 | F | Contaminated feed index |
| 19 | f_T | Temperature effect function |
| 20 | f_H | Humidity effect function |
| 21 | f_{pH} | pH effect function |