Model
The scientific core of MHASpread — mathematical formulation, transmission mechanisms, and control architecture.
MHASpread operates at two coupled spatial scales:
- Within-farm scale — stochastic SEIR dynamics for each host species in isolation
- Metapopulation scale — spatial kernel and animal-movement network connecting farms
Both scales are resolved daily in a discrete-time stochastic simulation loop.
Section Overview
| Page | Content |
|---|---|
| Model Overview | Compartmental structure, differential equations, stochastic framework |
| Transmission Dynamics | Species-specific $\beta$, spatial kernel mechanics, trade-network transmission |
| Control Strategies | Depopulation, ring vaccination, movement standstill, contact tracing |
Mathematical Notation
The table below summarises the core symbols used throughout the Model section.
| Symbol | Meaning | Units |
|---|---|---|
| $S, E, I, R, V$ | Compartment sizes (susceptible, exposed, infectious, recovered, vaccinated) | animals |
| $N_i$ | Total population at farm $i$ | animals |
| $\beta$ | Transmission coefficient | animal$^{-1}$ day$^{-1}$ |
| $\sigma$ | Mean latent period | days |
| $\gamma$ | Mean infectious period | days |
| $\phi$ | Baseline between-farm transmission probability | dimensionless |
| $\alpha$ | Spatial kernel decay rate | km$^{-1}$ |
| $d_{ij}$ | Euclidean distance between farm $i$ and $j$ | km |
| $P_{E_j}(t)$ | Probability that farm $j$ is exposed at time $t$ | dimensionless |
Continue to Model Overview →