A tramission model for 2019-nCov
Classify the people into four categories by isolated or not and sick or not:
| Number | sick | healthy |
|---|---|---|
| Isolated | I | K |
| Not isolated | J | ∞ |
We have:
- dJ = (b - a) * J * dt
- dI = (a * J - r * I) * dt
where a denotes the isolation rate, b the infection rate and r the cure rate.
By solving the partial differential equation above, we get: I = I0 * exp(-r * t) + (a * J0 / (b - a + r)) * exp((b - a) * t)
Furthur modification: the isolation rate a = sigmoid(pt + b) and increases with the time.
Final prediction:
