Initialization of State for Eigenvector

[stevencarlislewalker]

0. Start with an 'original' model.
1. Remove all accumulators from the state vector.
2. Remove all 'exogeneous' effects (e.g. time-varying parameters, vaccination).
3. Choose one exposed state and initialize it to a small number (e.g. $10^-5$).
4. Define a vector, $\sigma$, that sums to one with one value for each susceptible state (could be a constant vector for a uniform distribution ... but could be the normalized age distribution if the S classes differ only in their age ... ).
5. Set the values of the susceptible states to the values in $\sigma (1 - 10^-5)$.
6. Set all other state vectors to zero, resulting in a state vector that sums to 1.
7. Run simulations for 100 (or so) time-steps and get the final state vector.
8. Remove any susceptible, dead, or recovered classes from this final state vector.
9. Normalize this final state vector so that it sums to 1, to produce the eigenvector, $v$.
10. Create a new state vector, $s$, which will become the initial state vector for simulations from the original model.
11. Define the total population size, $N$, as the actual population being modelled by the original model.
12. Define the initial number of exposed/infected/infectious/other individuals, $I_0$ in the original model.
13. Set the susceptible states in $s$ as $\sigma (N - I_0)$.
14. Set the dead and recovered states in $s$ to $0$.
15. Set the remaining states in $s$ to $v I_0$