---
# System prepended metadata

title: Meeting 3/5
tags: [meeting note]

---

# Meeting 3/5
###### tags: `meeting note`

```graphviz
digraph Emodel {
    node [shape=box] S, F, I_pre, I_asym, I_sym, V1, V2, R, E, D
    S -> V1
    S -> E [label="Infected"]
    V1 -> E
    V1 -> V2
    V2 -> E
    E -> I_pre
    I_pre -> I_asym
    I_pre -> I_sym
    I_asym -> R
    I_asym -> F
    I_sym -> D
    I_sym -> R
    I_sym -> F
    F -> E
    
    {rank = "same"; S; V1; V2}
    {rank = "same"; R; F; D}
    
    rankdir = "LR"
}
```
- make the initialization model more general
- $I$ can be presymptomatic, symptomatic, asymptomatic
- Vaccination first dose $V_1$ and second dose $V_2$
- vaccination efficency wanning


## Optimization

- data $D=\{(x_i,y_i)\}$ where 
    - $x$ is multi-dimension vaccination strategy
    - $y\in\mathbb R$ be our objective
        - infection, death, YLL, e.t.c.
- randomize choose a number of $x_i$, sovle their corresponding $y_i$ by our network simulation
- by linear regression, model $D$ as 

$$
Y=
\begin{pmatrix}
y_1\\y_2\\\vdots
\end{pmatrix}=X\beta +\epsilon
$$

- adding some constraints, to be a linear program
    - solve by linear program solver
    - sovle by some optimization algorithm