# SEIR 정리

Minhan Cho·2023년 1월 12일
0

## SEIR model

### SEIR without vaccination

$N$: total population
$S$: suspected(susceptible)
$E$: exposed
$I$: infected
$R$: recovered

$N = S + E + I + R$

$S, E, I, R$는 때때로 integer가 아니라 proportion으로 사용되기도 함 (e.g. $S \rightarrow \frac{S}{N}$)

### SEIR with vaccination

Annas, S., Pratama, M. I., Rifandi, M., Sanusi, W., & Side, S. (2020). Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia. Chaos, Solitons & Fractals, 139, 110072.

$N$: total population
$S$: suspected(susceptible)
$E$: exposed
$I$: infected
$R$: recovered

$N = S + E + I + R$

below is endemic point(equilibrium point)

$\nu$(vaccination)가 새로 추가된 변수

### Generalized SEIR

Peng, L., Yang, W., Zhang, D., Zhuge, C., & Hong, L. (2020). Epidemic analysis of COVID-19 in China by dynamical modeling. arXiv preprint arXiv:2002.06563.

$N = S + P + E + I + Q + R + D$

$\alpha$: protection rate(마스크 같은 거 잘 끼고 다녀서 보호받는 비율)
$\beta$: infection rate
$\gamma^{-1}$: average latent time (잠복기)
$\delta^{-1}$: average quarantine time
$\lambda$: cure rate
$\kappa$: mortality rate

• 의문: birth/death rate인 $\mu$는 어디에..?

## SEIR with more variables

### generalized SEIR + C

López, L., & Rodo, X. (2021). A modified SEIR model to predict the COVID-19 outbreak in Spain and Italy: simulating control scenarios and multi-scale epidemics. Results in Physics, 21, 103746.

• SEIRQD 사용하는 generalized SEIR + C for compartment: 감염돼서 격리된 Q(quarantine)와 달리, C(compartment)는 '거리두기'의 영향을 받는 인구라고 생각하면 됨

### SEIR-P

Mwalili, S., Kimathi, M., Ojiambo, V., Gathungu, D., & Mbogo, R. (2020). SEIR model for COVID-19 dynamics incorporating the environment and social distancing. BMC Research Notes, 13(1), 1-5.

• 사람에 집중한 SEIR + 병원균(P)을 합친 모델로, Infected 중에서도 증상발현자/무증상발현자를 나눠서 계산

### SEIR + gov.policy

Mandal, M., Jana, S., Nandi, S. K., Khatua, A., Adak, S., & Kar, T. K. (2020). A model based study on the dynamics of COVID-19: Prediction and control. Chaos, Solitons & Fractals, 136, 109889.

• policy가 다른 식으로 encoding되는 줄 알았는데, 그것은 아니고, lockdown 등 gov. policy 하에 해당되는 인원들을 또 따로 분류하기 위해 parameter $p$를 따로 설정한 것에 불과함

## SEIR + ARIMA

Hu, K., Yang, J., Hou, C., Bi, Z., Wang, J., & Zhang, Y. (2022, July). Omicron BA. 2 Prediction Research Based on SEIR-ARIMA Mixed Model. In 2022 3rd International Conference on Information Science, Parallel and Distributed Systems (ISPDS) (pp. 116-121). IEEE.

• SEIR과 ARIMA의 prediction값을 이용해서 linear regression으로 final prediction 구했다고 함
• Jilin Province from 2002.3.8 to 2022.3.28 (20 days)
• RMSE, MAPE 등 결과 없음: 결과가 그다지 좋지 않았던 것 아닌지?

## Misc

Yang, C., & Wang, J. (2020). A mathematical model for the novel coronavirus epidemic in Wuhan, China. Mathematical biosciences and engineering: MBE, 17(3), 2708.

SEIR on Wuhan이라 일단 달아놓기는 하는데...

multidisciplinary