Epidemiology

Basic Definitions

attack rate: the % of people who get sick after exposing to something

relative risk: the % who become ill in one group divided by the % who become ill in another group, i.e. the ratio of two attack rates

case & control 实验组与对照组？

incidence & prevalence: Thinking about a tank of prevalent cases, then the incident cases shoud come in while dealth or recovery should come out.

prevalence: number with the disease/population size

prevalence depends on incidence rate and duration:

$$P/(1-P) \approx IR \times D$$

incidence: number of new cases/population size at risk

case-fatality ratio(CFR): the percent of people with the condition who die in a time period (death/cases)

age-adjusted death rate:

$$\sum_{\text{age group}} age \% \times \text{CFR by age}$$

life expectation

$$(\sum_{eachAgeGroup} death \times midpoint)/total$$

Sometimes there is no midpoint and we will use the upper bound of each age group.

disability-adjusted life year(DALY): the day you could live times your life quality (from 0 to 1)

When there will be multi-possible outcomes, use:

$$\sum \text{the day you could live} \times quality \times possibility$$

potential years of life lost(PYLL):

$$\sum_{eachAgeGroup} \times CFR \times lifeExpectation \times confirmedCase\%$$

Modeling

R0 - the number of people that one person could spread to

We could reduce R0 by:

• vaccinating and reduce the number of people who are susceptible
• quaranting, to reduce transmission (or culling animals)

SIR Model

• susceptible
• infected
• Recovered or removed

S + I + R = 1

Given transmission rate $\beta$ and recovery rate $\gamma$:

$$\delta S(t)/\delta t = -\beta S(t)I(t)$$

$$\delta R/ \delta t = \gamma I$$

$$\delta I / \delta t = \beta SI - \gamma I$$

$$R_0 = \beta / \gamma$$

SEIR Model

• susceptible
• exposed
• infected
• recovered

Or, you have to add births, deaths, migration or carriers of a disease.

After adding death parameter $\mu$ =birth parameter $\nu$, where $\rho$ is the death possibility of the disease:

$$\delta S(t)/\delta t = \nu -\beta S(t)I(t) - \mu S$$

$$\delta R/ \delta t = (1-r)\gamma I - \mu R$$

$$\delta I / \delta t = \beta SI - (\gamma+\mu)/(1-r) I$$

$$R_0 = \beta(1- \rho)\nu/(\mu + \gamma)\mu$$

To stop an epidemic, we need R0<1.

$$S< \gamma \beta$$

• make S small by vaccinating
• make $\beta$ small by washing hands or social distancing
• make$\gamma$ large by quarantine(shorten$1/\gamma$)

Vaccination

herd immunity: we only need to vaccinate a portion of people to eradicate an infection, the portion is:

$$p_c = 1-1/R_0$$

periods

incubation period: the time between infection and onset of clinical disease/symptoms

latent period: time between infection and becoming infectious