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Model Introduction
Model Introduction
There are several models can be used in simulating the current situations of the epidemic: SI model, SIS model, SIR model and SEIR model.
But before knowing the model, we would like to know the four types of people during the epidemic: Susceptible, Exposed, Infected and Recovered.
Susceptible: Individual is able to become infected
Exposed: Individual has been infected with a pathogen, but due to the pathogen’s incubation period, is not yet infectious.
Infected: Individual is infected with a pathogen and is capable of transmitting the pathogen to others.
Recovered: Individual is either no longer infectious or “removed” from the population.
Mainly parameters will use in the model is
Infected rate, recovery rate, incubation rate, initial infected people, fraction infected people in this area.
SI model
SI model
SI model used those only susceptible get infected and will never be recovered.
SIS model
SIS model
SIS model used those Infected can be recovered as susceptible
SIR model
SIR model
SIR model as those infected can be recovered as susceptible. The recover here not limit to treated to health , but also means those infected been quarantine can't be access to other suscepitble.
SEIR model
SEIR model
SEIR model applied to those epidemic have some people who are infected by others but with no instant reaction symptoms. They will wait couples of days to show their sick.
SI and SIS
Example -
SI: HIV SIS: Cold
β: infection rate in SI
γ: recovery rate in SIS
SIR
Example: measles
ξ: Recover rate
SEIR
Example: Ebola
ξ: Recover rate
σ: intubation rate
Background Introduction
Background Introduction
Before jump to the compare among three main infectious disease, I'd like to introduce some basic concepts in their
Infection Rate (R0) :
The average number of infected people will pass the disease to susceptible without any control.
For example, if the infected have acess to 10 people, and 2 people get disease. Then the infection rate is 2.
We hope the Infection rate is below 1 to make situation become better. In order to achieve that we can staying at home, avoid meeting people.
Incubation period:
the period of time between exposure to an infection and when symptoms begin
Compare MERS, SARS and COVID-19
Compare MERS, SARS and COVID-19
The table below shows the basic features of the three disease. We can see that, although coronavirus is not that high fatalities rate, it do have high infection rate and long incubation period, which means it hard for people to know whether if they get disease.
Current Situation
Current Situation
We can see that nearly all countries have confirmes cases of COVID-19.
Europe has the highest confirmed death cases due to the COVID-19
Model Fitted
Model Fitted
Cluster Analysis
Cluster Analysis
Before we start doing cluster, I think that the scale of confirmed case may have influence. So , I use the log transform here. Using dtw kmeans based on confirmed cases here, base on our domian knowledges, I just naively think there should 4 kind of countries:
Not happen, starter, break out and passed. And we get similar answers.
Class 1 : only small numbers of confirmed cases. They are not in breakout. But it just matter of time.
Class 2 : Had several confirmed case, it's sever than the class 1. But it's not breakout, it;s just start.
Class 3 : Not breakout but with large number infections
Class 4 :Totally Breakout
Class 1 : Small number
Class 2: just start
Class 3: before breakout
Class 4 : Totally Break out
SIR model Simulation
SIR model Simulation
So , we use US and China as an example here.
The basic informations are listed in the table below :
So, first, we simulate using SIR model in python
China SIR Model Simulation
We do find infected will get over 60% total population in China situation. And the situation will become better in 20 days.
US SIR Model Simulation
US situation is much worse than China, neary 80% of population will get infected and the situation become better until 30 days.
SEIR model simulation
SEIR model simulation
here, we use SEIR model to simulate the situation in China and US. The calculator is website is epidemic calculator.
From the plot above, we do find after taking quarantine action, China situation get better. And now Corona are almost under control in China.
No Control in US
If US don't take any controls, we can find that abotu 300million peole may get impacted.
Control in US
If US do take any controls, the impacted people are decrease a half, surged at 120 million.
Conclusion
Conclusion
we do think quarantine is a good way to keep ourselves safe
Wash your hand, keep clean, make yourself safe.
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