Prediction and analysis of the spread of COVID-19
1. Traditional model
1.1 prediction and analysis of COVID-19 epidemic spread based on SIR model
The model is established by differential equations. First Δ t \Delta t Δ Number of new patients in t:
The first item describes the number of uninfected persons transmitted from infected persons to uninfected persons at time t , which is interpreted as the number of uninfected persons contacted by the total number of infected persons at the daily contact rate, and becomes the number of uninfected persons transmitted from infected persons to uninfected persons at time t (therefore, it should be multiplied by s (T) ; The second item describes the infected person cured at the time of T; The third item describes the infected person who died at the time of T.
Remove n from the above expression, divided by Δ t and taking the limit, the following limit equation can be obtained:
It can be used to analyze the change law of each proportional variable with time
Of course, the biggest highlight of this article is that the function of y about s is written according to the limit equation, the derivative of the function and the standing point are determined, and the following laws are determined.
In our problem, we are facing a non closed dynamic problem, that is, the population of a region is not fixed, and there are inflow and outflow. The specific form is shown in the following figure:
The idea now is that these two quantities are not used as modeling variables, but rather to control the initial values of S and e at each time. Both the input population and the output population include the possibility of S and E, but their proportions are affected by: the degree of control ( whether the 48 hour nucleic acid certificate is required)