Epidemiological Model Construction

Epidemiology, due to some coincidence, has become very popular over the past year. Interest in modeling epidemics began to arise among many, and more and more people are already aware of the ubiquitous SIR model. But are there other similar models? How difficult is it to create and modify at all? But first things first.





A few months before the first news about COVID-19 appeared, I for myself, so to speak, for educational programming purposes, began writing an epidemic visualization program. In this simple program, circles of different colors moved across the field and infect each other. Six months later, somehow this already became the topic of my thesis (specialty "bioengineering and bioinformatics") and I had to really delve into the mathematical modeling of epidemics to write articles. Fortunately, the Internet suddenly began to fill with epidemiological materials. I mean, I started working some time before epidemiology became mainstream.





Before discussing my developments, I wanted to tell a little about what I learned about mathematical modeling of epidemics.





Just about the SIR model

SIR, , . , , , , , , .





, , .





SIR . , , : S (susceptible – , , , , ), I (infected – , ) R (recovered – , , , ). , 100 % S () . , 100 , S = 100, I = 0, R = 0. , , , , . : S = 99, I = 1, R = 0. .





, , : (β). 1/N (N – ), , . (β), ( : , ..).





:





:









, 0.99*β.





, - (γ), . , 10 , γ = 1/10. :





, , 0.99*β 1*γ. 1*γ. .





:





SEIR

SIR . . - SEIR , SIR.





SEIR (E – exposed, , ). SIR, I, E. E (α, ) I.





SIR . , SIR, , « ». () .





. : (SIQR, Q – quarantine), (SIRS, R S), ( S: S1, S2, …, ), ( I: I1, I2, …, , ) .. .





. , :





The spread of tuberculosis

- .





DEMMo ( )

DEMMo. DEMMo – Designer of Epidemic Math Models ( ). - . ( ), ( ) (/ / ). .





Results of various models implemented using the program
,

python. PyQt5. github ( git ) windows . , . , , , . . ..





The code is very poorly documented, and some of the comments are in Russian, and some in English. I know it's bad, I repent. Hopefully I'll do it. If there are any specific advice from experienced programmers, I will be very happy.

Contact mail: demmo.development@gmail.com





It just so happened that the relevance of the topic of my diploma has increased dramatically over the past year and a half. I hope the mainstream did not scare anyone away and someone was interested and informative. Thanks for attention.








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