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An SEIR model of COVID-19, based on kinetic partial differential equations

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PlagueIncModel

Ideas

We are trying to establish a model which could be used to predict the numbers of deaths and infective of the noovel Coronavirus outbreak in Wuhan, China. The model is based on kinetics and we've made some basic hypothesis. Now that the virus is spreading all over the world. There's more data to train, optimize and validate the efficiency and accuracy of the model.

Categories of individuals

Susceptable, S

The healthy, uninfected crowd which have a probability of becoming the infective.

Exposed, E

Infective(Segregated), I0

Infective(Unsegregated), I1

Dead, D

Recovered, R

Equations

Kinetics

Coronavirus Data in Mainland China

Data Source Announcement

The data shown below are all captured from the website of National Health Commission of PRC(中国国家卫生健康委员会 http://www.nhc.gov.cn/) and Local Health Commission in China(Wuhan, e.g.). All figures are based on fact, if you have any question, please check the website above. Data is entered by hand, so there could be mistakes and please do correct us if so.

Date Day Skeptical Comfirmed Dead Cured DeathRatio CureRatio dD/dt dR/dt
2020/1/5 5 0 59 0 0 0.0% 0.0%
2020/1/11 7 0 41 1 4 2.4% 9.8% 0.5 2.0
2020/1/15 15 0 41 2 12 4.9% 29.3% 0.1 1.0
2020/1/16 16 0 45 2 15 4.4% 33.3% 0.0 3.0
2020/1/17 17 0 62 2 19 3.2% 30.6% 0.0 4.0
2020/1/18 18 0 121 3 24 2.5% 19.8% 1.0 5.0
2020/1/19 19 0 198 3 25 1.5% 12.6% 0.0 1.0
2020/1/20 20 54 291 6 25 2.1% 8.6% 3.0 0.0
2020/1/21 21 37 440 9 28 2.0% 6.4% 3.0 3.0
2020/1/22 22 393 571 17 28 3.0% 4.9% 8.0 0.0
2020/1/23 23 1072 830 25 34 3.0% 4.1% 8.0 6.0
2020/1/24 24 1965 1303 41 38 3.1% 2.9% 16.0 4.0
2020/1/25 25 2684 1975 56 49 2.8% 2.5% 15.0 11.0
2020/1/26 26 5794 2762 80 51 2.9% 1.8% 24.0 2.0
2020/1/27 27 6973 4535 106 60 2.4% 1.3% 26.0 9.0
2020/1/28 28 9239 5997 132 - - - - -
2020/1/29 29 12167 7711 170 - - - - -
2020/1/30 30 15238 9720 213 - - - - -
2020/1/31 31 17988 11721 259 - - - - -
2020/2/1 32 19544 14411 304 - - - - -
2020/2/2 33 21558 17238 361 - - - - -
2020/2/3 34 23214 20471 425 - - - - -
2020/2/4 35 23260 24363 491 - - - - -
2020/2/5 36 24702 28060 564 - - - - -
2020/2/6 37 26359 31212 637 - - - - -
2020/2/7 38 27657 34612 723 - - - - -
2020/2/8 39 28942 37251 812 - - - - -
2020/2/9 40 23589 40171 908 - - - - -
2020/2/10 41 21675 42638 1016 - - - - -
2020/2/11 42 16067 44747 1114 - - - - -
2020/2/12 43 13435 58761 1259 - - - - -
2020/2/13 44 10109 63851 1380 - - - - -
2020/2/14 45 8969 66492 1523 - - - - -
2020/2/15 46 8228 68500 1665 - - - - -
2020/2/16 47 7264 70548 1770 - - - - -
2020/2/17 48 6242 72436 1868 - - - - -
2020/2/18 49 5248 74185 2004 - - - - -
2020/2/19 50 4922 75002 2118 - - - - -
2020/2/20 51 5206 75891 2236 - - - - -
2020/2/21 52 5365 76288 2345 - - - - -

Current Progress

Death Rate - Infective Graph

We first drew a curve of death rate against infective, and we find a strong linear relativity between these two variables. The graph is shown below. avatar Then we drew a curve of the cured against time, and we found a strong linear relativity between them, which means the cured is steadily increasing with time.

Cured Crowds - Time Graph

avatar

Cure Rate - Infective Graph

avatar

Basic Statistics

This graph contains the basic statistics of the 2019-nCoV plague originated from Wuhan, Hubei Prov., China. Deathrate is illustrated as red line according to the right axis, and the infective(comfimred and uncomfirmed), death are illustrated in lines with data dots. avatar

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An SEIR model of COVID-19, based on kinetic partial differential equations

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