Coronavirus: Covid 19 - Disease spreading

This is a technical document specific related to disease spreading. For a more general discussion about the corona virus please see: Coronavirus Covid-19

Contents

Reflection

1. Introduction

This documenten discusses the technical issue how a contagious disease spread through a population.
The way this is done is by means of examples
The examples only demonstrate the situation when people have the disease and when they spread the virus.
The example stops when they are tested and when they go in quarantaine. This can mean a hospital. The situation what happens there after is not considered i.e. that they are released from hospital or that they die.

The examples are summarized in a table.

    column 1 New Infections shows the number of new infections for each day. Those infections are a result because all persons that have the disease at least contaminate one other person.
  1. column 2 Total Infections shows the number of total infections. Column 2 is the sum of column 1
  2. column 3 In quarantaine shows the number of people that tested that have the disease for each day.

2. Example 1 - 1 day

Picture 1
The disease starts at day 1 with person #1. Each person spreads the disease to 1 person. Each person goes into qaurantaine after 1 day and then spreading caused by that person stops.
  1. At day 1 person #1 will be infected. Nobody will go into quarantaine.
  2. At day 2 person #2 will be infected by person #1. Person #1 goes into quarantaine.
  3. At day 3 person #3 will be infected by person #2. Person #2 goes into quarantaine.
  4. At day 4 person #4 will be infected by person #3. Person #3 goes into quarantaine.
  5. After 10 days: 10 persons had the disease, 9 persons will be in quarantaine and one person has the disease 
             New         Total           In           Total         Active
At day   infections   Infections     quarantaine   quarantaine    infections
  1          1            1               0             0              1
  2          1            2               1             1              1
  3          1            3               1             2              1 
  4          1            4               1             3              1 

                                     Stable situation
What this example shows (in principle) what happens if you have a population 100 patients who are infected with the corannavirus. The assumption is that each individual infects exact one person and there after goes into quarantaine: the population stays constant. Goes into quarantaine means that he or she stops infected other people.
Each row in the spread sheet shows the situation for one patient by patient number: When infected, by which patient and which patient is infected and the day when in quarantaine.
For example: patient #2, shown in row #2, is infected by patient #1 at day #2, infects patient #3 at day #3 and goes into quarantaine the same day (As indicated by the yellow square).
See next example for a better explanation.

3. Example 2 - 2 days

Picture 2
The disease starts at day 1 with person #1. Each person spreads the disease to 1 person/per day. Each person goes into qaurantaine after 2 days and then spreading caused by that person stops.
  1. At day 2 person #2 will be infected by person #1. Nobody will go into quarantaine.
  2. At day 3: #3 will be infected by #1, #4 will be infected by #2.
    Person #1 will go into quarantaine. This is indicated by the yellow square.
  3. At day 4: #5 will be infected by #2, #6 by #3, #7 by #4.
    Persons #2 will go into quarantaine.
  4. At day 5: #8 will be infected by #3, #9 by #4, #10 by #5. #11 by #6. #12 by #7.
    Persons #3, and #4 will go into quarantaine.
  5. At day 6: #13 by #5, #14 by #6, #15 by #7, #16 by #8, #17 by #9, #18 by #10, #19 by #11 and #20 by #12
    Persons #5, #6 and #7 will go into quarantaine.
  6. At day 7: #21 will be infected by #8, #22 by #9, #23 by #10, #24 by #11, #25 by #12, #26 by #13, #27 by #14, #28 by #15, #29 by #16, #30 by #17, #31 by #18, #32 by #19 and #33 by #20, Persons #8, #9 #10 #11 and #12 will go into quarantaine.
When you look at this data in total you get: 
             New         Total           In           Total         Active
At day   infections   Infections     quarantaine   quarantaine    infections
  1          1            1               0             0              1
  2          1            2               0             0              2 
  3          2            4               1             1              3 
  4          3            7               1             2              5
  5          5           12               2             4              8 
  6          8           20               3             7             13 
  7         13           33               5            12             21 
  8         21           54               8            20             34  
  9         34           88              13            33             55 
 10         55          143              21            54             89
In picure 2:
  • patient #2, shown in row #2, is infected by patient #1 at day #2, infects patient #3 at day #3, infects patient #4 at day #4,and goes into quarantaine the same day (As indicated by the yellow square).

4. Example 3 - 3 days

Picture 3
The disease starts at day 1 with person #1. Each person spreads the disease to 1 person. Each person goes into qaurantaine after 3 days and then spreading stops.
  1. At day 2 person #2 will be infected by person #1. Nobody will go into quarantaine.
  2. At day 3: #3 will be infected by #1, #4 will be infected by #2. Nobody will go into quarantaine.
  3. At day 4: #5 will be infected by #1, #6 by #2, #7 by #3, #8 by #4. Person #1 will go into quarantaine.
  4. At day 5: #9 will be infected by #2, #10 by #3, #11 by #4, #12 by #5, #13 by #6, #14 by #7, #15 by #8.
    Person #2 will go into quarantaine.
  5. At day 6: #16 by #3, #17 by #4, #18 by #5, #19 by #6, #20 by #7, #21 by #8, #22 by #9, #23 by #10, #24 by #11, #25 by #12, #26 by #13, #27 by #14 and #28 by #15
    Persons #3, #4 will go into quarantaine.
  6. At day 7: #29 will be infected by #5, #30 by #6, #31 by #7, #32 by #8, #33 by #9, #34 by #10, #35 by #11, #36 by #12, #37 by #13, #38 by #14, #39 by #15, #40 by #16, #41 by #17, #42 by #18 ... #52 by #28 Persons #5, #6, #7 and #8 will go into quarantaine.
  7. At day 8: #21 will be infected by #8, #22 by #9, #23 by #10, #24 by #11, #25 by #12, #26 by #13, #27 by #14, #28 by #15, #29 by #16, #30 by #17, #31 by #18, #32 by #19 and #33 by #20, Persons #9, #10 #11 #12 #13, #14, and #15 will go into quarantaine. 
             New         Total           In           Total         Active
At day   infections   Infections     quarantaine   quarantaine    infections
  1          1            1               0             0              1
  2          1            2               0             0              2
  3          2            4               0             0              4 
  4          4            8               1             1              7 
  5          7           15               1             2             13 
  6         13           28               2             4             24 
  7         24           52               4             8             44 
  8         44           96               7            13             81  
  9         81          177              13            28            149 
 10        149          326              24            52            274
  1. Total Active infections= Total Infections - Total quarantaine

5. Example 4 - 1.5 days

Picture 4 
             New         Total           In           Total         Active
At day   infections   Infections     quarantaine   quarantaine    infections
  1          1            1               0             0              1
  2          1            2               0             0              2
  3          2            4               2             2              2 
  4          2            6               1             3              3 
  5          3            9               2             5              4 
  6          4           13               2             7              6 
  7          6           19               4            11              8 
  8          8           27               4            15             12 
  9         11           38               7            22             16 
 10         15           53              10            32             21

                                      1.5 days

6. Example 5 - 0.5 days.

Picture 5 
             New         Total           In           Total         Active
At day   infections   Infections     quarantaine   quarantaine    infections
  1         16           16               8             8              8
  2          8           24              12            20              4
  3          4           28               6            26              2 
  4          2           30               3            29              1 
  5          1           31               2            31              0 
  6          0           31                                            0 

                                     0.5 days
  1. The simulation start with 16 patients.
  2. During day 1, 8 patients go into quarantaine. This are the patients #1,#3,#5,#7,#9,#11,#13 and #15. That is why at the end of the day there are 16-8 = 8 active infections. The other 8 patients give one infection (the next day), that on average 1 infection for every 2 days.
  3. It is important to emphasize that this is on average 1 infection for each 2 days and not every 0.5 days, because that is misleading. As such we should also not mention an average of 0.1 days but: on average 1 infection every 10 days

Reflection - General Conclusion

The most important means to eradicate the corona virus is to detect as fast as possible every one who has the disease (or has a high chance to get the disease) and to bring these people in quarantaine or in a hospital.
Created: 23 April 2020

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