Coronavirus (The numbers game)

[showmethesnow]

As I mentioned yesterday, this is all a numbers game. Now this will be a very crude idea how it plays out and will only include the major players and not include other potential factors that will typically have much smaller impact. Would also like to add these are my thoughts alone (right or wrong) through reading a little on the matter over the years as well as how I see the math playing out. So I more then welcome criticism or debate so I can fine tune my thoughts or make major readjustments. 

Now below we have a small sample size of 20 individuals within a host pool that a virus has now been introduced. 

Now there are several things we need to consider to figure out how this will all play out. First, the probability of transmission on an encounter with an uninfected individual. Second, How many encounters will we see in a given day. Third how many days will this individual be contagious. And lastly how contaminated is the pool (In this case it is a clean pool with no infections except for patient zero). Now there are other factors that can come into play as well and actually be major players. These are two I can think of offhand. First, how quickly does the virus so incapacitate an individual where they are bed ridden and their encounter rate drops to a fraction of their typical day (this is why it is so important to keep infected and non-infected separated with hospitals). Second and of a more morbid nature is how deadly is the virus as this takes potential spreaders out of the equation (care needs to be taken with those that have passed because quite often they can still be contagious well after the fact).

 

So let's get back to the virus that has been introduced into the self contained clean pool of hosts above. I am going to keep the numbers very simple here to give the general concept and we are going to let it play out without any outside interference.

This is just an example to show how a virus (not necessarily coronavirus) will play out in a perfect bubble. 

Let's assume everyone in this pool has 5 interactions a day with different random individuals. Now let's place the probability rate of transmission for each encounter at 10 %. Then we are seeing an infection period of 4 days. And finally we are looking at a pool that is clean from infection. Now I am going to keep the math here as bare bones as I can without throwing in statistics which would makes this far more complex. Just know that it will give you a rough ballpark figure of the numbers we are talking about. So let's follow this infected individual over his 4 day infectious period. Now assuming a 10% infection rate with 5 encounters a day we are looking at a 50% chance of someone getting infected ((10+10+10+10+10)/100). Now lets expand that for 4 days (4*(10+10+10+10+10)/100) which gives us 200%. Broken down lets say this means 2 new infected individuals.

 

So this is what we see at day 5 after the patient zero is no longer infectious. We now have 2 new carriers that are having 5 encounters a day. So 10 encounters a day. But we also are now seeing an inhibiting factor thrown in, though very minor at this time, that will start to impact the rate of growth in this process. This would be patient zero who has already contracted the disease and is now immune to it and can no longer be a spreader. So what happens, as the example below shows, he now is cutting into the carriers encounter rate with uninfected individuals. On this particular day we are now seeing 9 possible infectious encounters instead of 10. Now there is also one other inhibiting factor as well. If you have the virus and are a carrier you can't very well catch it once again from another carrier so these 2 carriers encounters with each other are also cutting into the encounter rate.  In the example below this means that over a 4 day span instead of 40 encounters with uninfected individuals we can cut it by 4 to give us 36 encounters so we are now seeing a 340% probability over a 4 day span. ***Now rounding down would give us 3 new infections through the next period but in this case I am going to use 4 new cases.***

 

 

We are now at day 10. We now have 4 infections and 3 immune individuals. The encounter rate from these 4 individuals over the next 4 days will be 80. But the number of encounters with other infected and the immune is now at 24 and is starting to become a factor. So lets figure out the % we are looking at over the next 4 day span. 80-24= 56 encounters at 10% infection rate equals 560%. So lets say we now have 6 new infections for the next 4 day period.

 

 

So here we are at day 15. 6 new carriers and 7 individuals that are now immune. With the 6 new carriers we would see an encounter rate of 120 over the 4 day span. Of those 120 encounters 72 cases are with a nonviable host.  So now we are looking at 480% infection rate over this 4 day period. So basically 5 new infections will occur through this period. If you will note this is lower then the previous 4 day span which saw 560% rate and 6 infections. We have now entered a period of time where we are seeing diminishing returns. So we are now seeing a major impact with the inhibiting factor (infected and immune individuals) as the pool gets dirtied. This is the downward curve we are seeing on all these graphs. So let's move this forward one more 4 day period and see what we have with the 5 new carriers.

 

This is where we are at at day 20. 5 new carriers but now we have 17 that can not get reinfected. At this point we are only seeing 3 that are not infected. So what are the chances now that these 3 uninfected individuals can get infected. Let's see. 5 individuals combining for 100 encounters over a 4 day period subtracting 90 inconsequential encounters gives us 10 legit encounters (100%) giving us 1 new infection. After this last infection we have basically achieved herd immunity leaving 2 individuals untouched or 10% of the population.

 

Now all of the above is just a very crude idea of what happens in a perfect bubble using very simple math. In the true world there are so many more variables. You have mitigation and containment possibilities. The variables we used in the above examples will be different. Hereditary traits, geography, possible vaccine, population density, etc.., etc..., etc... can all greatly influence what we actually see. Where as the math I used was very bare bones simple the statistical math the experts use quickly becomes very complex as you throw more and more variables into the equation.

Now over the coming few days/weeks as I find time (it seems I have plenty of time now) I plan on expanding on the above and even moving out in different directions as well as explaining the whys of some of the numbers I have thrown out.  I more then welcome any healthy criticism and/or additions to the material from others all I ask is that we please try to keep it as apolitical as we can and focus on the science.

[showmethesnow]

Now every outbreak starts with a patient Zero as shown above on the first example. As of now patient zero seems to have originated in Wuhan in late December from animal to human transmission. But that may not actually be correct if reports that have come out of some victims/deaths beforehand as early as early/mid November are in fact true. I will explain in a little bit what this may imply.

There are several theories on how this transmission occurred. But the major one is that there was animal to human transmission in a Wuhan wet market. The other one that has some support is that this was a bio-engineered virus (weaponized) that escaped from a level 4 bio-hazard lab in Wahun. Now there are others out there but they have very little support at this time. Won't even discuss China's (CPC) claim that this was a virus created in a US army base and then intentionally sent over there.

Now the major theory is pretty self explanatory. Either the vendor or customer/s contracted it from an animal within the market (believe they are talking a bat at this time). 

As for the second one, escaped from a biolab, well it has met with some resistance and down played. The reason being that the experts claim the markers on the virus suggest this was most definitely not a man-made virus and was naturally occurring. The CPC (Communist Party of China) claims this is proof that the virus never escaped from the bio-lab. One problem with their claim is that just because it was naturally occurring doesn't mean that it didn't escape from the lab. It just means that it wasn't bio-engineered by them. Now there are some possibilities here. First, the lab also used animals in their experiments, some of the same animals that that would be found in the wet market probably coming from the same sources. So now we have the possibility of the virus physically being in the lab. Now one possibility is an employee contracted it in the lad and then brought it out of containment. Now there is also another possibility as well. If they are true, there were reports that China arrested an employee shortly after the outbreak for selling test animals from the lab to the wet market.

Now let's jump back to the possibility that the reports on earlier cases (as early as November) are in fact true. These case were reported to be outside of the Wuhan region. This might imply a couple of things. First, it might be verification that the animal with the virus was being transported up to Wuhan and people involved with the handling of the animal may have contracted the virus. Now there is also one other possibility. We may have very well seen a small flare up elsewhere which may or may not have been contained. This brings in the possibility that ground zero may have actually happened elsewhere but the virus didn't gain traction until Wuhan. This also brings another possibility up as well. Was there a small flareup that was contained that the Chinese brought samples up to it's lab to study where it subsequently got loose. Now if there were in fact earlier cases we will have to study where these cases were, the number, and clustering and the time frame involved between the cases. These will give us an idea of which of the possibilities above is most likely, if not present another whole scenario.

Not sure if we will ever really know the answers to these questions though. Chinese have been very closed mouth with the details (much of what we are getting are from other internal sources), they are destroying evidence that would help decipher what happened , they are refusing any outside investigators into the region and they are feeding the world faulty information. None of this helps to promote the ability to decipher what happened, where mistakes were made, and how we can improve our chances down the road.

[CAPE]

1 hour ago, showmethesnow said:

Now every outbreak starts with a patient Zero as shown above on the first example. As of now patient zero seems to have originated in Wuhan in late December from animal to human transmission. But that may not actually be correct if reports that have come out of some victims/deaths beforehand as early as early/mid November are in fact true. I will explain in a little bit what this may imply.

There are several theories on how this transmission occurred. But the major one is that there was animal to human transmission in a Wuhan wet market. The other one that has some support is that this was a bio-engineered virus (weaponized) that escaped from a level 4 bio-hazard lab in Wahun. Now there are others out there but they have very little support at this time. Won't even discuss China's (CPC) claim that this was a virus created in a US army base and then intentionally sent over there.

Now the major theory is pretty self explanatory. Either the vendor or customer/s contracted it from an animal within the market (believe they are talking a bat at this time). 

As for the second one, escaped from a biolab, well it has met with some resistance and down played. The reason being that the experts claim the markers on the virus suggest this was most definitely not a man-made virus and was naturally occurring. The CPC (Communist Party of China) claims this is proof that the virus never escaped from the bio-lab. One problem with their claim is that just because it was naturally occurring doesn't mean that it didn't escape from the lab. It just means that it wasn't bio-engineered by them. Now there are some possibilities here. First, the lab also used animals in their experiments, some of the same animals that that would be found in the wet market probably coming from the same sources. So now we have the possibility of the virus physically being in the lab. Now one possibility is an employee contracted it in the lad and then brought it out of containment. Now there is also another possibility as well. If they are true, there were reports that China arrested an employee shortly after the outbreak for selling test animals from the lab to the wet market.

Now let's jump back to the possibility that the reports on earlier cases (as early as November) are in fact true. These case were reported to be outside of the Wuhan region. This might imply a couple of things. First, it might be verification that the animal with the virus was being transported up to Wuhan and people involved with the handling of the animal may have contracted the virus. Now there is also one other possibility. We may have very well seen a small flare up elsewhere which may or may not have been contained. This brings in the possibility that ground zero may have actually happened elsewhere but the virus didn't gain traction until Wuhan. This also brings another possibility up as well. Was there a small flareup that was contained that the Chinese brought samples up to it's lab to study where it subsequently got loose. Now if there were in fact earlier cases we will have to study where these cases were, the number, and clustering and the time frame involved between the cases. These will give us an idea of which of the possibilities above is most likely, if not present another whole scenario.

Not sure if we will ever really know the answers to these questions though. Chinese have been very closed mouth with the details (much of what we are getting are from other internal sources), they are destroying evidence that would help decipher what happened , they are refusing any outside investigators into the region and they are feeding the world faulty information. None of this helps to promote the ability to decipher what happened, where mistakes were made, and how we can improve our chances down the road.

The bio lab angle is more interesting/juicy, but most likely patient 1 was some sloppy fool who got bat urine or blood in his eye while slaughtering it for a customer.

[showmethesnow]

1 hour ago, C.A.P.E. said:

The bio lab angle is more interesting/juicy, but most likely patient 1 was some sloppy fool who got bat urine or blood in his eye while slaughtering it for a customer.

I am not sure what to think at this point. Typically I would side with you even though we do have the coincidence of this being the only Level 4 lab in existence in China to the best of my knowledge. But, and let me adjust my tin foil hat before I continue,  there are other things going on that put a big question mark in my mind. Now I just sort of brushed over some of the things I have read the last couple of weeks, there are more things out there. We are seeing researchers/doctors involved in the outbreak in Wahun being muffled with a couple/few that have disappeared off the face of the earth. We have also seen one of them die with the listed cause of death as Coronavirus. This seems reasonable except when you start seeing what is happening with the other professionals it starts to put a doubt in your mind. We are also seeing the destruction of records about the outbreak in Wahun.

Now the CPC has basically put a clamp on information coming out . All information has to go through them and get their stamp of approval. So much of the information is second hand so it is very difficult to know what to believe and not to believe. Now what I have mentioned so far has a good chance of being correct because much of it has come from these same doctosr/researchers that are in the middle of the crap. Now there is other information coming out but it is coming from the average Joe so it is hard to gauge. information that if true really drives home how hard the CPC seems to be trying to erase all information in regards to the outbreak in Wahun. But the fact that we are seeing quite a bit of collaboration of the facts from others starts to make you believe that the information may be true. Now this could be nothing more then the CPC trying their damnedest to save face in the worlds eyes. But to me it is really starting to look as if they are trying desperately to cover up something. 

eta: There was one other thing I forgot to mention. There was a large aberration through this period with cell phone service.  There was a cut to service of over 2 million phones. Now I am not sure exactly where these were cut from. Whether in was nation wide or focused on a certain region but it tells me that the CPC might have been trying to cut contact for these individuals to the outside world.

[PhineasC]

The wet markets will not be closed and this will keep happening. This is exactly how SARS started.

[showmethesnow]

Now the the topic I first threw up was about spread in a self contained bubble of a small community without interference (below at day 10). But let's see what happens when we expand on that.

Below we have a collection of communities. Our infected community is in the center in red. Now let's see what happens when we have interaction between all these communities. The virus in this example has a life cycle of 8 days from initial infection until the host is no longer contagious. Now lets assume we have an infected travel who just caught the virus departing to each of these communities. In example A we are seeing 14 days to that community. Well above the 8 day life cycle of the virus so we see no spread. In example B we have a traveler heading to a community only three days away so there will be spread. Any infected traveler now departing from that community as they travel to the farthest out community now runs into the same issue as example A where the travel time is longer then the life cycle of the virus. So we see no spread. But let's look at example C. Travel time to the farthest out community is 11 days. It is beyond the 8 day life cycle of the virus so you would think they would be spared. But that is not the case. What we have are steeping stones for this virus to hop scotch to that point. In fact the virus can take 2 different routes to reach the farthest community. It can hopscotch from community 1 to 2 then move forward or it can move directly to 2 and then proceed, as both these routes are within the life cycle time frame.

 

 

Now let's see what we have a month later. Note that we have seen the infection limited as we now have another limiting factor to its spread. And that is travel time from one group of hosts to another potential group of hosts. Now this example is based on individual travelers departing to each of these communities. It does not take into account the possibility of groups of individuals traveling together where they can infect each other on the trip thus expanding the life cycle of the virus substantially.  Now these travel time are unrealistic in our current age when people can now travel from one side of the globe within hours. These times are more representative of a bygone period of time. So I guess what I am saying is that we no longer have the luxury of this very important limiting factor in play as they did years ago which would quite often see outbreaks burnout before they could reach the more distant communities/nations.

 

[showmethesnow]

Okay we just looked at a case of where travel time was a limiting factor on outward spread, where it could only move outward as quickly as the the fastest mode of travel by the host. In the example above we were talking the fastest mode being that of a horse. Now I want to expand on that a touch. There are natural barriers put in place that will either stop the spread or make it very difficult to continue. In the example below we see mountains to the north and an ocean to the east. Now these barriers may or may not stop it (depending on if travel is possible over/through/around) but regardless they are a major impediment to its spread in those directions. 

 

So let's see how this would play out over time using travel time and natural barriers and assuming there are available host throughout.. Each red circle is a week further in time. Notice what we are seeing is a ripple effect such as you would see if you dropped a rock into a pool of water. But we are also seeing these ripples die as they meet the natural barriers (Ocean/east, mountains/SW)

These two factors alone (travel time and natural barriers) play an extremely important role in limiting the spread of a disease. In earlier centuries these quite often put the brakes on any major outspread of disease throughout Europe and Asia.

Now on my next post that I will throw up later today I want to show what happens when you take these two limiting factors to a virus' spread out of the equation. It is not a pretty picture and one reason I believe we are more likely then ever to experience out breaks in this world that will make the ones we saw in past years pale in comparison.

[showmethesnow]

Is there anyone even interested in my postings here? If not I will just let this thread die a lonely death. I have better things to do then spend a couple of hours writing them up. Like playing online slots.