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Viral Proliferation 
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Joined: Thu Jun 04, 2015 2:59 pm
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Post Viral Proliferation
No, seriously, listen to this.

Imagine a sphere with a surface area of six thousand square meters.

On this sphere, one thousand computers of negligible size are evenly spread out across the surface.

Each computer has one "pointer".

This "pointer" can delineate any circular 5 square meter area of the sphere. (even an area on the other side of the sphere)

The computers are completely independent of one another except when two computers delineated areas overlap.

In such a case the computers can communicate.

The size of the overlapped area does not affect any aspect of the data transfer.


And

Every month the pointer of every computer will "point" to a random patch of ground.

(If you don't want to do the math than you can assume that the pointers are pseudo random and are guaranteed to meet with at least one computer every month.)


One day, however, a special computer spreads a virus.

The effect of this virus is to duplicate inside the infected computer and spread to another computer when their areas overlap.

I was wondering how quickly it would take the virus to infect the entire population in three circumstances.

1) The virus originates in one computer, and spreads to another.

Once inside this second computer, it will duplicate and send a copy of itself to another computer.

Every copy, however, will only duplicate once and infect another computer.

If an infected computer makes contact with multiple other computers, the virus will send copies to all of them, but it will not spread a copy on the next month.

If a freshly infected computer with a copy to send meets a computer that is also infected, It will withhold the virus and wait until it meets an uninfected computer.


2) The virus is the same as the one above, except it will make copies and send them three times after it has been infected.

3) This virus will manufacture and distribute copies every month (even if it continually meets infected computers).



The reason I am asking this is that I am assuming that the differential rates of virus reproduction will lead to different "bandwidths" in terms of how quickly the virus will spread.

And assuming that the virus uses a great deal of energy to copy itself,

and that it plans to make more copies and send them through the same process,

and that the "rate of bandwidth increase" (the y axis), decreases as you approach the higher values of "number of months of duplication" because if we assume that a finite amount of months of exponential growth will reach the goal of total infection, than a virus that continues making copies past that number of months will be wasting energy.

In essence, what is the optimal number of copies a virus would have to make in order to get a respectable infection rate as well as not waste too much energy.

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Sat Dec 05, 2015 5:11 pm
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Joined: Thu Jun 04, 2015 2:59 pm
Posts: 39
Post Re: Ok everyone, listen to this.
Anyone know how to submit pics?

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Sat Dec 05, 2015 5:17 pm
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Posts: 39
Post Re: Ok everyone, listen to this.
yiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiig
yiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiig
yiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiig
yiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiig
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yiiiiiiiiiiiiiiiiiiiiiiiiiig
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xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx



This is the graph I had in mind.

Imagine the "i's" as white space or shading and the G's as points.

Who's the artistic genius now, Arioch?

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Sat Dec 05, 2015 5:24 pm
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Post Distribution efficiency problems...
Can you please choose a topic name that is not so random?

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Sun Dec 06, 2015 1:27 am
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Post Re: Viral Proliferation
Renamed the topic to be more accurate to subject matter.

**cough**

So, from what I can parse of the Op, the subject is:

1. There's a computer network
2. There's a virus in the network
3. What's a respectable rate of replication given:
4. Something about energy cost

For a post that goes into a lot of irrelevant detail skirting around the subject, you seem to have failed to include some critical data.

So let's break this down. You're talking about a computer virus spreading through a network and want to find out what a respectable replication rate is. For some reason, energy is a factor in this, but I cannot for the life of me fathom why.

In nature as well as in computer networks, the most respectable rate of viral replication and proliferation is "As much as physically possible", so we're talking on the order of thousands to millions or more depending on the virus and how efficiently it can force its host to produce copies. The absolute minimum is two. One virus creates two creates four creates eight etc. etc.

With the information at hand, the answer to the question of a respectable replication rate is: Anywhere between two and infinity.

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Sun Dec 06, 2015 4:05 am
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Post Re: Viral Proliferation
This is also incredibly off-topic.

I highly suggest asking questions like these on a forum that is more appropriate to your subject.

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Sun Dec 06, 2015 4:47 am
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Post Re: Viral Proliferation
Razor One wrote:
Renamed the topic to be more accurate to subject matter.

**cough**

So, from what I can parse of the Op, the subject is:

1. There's a computer network
2. There's a virus in the network
3. What's a respectable rate of replication given:
4. Something about energy cost

For a post that goes into a lot of irrelevant detail skirting around the subject, you seem to have failed to include some critical data.

So let's break this down. You're talking about a computer virus spreading through a network and want to find out what a respectable replication rate is. For some reason, energy is a factor in this, but I cannot for the life of me fathom why.

In nature as well as in computer networks, the most respectable rate of viral replication and proliferation is "As much as physically possible", so we're talking on the order of thousands to millions or more depending on the virus and how efficiently it can force its host to produce copies. The absolute minimum is two. One virus creates two creates four creates eight etc. etc.

With the information at hand, the answer to the question of a respectable replication rate is: Anywhere between two and infinity.


The absolute minimum is one...the virus could still spread if each copy only produces 1 offspring, though growth will be linear and will stop with the first failed replication. Probabilistic replication or replication failures could also lead to a non-integer rate.

I agree about the irrelevant and lacking detail. It sounds like there's a collection of computers, each of which points to another...as far as I can tell, nothing actually depends on the spherical geometry. And the notion that there's a major energy cost to a virus sending a copy of itself to another computer is odd, as is the idea that the virus would want to minimize that cost. As far as the virus is concerned, energy spent doing something other than replication is wasted energy, it'll want to use all available energy to replicate. There can be other factors influencing when the virus replicates, but they aren't stated.


Sun Dec 06, 2015 7:39 am
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