Viral Proliferation
Posted: Sun Dec 06, 2015 12:11 am
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.
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.