# Minimum time required to infect entire human population with a virus

I have an idea for a short SF story, where an alien race infects a tiny village with a virus, which eventually spreads to entire Earth. And I need to know what minimum time is required to infect the entire population?

As I remember, there was an assumption in the movie "Outbreak" that initial infection of a small American city with around a hundred initial infected carriers would spread to the entire United States within three days. Assuming the number of commercial flights every day (around 22 thousand per day over Europe only), can we assume that those three days would be enough to spread infection over the entire globe?

The main assumption here is that the virus does not kill immediately (or never). Carriers can successfully infect (many) others while still being alive1. So, this question seems not to be a duplicate of this one.

Update (after comments): Let's assume, that carrier can infect other person immediately after its own infection and it can survive in dead carrier body, that there is no cure for it and that there is no cure for that. But -- important in my story -- it infects only humans (sort of alien's humanity wipe-out or genocide). If I'm asking about minimum time required to infect entire planet, then take every aspect, that may enlarge this period at minimum and remove all possible obstacles = best infection scenario.

Edit: Would my "problem" and Vincent's model change radically, if we'd assume, that every carrier dies immediately after infecting next carrier?

1 If I remember correctly, there was some work made out there that proved when virus kills carrier within less than 5-6 hours since the initial infection, then such epidemia could never spread into the entire world, because it would not cross continents' borders -- unpiloted planes would fall, uncontrolled ships would sink etc. before reaching new continents.

• May I push on your requirements for infecting the "entire population?" Places like Chicago and London will be infected quickly, but groups such as the Sentinelese may not be infected in a thousand years. Also, what can be infected by the virus? A virus which can infect birds as well as humans will grow faster. A virus which can hit birds, humans, rats, mosquitos, houseflies, and more, plus survive in the harsh UV rays of the sun will grow even faster. – Cort Ammon Jan 9 '15 at 21:05
• Re your subnote: It depends more on the viability of the virus to survive in a dead host. If the virus remains viable, eventually the ship will be found, planes can continue on autopilot before crashing into a populated city, etc. – JohnP Jan 9 '15 at 21:06
• What you mean by the "entire population" makes a difference, as Cort Ammon notes. It also matters where the initial infection takes place. If it starts at, say, Chicago O'Hare or Frankfurt International Airport, a particularly contagious disease could probably reach most of the world in days. If it started in a more remote area where people are mostly limited to local travel, it would take much longer. – KSmarts Jan 9 '15 at 21:17
• Answer depends on way too many variables What is incubation period before infected carrier can spread virus? How virus is spread (touch/breath/body fluids/sex)? Does infection have visual signs? Can it be avoided, and how? Is being infected dangerous or desirable? Is it curable? Can you be vaccinated against it? Is vaccine available? – Peter M. Jan 9 '15 at 21:55
• @Peter Masiar et all: Sorry, I wasn't too specific! :). Let's assume, that carrier can infect other person immediately after its own infection and it can survive in dead carrier body, that there is no cure for it and that there is no cure for that. But -- important in my story -- it infects only humans (sort of alien's humanity wipe-out or genocide). If I'm asking about minimum time required to infect entire planet, then take every aspect, that may enlarge this period at minimum and remove all possible obstacles from this equation. Minimum possible = best infection scenario. – trejder Jan 10 '15 at 8:55

I just noticed you mentioned alien made virus... this makes things easier as the virus might already have the perfect characteristics for the job.

Ideally, the incubation period is about 24 hours long or less and that's pretty fast. Then, the infected can transmit the virus to others. After the firsts hours, he already show some sign of the virus. It was made to be airborne, so he cough a lot, transmitting the virus to others. The virus cannot replicate itself in mid air but it's small size allow him to remain in the air as long as the water particles are still there. Until someone else absorb them.

Since it was made by aliens, I suspect they have the ability to make that the virus influences on the people's behaviour. I would not go as far as saying their can control their mind because it's does not really make sense but it's an idea.

Now the real situation: How many people will be affected by that time? Or how many people can one person infect?

As a modified version it can have the optimal characteristics:

• Short period of incubation
• Quickly gain the ability to infect others
• Virus is airborne and persistent
• Symptoms are common with other diseases making it hard to notice at the beginning.
• Although the person get sick, it is very light at first but get worst after some time. Maybe after 2 or 3 weeks. This gives the infected plenty of time to infect others.

So in 2 weeks, one could suppose it is more than possible to contaminate all your family, your coworkers, your schoolmates, your friends and everyone you meet at least than 1 or 2 meters even if it's just for a short time. That could be over a hundreds people contaminated for most of us.

If everyone infects 50 people on average per day, everyday the number of infected is multiplied by 50 since the incubation period is 24 hours.

• day 1 = 1,
• day 2 = 50,
• day 3 = 2500,
• day 4 = 125 000,
• day 5 = 6 250 000,
• day 6 = 312 500 000,
• day 7 = 1 562 500 (and the first infected starts to feel bad),
• day 8 = ...everyone?

I'm not sure if the model is good because that speed of transmission is incredibly fast but even lowering the number of infected to 25 per days for each individuals will still make it reach the 7 billions very quickly.

And for some fun, try the game Plague, Inc. in trying to eradicate all humans from the surface of the Earth.

• I'd like to add one variable: the absence of symptoms while people are already infected. If there is a relatively large period in which it is not clear that someone is infected, this would prevent measures people take until its too late. – Jan Doggen Jan 10 '15 at 23:32
• There is one flaw in your model - as people infect each other the number of people available to infect drops. (i.e. if all 24 of your friends are already infected you can't infect anyone). – Tim B Jan 11 '15 at 10:16
• @trejder No, it makes no difference (well actually it stops the spread as you have no expansion if it's really 1-1 transmission. You need viral spread). Basically the issue is that in a connected network there are only so many links, once every connected node is already infected then there is no-where further for it to spread from on that node. – Tim B Jan 11 '15 at 14:26
• @trejder I think it changes a lot of things. First, I think it can't be a virus. Second, it will take a lot longer to spread unless the period of incubation is really 0. It is hard to imagine what it would look like in a crowd. The infected arrives in the crowd not knowing he is infected. He contaminate someone because he's too close , he dies. The new infected instantly contaminate someone else. repeat until everyone is dead or too far to be contaminated. – Vincent Jan 11 '15 at 18:13
• @trejder it sounds like magic ;) Guess it's possible – Vincent Jan 11 '15 at 23:08

In the current day, it would take a surprisingly long time. There are isolated tribes that still have very infrequent contact with the outside world. The virus would spread rapidly through the developed world and I'd expect most people to be infected within a few years but there will always be people on isolated bases, in quarantine, in isolated tribes, etc.

It would take years longer to reach them, possibly even centuries for some of the truly isolated tribes.

There are a lot of scientific studies about the spread of diseases, if you want a detailed analysis you should read up on them.

The alien race can vastly speed up the process though, they just need to seed the virus across the atmosphere, ironically focusing on those parts of the world that are least settled and least connected. The connected areas will infect themselves fast enough.

• Your answer actually very surprised me. My mentioned example ("Outbreak" movie from 1993) assumed entire USA being infected within 3-5 days. You're expecting most (all) developed world to be infected within... few years? How can that be true? While, I totally and completely agree with all your arguments and general point of view, I must admit, that I have absolutely no idea, from where did you take that "years"? Without any further study (of the scientific works, you mentioned) I'd assume entire developed world to be infected within 1-2 weeks. – trejder Jan 10 '15 at 22:10
• BTW: On the other hand, you proposed idea with seeding the virus across the atmosphere is something, that I haven't thought about and what really sounds interesting. – trejder Jan 10 '15 at 22:11
• @trejder Oil Rig workers often work for months at a time. (Although crews change more often than that). Nuclear submarine workers can be out for 6 months or longer. Isolationists/survivalists live in the wilderness for months at a time, as do some of the more paranoid and/or rustic cults and subcultures. Villages in the arctic circle that get cut off for months at a time. Scientists in Antarctica there for months at a time. etc. etc. The list goes on and you said you wanted everyone. – Tim B Jan 11 '15 at 10:19
• @trejder You will get 90% fast, all the major population centers for example, but that last 10% will be steadily slower and slower to reach. – Tim B Jan 11 '15 at 10:20

Assuming this virus is engineered, make it so there are no symptoms, but still communicable. If nobody knows they're infected, they go on about their daily routines, travelling for work/vacation, and so forth. An unaware populace would spread it orders of magnitude faster than with a contagion that is noticeable. Seeding the atmosphere would affect remote regions effectively.

If extermination is the main goal, all it would take is time, and then flipping a killswitch when the time is right. That being the case, the amount of time required to spread wouldn't matter much, as the end goal is eventually accomplished.

Social stratification would be a significant factor. It's all well and good to say that "this city has been infected," but the fact of the matter is that the infected is likely to be a relatively wealthy traveller or somebody who comes into contact with people who do international travel.

We can easily add weeks onto any timetable by recognizing that huge swathes of an urban population don't visit 'downtown' often for weeks or months at a time, especially in towns that constitute commuter belts you get the 'real' population of the town and the proportion that live and sleep there but spend most of their time in other cities, doing their shopping in transit or having it delivered (etc.)

An airborne virus is not likely to infect next door neighbors, or even people in a shop etc that an infected person visits, tho we can assume it is extraordinary in this regard, dispersal would still take more than a month [at the very least] even for relatively well connected locales, and that's after significant infection at the source begins spreading outwards.

No virus is perfect, it has to be chemically active otherwise it wouldn't beable to infect anybody..this is one reason why diseases don't wipe out all life on earth..they have needs and react with their environment just like other constructs.

Whilst I'd agree with XOr's answer, there's no such thing as an infection which causes no symptoms, it's impossible in that.. for a virus to bind with a host it must bind to some part of the host.. either it takes the place of something else meant to 'attach' to that enzyme/cell/compound, or it creates it's own 'blob' or bond in the host, either way it will impact normal operation. Even should this virus have a 'miniscule' footprint, what happens if a host is infected by billions of instances of this virus? What makes that impossible?

The easiest way to make this impossible is to engineer the virus such that it can only bond to a host at a very specific and rare chemical conjunction, which clearly makes infection less likely in the first place.

But if we overcome that..we still have the problem of "how is this virus replicating?" normally it would be using resources hijacked from the host, which is a symptom and causes other symptoms. If it creates very few copies of itself to restrict impact..then it's not going to be very effective at spreading infection, at least not quickly...and if it doesn't spread quickly/consistently the chances of spreading to isolated venues becomes increasingly more remote because inciences of interaction are reduced.