# Is it reasonable for a city to be almost completely wiped out after two weeks?

We are in an average, modern middle sized city with about 500,000 people. I am trying to turn everyone here into zombies with a unicellar fungus. Assuming we start with only one person infected, is it reasonable for having at least 90% of the population to be either dead, zombified, or evacuated by the end of two weeks?

• It's untreatable
• It is airborne (Infected people breathe out spores which infects others when inhaled), but can also be transmitted through bodily fluids
• You only start showing symptoms after being infected for 3~5 days, and you turn into a sterotypical 28 Days Later zombie after being infected for 6~7 days. Infected people can pass on the fungus to others during the incubation period.
• If you were infected by a zombie bite, you will start showing symptoms after 1~2 days and turn into a zombie after 3~4 days.
• Patient Zero has already been infected for one day at the start of the two weeks. He isn't a zombie yet and isn't aware that he is infected. He has no reason to suspect so since he has no external injuries or noticeable symptoms.

In response to the edit of the question: This depends on how infectious the zombies are. In the answer below, I mention the basic reproduction number of the infection. If it is high enough, then yes.

Since as per the comment, asymptomatic carriers are infectious, the mathematics becomes slightly easier. To make things even simpler, assume that each zombie infects 4 people on the first day and then dies. The r number of 4 is not outrageously high, as infections go, but assuming that all 4 happen in one day would be rather unusual.

• On day 0, you have $$1$$ zombie.
• On day 1, you have $$1 \times 4$$ zombies.
• On day 2, you have $$1 \times 4 \times 4 = 1 \times 4^2$$ zombies.
• On day 3, you have $$1 \times 4 \times 4 \times 4 = 1 \times 4^3$$ zombies.
• On day 12, you have $$16,777,216$$ zombies.

The main uncertainty is that the day 11 survivors have had 11 days to learn how to avoid zombiefication. If they are bad, they are dead. Only good survivors left.

That depends entirely on the behaviour of the zombies and the survivors.

• Assume you have a pool of 10 million people. A rather larger city, actually. And you have one zombie.
• While you are at low numbers of zombies, the right model is to ask how many people that zombie infects per day. To make the maths simple, set in at 1 infection per week. (That is similar to the basic reproduction number, except that here zombies remain infectious forever ...)
• At the start of the 1st week, you have 1 new zombie.
• At the start of the 2nd week, you have 1 old zombie and 1 newly infected (1 is the total number of zombies in the 1st week).
• At the start of the 3rd week, you have 1 old zombie, 1 new zombie, and 1 newly infected (1 is the total number of zombies in the 2nd week).
• At the start of the 4th week, you have 2 old zombies, 1 new zombie, and 2 newly infected (2 is the total number of zombies in the 3rd week).
• At the start of the 5th week, you have 3 old zombies, 2 new zombies, and 3 newly infected (3 is the total number of zombies in the 4th week).

This is known as the Fibonacci sequence. After approximately 35 weeks, you have reached 10 million. But only if every zombie infects one person per week. If you have 9 million zombies in week 35, and 1 million uninfected, then obviously not every zombie will infect one person per week. And even before that, most zombies will merely shuffle around and find nobody.

So at high numbers of zombies, and low numbers of survivors, the right question becomes how long each survivors hold out.

• Assume that in each week, there is a 50% chance that a survivor gets zombified. Assume one million survivors to when you start.

• At the start of the 1st week, you have 1,000,000 survivors.
• At the start of the 2nd week, you have 500,000 survivors.
• At the start of the 3rd week, you have 250,000 survivors.
• And so on.

That is known as exponential decay.

Combined, you get something with slow growth at the beginning, rapid growth in the middle phase, and then a long, long time until the last survivor gets zombified.

• Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Worldbuilding Meta, or in Worldbuilding Chat. Comments continuing discussion may be removed.
– L.Dutch
Mar 3 at 17:31

Considering the recent COVID experience, I'm pretty sure two weeks is quite a short period.

Being the author, you can, of course, present this fungus as a very primitive yet fertile entity that once it infects the body makes a massive explosion of microspheres or whatever way to reproduce itself you imagine.

If after 2 to 4 hours of being infected a person is ready to spread the fungus to other hosts, and these infecting particles can

a) be suspended in the air, b) survive on surfaces and infect hosts through the skin,

I think you can make it credible (and scary as hell!).

Just imagine a music show where a couple of people attend and there you have thousands of people infected after 4 hours, traveling back to their homes on the other side of town and infecting every single person they get physically close to.

A fungus nightmare that travels on public transport...

• A truly 'infectious' music show :) Mar 3 at 4:40
• On the fungus nightmare that travels on public transport, a former college had a paper that showed the mosquitos found in the london underground are their own separate species, which is both a fun fact and something I've been dying to put into an outbreak related story
– lupe
Mar 4 at 9:34

How fast it spreads depends on how contagious you want your fungus to be.

$$z(t) = (1 + r)^{t-6.5} + b(1 + r)^{t-10}$$

r = rate at which the airborne fungus spreads (infections/person/day)

b = rate at which zombies bite people (bites/zombie/day)

t = time elapsed (days)

According to WebMD, "someone who has the flu will probably give it to an average of 1.1 to 2.3 others. But one person with measles might spread it to 12 to 18 others."

The flu is contagious for about 7 days, giving it an infection rate of 0.16-0.33 infections/person/day. The average measles patient infects 12-18 people over the 15 days they're contagious, giving it a rate of 0.8-1.2.

If the fungus is about as contagious as the flu (0.16-0.33) and each zombie bit 1 person each day, then there would be only 5-12 zombies by the end of the 2 weeks. If it were as contagious as the measles (0.8-1.2) and each zombie bit 4 people (very generous), then there would be 124-464 zombies.

In order to take over 90% of a medium-sized city of 500,000 people, with each zombie biting only 1 person each day, the fungus would need to be several times as infectious as measles (r = 4.67; ~30 people infected by Patient Zero).

How many people the zombies bite doesn't affect the number very much, since the first person bitten would only turn after day 10.

• So, it's not possible, right? Mar 3 at 11:51
• I said it depends on how contagious you want it to be. A fungal disease 5x more contagious than measles could easily cripple NYC in 2 weeks. Mar 3 at 11:57
• Are there any good ways I can make it 5x more contagious than measles? edit: I will change the question so the city will count as middle sized Mar 3 at 12:06
• You don't have to do anything to it. It's a fictional disease. You can just say that it's 4-5x more contagious than measles. Infecting 5 people a day with an airborne disease isn't too far fetched, especially in a dense urban area. Mar 3 at 12:11
• "2,534.4 persons per square mile: Overall urbanized area population density in the U.S." - Census Bureau Mar 3 at 12:32

TLDR; not with a fungus, unless you invoke magic. A magical fungus? Sure.

That's why we only get pandemics ever 20 years or so, and SEVERE pandemics, like 1918 flu and COvid,less often. Degree of spread and speed of spread depend on how many ppl get infected from each present case,(R0) and how soon they can infect others (incubation period); also how long they're contagious. There's another factor, kappa, which is how much variability/dispersion there is in R0.(see the science mag article)

In societies, it also depends on how soon ppl show symptoms, how distinctive and severe they are, and how society responds.

The shorter the incubation period until recognizable symptoms, the slower the spread.(Imagine a disease that kills everyone within 10' instantly. While it would spread fast at first, we would respond pretty soon with flamethrowers and napalm.)

Conversely a disease with no early symptoms would spread further because nobody would take action to prevent spread.

Fungi grow too slowly and generally don't spread from person to person. Coccidioidomycosis (and similar airborne fungi infections) come on over weeks. Airborne fungi DON'T spread from person to person. They spread from materials like bird droppings where the fungus can grow, because they don't grow well in ppl or animals. Generally, fungi are very poorly contagious. About the worst is foot fungus, which only spreads because of the environment, warm, wet floors.

You probably need an airborne virus, like measles or Covid. When diseases first appear, they're less well adapted to hosts. They tend to get better w time-Early Covid had R0 of 3, current versions more like 11, similar to measles.

HOWEVER, R0 does NOT just depend on the disease. It also depends on how the host behaves. HIV, for example, was able to spread widely in the MSM population, because back in the 1970s a few ppl tended to have many many partners AND it had a long latency period. The initial infection is flu-like or milder. It takes years to progress to AIDS. When ppl started using condoms and checking for STDs w new partners, R0 went way down. The first known HIV case was ~1959, BTW. It took a long time to get established.

If the infectious zombie disease excited public opinion early on, and everybody stayed home, it wouldn't spread at all. So, longer incubation=> wider spread; less early or less dramatic symptoms all increase spread.

Is this a bioweapon or a natural infection? Generally when natural organisms first infect a new population, they aren't well adapted to the host, so they DON'T spread well-look at H5N1 bird flu, which has been killing millions of birds around the world for about 10 years, infected and apparently spread in minks in Denmark, sea lions in S America, and has infected a few humans, but hasn't managed sustained transmission person-to-person...yet. With a 30-50% mortality rate in known infections, (probably a small fraction-nobody would notice mild infection) it could be the next big pandemic.

When we understand the virulence factors, laboratories can design organisms that are more virulent, so they might spread faster from the start. Conversely,SARS-Cov-2 was similar to other coronaviruses that already spread pretty well in people. It took a detour thru the animal world, and came back with some goodies from animal viruses that made it great for a new plague.

Biological Weapon Toxicity https://pubmed.ncbi.nlm.nih.gov/28722971/

Coccidioidomycosis (Valley Fever) in Primary Care https://pubmed.ncbi.nlm.nih.gov/32053327/

Point-source outbreak of coccidioidomycosis in construction workers. https://pubmed.ncbi.nlm.nih.gov/19845993/

Share

[Pneumocystis carinii is still a dangerous opportunist. The infection is continuously a threat to immunocompromised patients]. https://pubmed.ncbi.nlm.nih.gov/10024821/