What is the Zombie Death Toll?

Day 1
In a city like Shanghai, with 24 million people, 570 people die every day. Let's assume for the sake of argument that whatever causes zombies (alien slime, radioactive water, bacteria) has infected everyone in the city, so whoever dies turns into a zombie. That makes the math easy. That's 570 undead on day one.
Let's say each of them manages to kill, or cause to be killed, one person. Not greedy. You know, loved ones, neighbors, innocent bystanders.
The "cause to be killed" part is crucial because over a few days the death toll leads to mobs, riots, supply chain disruption, fires, anarchy, military crackdowns, martial law.... you get the picture. But I'm getting ahead of myself. On day two:

Day 2
570 more people die of natural causes, in addition to the  570 undead plus their 570 victims. Day two total: 1,710 dead. By this math, a city the size of Shanghai would fall in fifteen days.The world, assuming zombies enjoy frequent flier miles, in 23 days.

"But wait," you say. "That math is overly simplistic. Birth rates are three times as high as death rates."
Sure, even in the madness, babies are born. They went into production nine months before the apocalypse. So why don't we count them? Well... c'mon. Even if they lived through the entire apocalypse, that would make them 23 days old. The most popular baby name in the world? "Dessert."

"We're not going to stand around and get eaten," you say. "We'll fight!!!"
Okay, so we'll factor in the resistance. After all, one healthy human downs dozens of undead a day.
Without an existing database, calculations may vary, so let's ask this question first: Who is doing the killing?

Day 3
Here's the rub. For the first few days, those critical days, people will ignore the problem. They will go to work. They will go shopping. They will think about cancelling Tupperware parties, daydream about their future life as a millionaire, and proceed as planned. They will drive to Grandma's house to see if she's ok. (She's not. She's eating you.) Keep calm and carry on.

What did you do during the swine flue epidemic? How long was it before you headed for the hills? I imagine you never did. Which is why zombies would win.

Time is ticking. The landmark paper "Critical Response Time" by Rivas et al studied the spread of foot and mouth disease in Brazil. It indicated that the effective reproduction number must be less than one in order for an infection to die out. Therefore, a critical response time must prevent one zombie from killing one human.
Here's the catch. In no previous study has death lead to an increase in the disease. Typically when a host dies, so does the virus, bacteria, or parasite. In zombies, the exact opposite happens. This inverts all prior study. To prevent its spread, you must keep every patient alive. This is a difficulty when the prime driver is the natural death rate. In this case, death itself is the disease.

So let's say it takes a few days for the world to wake up. What would they do with the undead patients? Cure them? Result: rapid hiring in the health care field. Restrain them? Result: prison guards with Wall Street size signing bonuses. Call in the military? But they're still alive, like coma patients. What rights to they have? All of them! Without an end-of-life agreement signed and notarized, the first soldier to fire could be sued back to the stone age.
This is why developed nations would be the source of the greatest outbreaks. Military dictatorships fare better, lacking legal and moral protection.

Day 9
Eventually, around day nine, when society cracks and there's no more reality television to watch, the survivors flee, facilitating traffic accidents, lethal territorial disputes, resource hoarding, and a general contribution to extinction. Let's just say days 9 through 12 will require decades to sort out the appropriate Darwin Award winner.

Day 13
Eventually the lucky few hunker down and barricade themselves in. Here our number count drops from "exponential" to "steady", but by then there are upwards of six million zombies in Shanghai. One billion worldwide, if this were a global event. It's a safe bet our survivors die of starvation, disease, and dehydration within two weeks. Worst of all, as soon as one shut-in dies, they present a problem to the rest.

But I digress. The original question was, who, specifically, would take an active role in killing zombies?
The answer: the same people who march against regimes in Egypt, start the Russian revolution, and hang around Zuccotti Park for months on end - students. More specifically, unemployed college age men. What percentage of the population is that? In the US that's about 375,000, give or take. Remember, everyone else has school and work to attend.

In our original test city, Shanghai, 178,000 college graduates emerge into the daylight every summer. Zombies outnumber them by day eight. By day nine, those students are eating brains, not filling them.

As for the rest of us? Logarithmically, by the time we get around to reaching for the crowbar, it's already too late. The good news is, if you survive that long, there are no lines at the Apple store.