a large additional term dependent on the death rate affecting the death rate

I don't know what this means so I'll just ignore it.

In other words, the most desirable, populated areas will be hit the hardest.

Based on

this list of cities by population density, I've calculated that you'd need a bomb that has a blast radius of at least 11 metres to kill 200 people in Athens. A grenade has a fatality radius of 5 metres and an injury radius of 15 metres, so a soul bomb is at least twice as powerful as a fragmentation grenade, and that's not considering that a frag grenade is specifically designed to kill people (via fragmentation), so we can also expect a soul bomb to be a bit more explosive to make up for that, but unfortunately there's no way to calculate that let's just say it has a blast radius of 11m^2. Athens is still pretty dense compared to most cities in the world so the blast radius might be higher still but again, there's no way to reliably calculate that.

This section was made 3 months later on the 25th of February, 2015 because I forgot the original equation and I had to start again from scratch to remember it. This time, I'll record it so the equation is not forgotten.

Athens:

Population: 664,046

Area: 38.964 km^2

Density(m^2) = Population/Area(m^2). 664,046/38,964 = 17.04 per m^2

200(people who died)/17.04 = 11.737. Therefore, a soul bomb will kill 200 people in a city with a population density of 17.04 people per metre squared, requiring the blast area to be 11.737 metres squared. This was rounded down to 11 metres. However, this is for blast

area rather than blast

radius as mentioned above. I got the two terms mixed up previously, thinking there was no difference. 11.737 divided by pi is about 3.736, giving it a smaller kill radius than a grenade.