Basically, you are showing what happens with exponential growth.
Although I think your basic point is right, you missed some things that would greatly improve your model. (I used to teach statistics at the University level, and I still provide occasional expert witness work in the field. I’ve also done a bit of work with bio-statistics.)
If you want to have a more accurate model you will need to add a way to separate the dead and the recovered from the currently infectious.
You will also need to include a way to show growth slowing once the pool of uninfected people in a given area has shrunk significantly. Once a given area is wiped out there will be no more growth in cases from that location. A town can only die once.
At this stage these issues do not make a lot of difference in the numbers. But once this thing gets really going they will become major points.
If you want to get really complicated, and really SCARED, then give some thought to what happens when the medical system has been destroyed. How long it is from there until we have enforced movement restrictions. And how long the grid will hold up.
Pretty much, but with a twist. I've been attempting to account for the rate of change in the rate of transmission. Another FReeper has convinced me that my formulas overestimate to some degree. That overestimation becomes more significant the further you move out into the future. I'm working on a new approach, based on more simple concepts like compounded interest. But I still want to account for the change in the rate of transmission that naturally occurs over time.
Although I think your basic point is right, you missed some things that would greatly improve your model... If you want to have a more accurate model you will need to add a way to separate the dead and the recovered from the currently infectious.
Yeah, I mentioned that. But it isn't quite that simple... Are the recovered really immune? Can't they get it again? Are they still contagious for some period of time (seems so, to some degree... the virus is present in the semen of males for up to 6 weeks, I think).
You will also need to include a way to show growth slowing once the pool of uninfected people in a given area has shrunk significantly. Once a given area is wiped out there will be no more growth in cases from that location. A town can only die once.
To further emphasize this point, taken out a few months further than I posted, the number of cases goes into the trillions. Obviously that can't happen. I don't even think it will go into the billions, and perhaps not even into the millions. But at what point will the shrinking pool of uninfected persons start to have an effect? And how quickly? I'm not sure how to incorporate that. I would be open to suggestions.
This is an extremely complicated point that would take a lot of data I don't have available to me to represent. How much the pool has shrunk in Monrovia will be different from how much it has shrunk in Sierra Leone. I may be able to account for it at the country level, or at the macro level (i.e., the world), but any further down that that will be a challenge.
If you want to get really complicated, and really SCARED, then give some thought to what happens when the medical system has been destroyed. How long it is from there until we have enforced movement restrictions. And how long the grid will hold up.
Another great point that's going to require some thought.