We have this neat model for the spread of a disease. You can get the disease if you are susceptible, but not if you are resistant. These are denoted with S and R letters. Initially there is a big checkerboard of Rs and Ss. I initialized the system a number of times by pressing the Mix button. I think it looks pretty random. That is, I didn't see any clumping of Ss or Rs. I think ecologists have tests to detect clumping. But I'm not going to go that far here. I'm pretty sure it's random.
The number in the text field is a percentage of S individuals. If the number is 100 or greater, all of the individuals are S. If the number is 0 or smaller, all of the individuals are R. Neither of these cases are interesting to explore.
When you click on an S individual, an epidemic can start. Here is a picture of epidemic spread. I made all of the individuals initially S and I clicked in the middle. The epidemic spread outward from this initially infected individual in a square pattern of expansion. I took a snapshot during the spread. I did checked the Slow checkbox to be able to capture this snapshot more easily.
There is no randomness in the spread. If you have an infective neighbor and if you are an S individual, you get it.
Here is a screen snapshot at the end of the same simulation. You can see that everyone is now an R individual. And the graph of the number of new R individuals has a very regular pattern, again showing the absence of chance.
Here's a picture at the end of the epidemic when starting with 70% initial S individuals.
Note that the increase of new R individuals does not increase as fast or as evenly compared to the 100% S situation.
Here's the same thing, except I started in the corner. Note how I made the image smaller. I turned off some of the view items in the browser. So, now the applet just fits. What is interesting here is that the disease now takes longer to spread. But, of course, it now has to travel farther. Remember, it can only move one cell at a time. It can move diagonally. So, it could do it in 30 steps if everything were totally connected, like in the 100% S simulations I did above. But it sometimes has to move up, over and even around. So, it takes longer, I guess about 60 steps before it fizzles out.
I guess I've gotten familiar with the behavior of the simulation model. Now, I'm going to explore the significance of the starting percentage of S individuals. I done a few explorations and it's pretty amazing. At say 80% everyone dies, that is, everyone gets infected and becomes resistant. But say at 30% the disease keeps fizzling out. It doesn't spread very far. But I have to be organized about my explorations. I have to produce a graph and on the x-axis, which is the independent variable, I plot the percent initial S. I'm going to do this from 10 to 90 percent. But what do I plot on the y-axis?
Here's what I'm going to do. For each %S, I'm going to do 5 simulations, clicking on some individual in the center of the population. I'm going to record the number of S individuals before and after. Then, I'm going to calculate percent of the initial Ss converted to Rs. Here's my table:
|
percent S |
initial S |
final S |
% change |
|
10 |
58 |
57 |
1 |
|
10 |
62 |
61 |
1 |
|
10 |
57 |
53 |
7 |
|
10 |
60 |
59 |
1 |
|
10 |
61 |
55 |
10 |
|
average |
4 |
||
|
20 |
122 |
120 |
1 |
|
20 |
116 |
115 |
1 |
|
20 |
123 |
120 |
2 |
|
20 |
121 |
111 |
5 |
|
20 |
118 |
116 |
1 |
|
average |
2 |
||
|
30 |
188 |
186 |
1 |
|
30 |
178 |
145 |
18 |
|
30 |
191 |
184 |
2 |
|
30 |
169 |
122 |
25 |
|
30 |
178 |
172 |
2 |
|
average |
9 |
||
|
40 |
246 |
146 |
40 |
|
40 |
244 |
143 |
40 |
|
40 |
232 |
227 |
2 |
|
40 |
227 |
203 |
11 |
|
40 |
244 |
51 |
79 |
|
average |
34 |
||
|
50 |
306 |
51 |
83 |
|
50 |
294 |
8 |
97 |
|
50 |
302 |
10 |
97 |
|
50 |
301 |
8 |
97 |
|
50 |
288 |
8 |
97 |
|
average |
94 |
||
|
60 |
355 |
2 |
99 |
|
60 |
363 |
3 |
99 |
|
60 |
351 |
2 |
99 |
|
60 |
358 |
4 |
99 |
|
60 |
367 |
2 |
99 |
|
average |
99 |
||
|
70 |
442 |
442 |
100 |
|
70 |
429 |
429 |
100 |
|
70 |
398 |
398 |
100 |
|
70 |
415 |
415 |
100 |
|
70 |
426 |
426 |
100 |
|
average |
100 |
||
|
80 |
100 |
||
|
80 |
100 |
||
|
80 |
100 |
||
|
80 |
100 |
||
|
80 |
100 |
||
|
average |
100 |
||
|
90 |
100 |
||
|
90 |
100 |
||
|
90 |
100 |
||
|
90 |
100 |
||
|
90 |
100 |
||
|
average |
100 |
I quite actually doing the simulations after 70% initial S, as the disease always got everyone, 100%. Here's my graph (I did it in Paint) of the behavior--the influence of %S on the scope or percent spread of the epidemic.
This is really interesting, really non linear. It's sigmoidal, like logistic population growth, but I don't think it's really the same thing. It's sort of like you gotta to have some critical number of Ss for the thing to really go.
You know, I heard the same thing on the news. I think it was some disease like polio. The health department was worried that not enough kids were getting the immunization, and that an epidemic could start if the situation got worse. I don't know how polio spreads, but I recall my dad saying they had to close swimming pools when he was a kid because of the polio scare, so it's probably some form of close contact.
Implications of Disease for Conservation (Discussion)
We don't want diseases killing off endangered species. We should probably immunize animals in zoos. If we know how to do that. And I hope it's not too expensive. Maybe we should even do the same in places like Yellowstone National Park. Maybe all the grizzly bears could die from some disease.
But maybe immunization is not the best idea. Clearly, as this model shows, disease spread to neighbors. So, perhaps it would be better to keep animals further apart or perhaps to clump then with big gaps between the clumps, then the disease would not spread. But this probably depends on the exact mechanism. It might not work with mosquitoes. But where disease is an issue, I'd make small isolate reserves. This might not be the best idea for other considerations, but for disease it is probably good.