An epidemic is the spread of a disease in a population (a deme). Individuals of the population may or may not be susceptible to catching the disease. They may be resistant because of some genetically based condition or trait. Or, they may have had the disease at some earlier time and may still be immune to it.
Diseases spread from individual to individual. Sometimes there has to be direct contact, touching, coughing on, breathing on, and so forth. For other diseases, the disease organism enters something like the water supply and can then spread quickly and widely.
Shown below is a simple model for disease spread based on direct individual to individual contact. It is a spatially explicit model, a two-dimensional model. The individuals are set out on a 20 by 30 grid, thus with 600 total individuals in the population. Initially, there is some mix of susceptible (S) and immune or resistant (R) individuals in the population. The user controls the initial ratio of S and R individuals. To introduce the disease to the population, the user clicks the mouse on an S individual. The dynamics of the epidemic proceed from this event. At the first time step after contracting the disease, the individual is asymptomatic and uninfective. At the next two time steps, this individual becomes infective, and he will spread the disease to any adjacent S individual in one of his eight nearest-neighbor cells. After this infective stage, the individual becomes resistant. So, the sequence of stages that an individual passes through is:
S --> A --> I1 --> I2 --> R.
You are to explore the behavior of this model. Here is the applet. Instructions are given below.
First, explore the role of the S-R Mix button. Press it multiple times, noting the count of S individuals. Next, change the number in the %S text field. It should be an integer between 0 and 100. (What happens if it is not?) Change this number and then press the S-R Mix button. Do these operations till you understand the role each component plays in initializing the system.
Click the mouse on an S individual in the population. Watch what happens. When the dynamics have ended, click on the S-R Mix button to reinitialize the system. Note that the button and text field are inactive for three seconds after the secession of the dynamics; this is to allow you to record the percentage of S individuals at the end of the simulation. Now check the Slow checkbox. Once again, infect an S individual by clicking the mouse on it. What does the Slow checkbox do? Depending on the speed of your computer, you may or may not want to have the Slow checkbox checked in you explorations of epidemiology.
At the bottom left, some statistics on the fraction and the total count of S individuals in the population are given during and at the termination of the simulation. Also at the end of the simulation, a graphic is given showing the number of new R individuals created per time step.
Assignment
1. Compare epidemics that start in a corner of the population versus epidemics that start in the center.
2. How does the percentage of S individuals in the population govern the speed and the scope of the epidemic? Quantify the magnitude of the epidemic as a function of the initial percent S individuals. Use %S initial values of 10, 20, 30, 40, 50, 60, 70, 80, and 90 percent.
3. Comment on the significance of disease spread for conservation.
Please: explore these questions yourself before going to look at a sample lab book.