the following model is often used to measure the spread of an infectious disease. suppose that at the beginning of period 1 the population consists of 5 diseased people. during any period, there is a 0.05 chance that a given infective person will encounter a particular diseased person. if an infective encounters a susceptible there is a 0.5 chance that the susceptible will contract the disease. an infective lives an average of 10 periods to model this we assume there is a 0.10 probability that an infective dies during thee period. model the evolution of thee population over 100 periods and use your results to answer what the probability that the population wwill die out
To model the evolution of the population over 100 periods, we can use a simulation approach. Here's how you can do it:
1. Initialize the variables:
- Set the number of initial diseased people to 5.
- Set the number of initial susceptible people to 0.
- Set the number of initial infective people to 0.
- Set the maximum number of periods to 100.
- Set the probability of an infective dying in a period to 0.10.
2. Perform the simulation for each period:
- For each infective person, there is a 0.05 chance of encountering a particular diseased person. If encountered, that person becomes infective.
- For each infective person, there is a 0.5 chance of infecting a susceptible person. If infected, that person becomes infective.
- For each infective person, there is a 0.10 chance of dying.
3. Track the population during each period:
- Count the number of diseased, susceptible, and infective people at the end of each period.
4. Repeat steps 2 and 3 for 100 periods.
5. Analyze the simulation results:
- Calculate the probability of the population dying out based on the final population count:
- If there are no diseased or infective people at the end of the simulation, the population has died out.
- Calculate the proportion of simulations where the population died out.
By running this simulation multiple times, you can estimate the probability that the population will die out based on the given model.