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WHAT IS IT?

This is a simple model of an influenza epidemic. It seeks to investigate how much prior immunization of a population is optimal from a policy standpoint. Given the competing costs of innoculation versus lost productivity, the model allows the user to investigate which policy choices and assumptions about the virus minimize the loss of worker productivity.


HOW IT WORKS

The model populates a world of 1,226 people and contains four parameters: the number of people innoculated against the flu ("immunization"), the virulence of the virus, how broadly a sick person may communicate the virus ("infection-range") and the duration of the illness once a person becomes sick.

The simulation begins with a single sick person, who appears green, and a percentage of the population that is immunized prior to the simulation ("immunization"). This sick person may infect other people with a probability determined by the virulence of the virus (for example, a virulence of 0.20 means a given person has a one-in-five chance of getting sick at any given step in the simulation, but a virulence of 0.8 means a four-in-five chance of infection). A sick person cannot infect others who have been immunized. If a person is immunized, he or she cannot get sick and hence cannot communicate the virus to others.

The ill person can only infect neighbors within a radius of the "infection-range": a range of 1 means the ill person can only communicate the virus to the immediate neighborhood. A longer-infection range means the virus will spread throughout the society more quickly. The infection range is thus analogous to the density of social networks in a society: a longer range means a denser network.

Once sick, a person remains ill and infectious for a given period of time determined by the "illness-duration" variable. The longer the duration, the more opportunity a sick person has to communicate the virus to others within the infection range. Once the ill person has been ill for the time determined by the duration variable, the ill person becomes well again (and changes color back to blue). An ill person that has become well cannot get sick again, and can no longer communicate the virus.

The spread of the epidemic therefore is a function of all four variables. Prior immunization minimizes the spread of the infection; greater virulence increases the likelihood of communication; a longer infection range means the virus will spread more quickly; and illness duration determines the amount of time an ill person is a carrier of the virus and hence infectious.


HOW TO USE IT

You are a public health official who wishes to minimize the costs to society of a flu epidemic. Your success is measured by the "surplus" monitor, which measures the difference between your immunization budget, the cost of immunization, and the costs of lost worker productivity.

Each immunization shot costs $25; you have a budget for only half the population. You can immunize the entire society but you will run a deficit. Alternatively, you can immunize a percentage of the population, and accept the costs of some workers who are ill. A sick person costs society $5 in lost productivity each day. Your goal is to maximize the "surplus" monitor--that is, to maximize the difference between your budget on the one hand, and the costs of immunization and lost productivity on the other.

To run the model, select a percentage of the population to immunize on the "immunization" slider. Then click "setup" and then "go." Notice how the illness spreads around the population.

The plot to the right reports the number of people who become sick, the number who are immunized or become immune, and the "efficiency" of your immunization strategy. The efficiency is simply the percentage of the population that never becomes sick and does not receive prior immunization.

The output box above the plot reports your final budget surplus or deficit once the simulation is finished.


THINGS TO NOTICE

The model includes setup buttons for four different parameter configurations. These include a low immunization strategy with a virus of low virulence, a low immunization with a highly virulent flu, a high immunization-high virulence scenario, and high-low scenario. Under all four scenarios, the network range is assumed to be a radius of five, and the duration of the illness is assumed to be ten ticks.


THINGS TO TRY

Try to maximize your surplus under different assumptions about the flu epidemic. Which immunization strategy is ideal under conditions of high virulence? Does the density of social networks (the network-range variable) change your immunization strategy? How sensitive is your surplus to the duration of illness?

Now click on the "2" button to configure a low-immunization, high virulence scenario. Click "go" to run the model. What is your final surplus? Now set the immunization to 100 and click "setup" and run the model again. The only parameter you have changed from the "2" scenario is your immunization strategy. What is your surplus under the 100 percent immunization strategy? Which strategy is more cost effective, low or high immunization?


EXTENDING THE MODEL

The model assumes a relationship between costs of immunization and the costs of lost productivity: immunization ($25) is equal to the cost of five lost worker-days ($5). One interesting extension is to allow the modeler to vary the ratio of costs of immunization to the costs of lost productivity.



RELATED MODELS

See the "Aids" and "Disease Solo" models in the biology section of the NetLogo library (Wilensky 1998, 2005).


CREDITS AND REFERENCES

Model developed by:

David C. Earnest, Ph.D.
Assistant Professor of Political Science and International Studies
Old Dominion University
BAL 700
Norfolk, VA 23505
dearnest@odu.edu


References:

Wilensky, U. (1998). NetLogo AIDS model. http://ccl.northwestern.edu/netlogo/models/AIDS. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Wilensky, U. (2005). NetLogo Disease Solo model. http://ccl.northwestern.edu/netlogo/models/DiseaseSolo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.