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VIRUS 2 -- Marco J. de Vries
I have adapted and extended the original VIRUS model of Dr. Wilensky.

I added the assumption that recovered and immune people are still able to transmit the virus.
I added the following sliders
init-infected: sets the initially infected people, instead of the constant ten in the original model.
init-immune: gives the possibility to render a part of the population already immune from the start.
average-offspring: originally a constant (it is a variable with a considrable weight).
I added the following monitors
Viral deaths: monitors the count of people who have died of the disease.
population: monitors the count of the total population
In the place of total population, I added the % mortality of viral infection to the plotting routine.
Dying people will flash yellow briefly in the graph window.
I added 2 escape routines to prevent division by zero under extreme conditions.

WHAT IS IT? -- original description of Dr. Wilensky
This model simulates the transmission and perpetuation of a virus in a human population. Ecological biologists have suggested a number of factors which may influence the survival of a directly transmitted virus within a population. (Yorke, et al. "Seasonality and the requirements for perpetuation and eradication of viruses in populations." Journal of Epidemiology, volume 109, pages 103-123)

The model is initialized with 150 people, of which 10 are infected. People move randomly about the screen in one of three states: healthy and susceptible to infection (green), sick and infectious (red), and healthy and immune (white). People may die of infection or old age. When the population dips below the environment's "carrying capacity" (set at 700 in this model) healthy people may reproduce healthy and susceptible offspring.

Some of these factors are summarized below with an explanation of how each one is treated in this model.

The density of the population
Population density affects how often infected, immune and susceptible individuals come into contact with each other. You can change the size of the initial population through the PEOPLE slider.

Population turnover
As individuals die, some who die will be infected, some will be susceptible and some will be immune. All the new individuals who are born, replacing those who die, will be susceptible. People may die from the virus, the chances of which are determined by the slider CHANCE-RECOVER, or they may die of old age. In this model, people die of old age at the age of approximately 27 years. Reproduction rate is constant in this model. Each turn, every healthy individual has a chance to reproduce. That chance is set so that each person will on average reproduce four times if they live 27 years.

Degree of immunity
If a person has been infected and recovered, how immune are they to the virus? We often assume that immunity lasts a lifetime and is assured, but in some cases immunity wears off in time and immunity might not be absolutely secure. Nonetheless, in this model, immunity does last forever and is secure.

Infectiousness (or transmissibility)
How easily does the virus spread? Some viruses with which we are familiar spread very easily. Some viruses spread from the smallest contact every time. Others (the HIV virus, which is responsible for AIDS, for example) require significant contact, perhaps many times, before the virus is transmitted. In this model, infectiousness is determined by a slider.

Duration of infectiousness
How long is a person infected before they either recover or die? This length of time is essentially the virus's window of opportunity for transmission to new hosts. In this model, duration of infectiousness is determined by a slider.

HOW TO USE IT

Each "tick" represents a week in the time scale of this model.

The INFECTIOUSNESS slider determines how great the chance is that virus transmission will occur when an infected person and susceptible person occupy the same patch. For instance, when the slider is set to 50, the virus will spread roughly once every two chance encounters.

The DURATION slider determines the percent of the average life-span (which is 1500 weeks, or approximately 27 years, in this model) that an infected person goes through before the infection ends in either death or recovery. Note that although zero is a slider possibility, it produces an infection of very short duration (approximately 2 weeks) not an infection with no duration at all.

The CHANCE-RECOVERY slider controls the likelihood that an infection will end in recovery/immunity. When this slider is set at zero, for instance, the infection is always deadly.

The SETUP button resets the graphics and plots and randomly distributes 140 green susceptible people and 10 red infected people (of randomly distributed ages). The GO button starts the simulation and the plotting function.

Three output monitors show the percent of the population that is infected, the percent that is immune, and the number of years that have passed. The plot shows (in their respective colors) the number of susceptible, infected, and immune people. It also shows the number of individuals in the total population in blue.

THINGS TO NOTICE

The factors controlled by the three sliders interact to influence how likely the virus is to thrive in this population. Notice that in all cases, these factors must create a balance in which an adequate number of potential hosts remain available to the virus and in which the virus can adequately access those hosts.

Often there will initially be an explosion of infection since no one in the population is immune and the population density is at its maximum. This approximates the initial "outbreak" of a viral infection in a population, one that often has devastating consequences for the humans concerned. Soon, however, the virus becomes less common as the population dynamics change. What ultimately happens to the virus is determined by the factors controlled the sliders.

Notice that viruses that are too successful at first (infecting almost everyone) may not survive in the long term. Since everyone infected generally dies or becomes immune as a result, the potential number of hosts is often limited. The exception to the above is when the DURATION slider is set so high that population turnover (reproduction) can keep up and provide new hosts.

THINGS TO TRY

Think about how different slider values might approximate the dynamics of real-life viruses. The famous Ebola virus in central Africa has a very short duration, a very high infectiousness value, and an extremely low recovery rate. For all the fear this virus has raised, how successful is it? Set the sliders appropriately and watch what happens.

The HIV virus which causes AIDS, has an extremely long duration, an extremely low recovery rate, but an extremely low infectiousness value. How does a virus with these slider values fare in this model?

EXTENDING THE MODEL

Add additional sliders controlling the carrying capacity of the world (how many people can be on the screen at one time) and the average lifespan of the people.

Build a similar model simulating viral infection of a non-human host with very different reproductive rates, lifespans, and population densities.

Add a slider controlling how long immunity lasts so that immunity is not perfect or eternal.

CREDITS AND REFERENCES

To refer to this model in academic publications, please use: Wilensky, U. (1998). NetLogo Virus model. http://ccl.northwestern.edu/netlogo/models/Virus. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 1998 by Uri Wilensky. All rights reserved. See http://ccl.northwestern.edu/netlogo/models/Virus for terms of use.