Computational models of infectious disease transmission Jon Zelner Postdoctoral Fellow, Ecology & Evolutionary Biology @ Princeton University Postdoctoral Fellow, NIH Fogarty International Center Research and Policy for Infectious Disease Dynamics (RAPIDD) Program
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ICPSR - Complex Systems Models in the Social Sciences - Bonus Content - Professor Daniel Martin Katz (Guest: Jon Zelner)
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Computational models of infectious disease transmissionJon Zelner Postdoctoral Fellow, Ecology & Evolutionary Biology @ Princeton University
Postdoctoral Fellow, NIH Fogarty International Center Research and Policy for Infectious Disease Dynamics (RAPIDD) Program
Modeling transitions from between emotional states: discontent, neutral, content.
Individuals in neutral state are analogous to susceptibles and can become either content or discontent.
Additional parameter: a, random probability per unit of time that ego will change state from neutral to content or discontent.
Modeling the diffusion of emotions: SISa Model (Hill et al.)
Modeling the diffusion of emotions: SISa Model (Hill et al.)
Model was fit to Framingham Heart Study panel data.
Transitions between states are assumed to happen slowly (in units of years).
Fit to Framingham data using a linear regression model:
Y = 1 if alter transitions from neutral to content from t -> t+1.
Ego’s state is only predictor, a is model intercept.
SIR outbreak model in Netlogo
This model adds a spatial component.
As the number of individuals in the world increases, the rate of contact between them also increases.
SIR outbreak model in Netlogo
Download the Model from the course website:
http://computationallegalstudies.com/icpsr-class
File is Called “SIR Example Netlogo Model”
SIR outbreak model in Netlogo
Model Contains Commented Out Code that Can Be Turned on by Removing the ;;
Cannot have both Versions of ‘To Recover’ at once so you will have to choose
OFF ON
OFFON
Model Setup
This is what happens when you click setup.
Values are loaded into turtles and the world.
When you click ‘Go’:Move: Turtles spin into a randomly chosen direction and then move one step in that direction.
Infect: Turtles take a look at the other individuals on the patch they occupy after moving, see if any are susceptible turtles are there, and try to infect them if they are.
Recover: Infectious turtles check if they’ll be recovering on this tick, and if so, they switch their state from infectious to recovered/immune and can no longer infect anyone.
Update Turtles: This is our first bookkeeping operation: we’ll take a look and see if any of each turtle’s variables - e.g., how long the turtle has been sick for - needs updating, and if so, do it.
When you click ‘Go’:Update Global Variables: Updating the state of variables that impact the whole turtle world.
I.e., # of individuals who are currently susceptible, infectious and immune (these show up in the plot on the bottom-left corner of the display).
Tick! We advance the time forward one step - it’s very important to remember to call this or else nothing will ever happen in the model.
Update plot: Finally, we update the plot on the bottom-left corner, which tracks the number of individuals currently in each state, to reflect the changes over the last step.
Infect and recovery procedures
What happens in this model?Predictions from standard SIR model don’t hold, because contact structure is different.
But that’s kind of the point.
Analysis of this model is potentially more difficult because we’ve relaxed assumptions about contact.
What’s wrong with this picture?
Writing more efficient codeGive turtles a memory slot for how long they’ll be infectious if infected.
When infected, store the duration.
Turtles count how long they’ve been sick for and change state when they reach the limit.
Writing more efficient codeWalk Through the Netlogo Timing Tutorial