SIR model error - can't find bug, need help in locating potential source of deviation? - netlogo

Question

This question will be an interesting one. I was trying to replicate the results of a paper which concerned disease transmission in a system of freely moving agents (sounds like the perfect job for NetLogo). I coded up a simple SIR model in NetLogo pretty easily according to the details given in the paper, made sure my model parameters matched those listed, and let the simulation run. Everything ran perfectly until I checked how the experimental results matched with the predicted values (according to the results of the paper). They were off, and by a pretty sizeable margin. Thinking there was an error somewhere in the code, I triple checked everything, only to find nothing. I then made sure the ordering of events was correct (as the order of movement, infection, and recovery matters), and these also matched the paper. I mulled over the problem for quite some time until finally I opened R, coded up the exact same program in RStudio, and let it run, only to find that the results matched the prediction perfectly! The R code does the same thing I expect the NetLogo code to be doing, so I think that something is going on behind the scenes in NetLogo or I've a misunderstanding somewhere that is the source of the deviation... Note that since the result in the paper is a mean-field approximation, you would have to run the program a few times in order for it to approach the theoretical result.
I'm not sure where I'm going wrong, as my R code confirms the predicted values are correct, so I conclude that something somewhere in my NetLogo code is incorrect. I'm not too familiar with NetLogo, and I would really appreciate it if someone could help me find where in the following code the deviation may be occurring. The experimental average tends to be lower than the predicted one, suggesting that infection occurs faster than it should, but of all the changes I looked at, none of them solved this problem (e.g. infections do not occur one at a time per infectious turtle). Any suggestions/help would be very much appreciated.
A slimmed-down version of my code is presented below. This should run in a regular interface with the standard setup/go buttons. Results are stored in lists that can be plotted, and anyone curious can see the deviation as the simulation progresses via the Plot object. Thank you in advance.
;; Simple SIR model
globals [
;; variables for storing predictions
predS
predE
predI
predR
oldPredS
oldPredE
oldPredI
oldPredR
;; list to store experimental values
Slist
;; list to store predicted values
predSList
;; model variables
length-of-patch ;; length of habitat (a square of area length-of-patch^2)
infection-radius ;; the distance from an infectious individual a susceptible agent has to be within
;; in order to risk getting infected
total-pop ;; total population in the model
force-of-infection ;; probability of infection if within infection-radius distance
I0 ;; initial infected
recovery-rate ;; probability of recovery
]
turtles-own [
infected-status ;; 0 susceptible, 1 infected, 2 recovered
]
to setup
ca ;; clear
;; define the variables
set length-of-patch 31.62278 ;; the square root of 1000 (so the density is 1)
set infection-radius 1
set total-pop 1000
set force-of-infection 0.1
set I0 10
set recovery-rate 0.05
;; setup simulation
setup-patches
setup-agents
reset-ticks
;; initialize lists as empty
set Slist []
set predSList []
end
to go
;; update experimental values (density of susceptible individuals)
set Slist lput ((count turtles with [infected-status = 0]) / (length-of-patch ^ 2)) Slist
if (ticks = 0) ;; if ticks == 0, make sure initial value is the same as experimental
[
;; update predicted values with densities of agents
set predS ((count turtles with [infected-status = 0]) / (length-of-patch ^ 2))
set predI ((count turtles with [infected-status = 1]) / (length-of-patch ^ 2))
set predR 0
;; placeholder variables for iterative process
set oldPredS predS
set oldPredI predI
set oldPredR predR
;; store predicted S population in corresponding list
set predSList lput (predS) predSList
]
if (ticks > 0) ;; if ticks > 0, then update predicted values according to paper results
[
;; update predicted values
set predI (oldPredI + oldPredS * (1 - (1 - force-of-infection * oldPredI) ^ (pi * (infection-radius ^ 2))) - recovery-rate * oldPredI)
set predR (oldPredR + recovery-rate * oldPredI)
set predS ((total-pop / (length-of-patch ^ 2)) - predI - predR)
;; placeholder variables
set oldPredS predS
set oldPredI predI
set oldPredR predR
;; store values in corresponding list
set predSList lput (oldPredS) predSList
]
;; perform movement, infection, and recovery, in that order
move-agents
infect-agents
recover-agents
if (count turtles with [infected-status = 1] = 0) [
;; if no one else is infected, stop
stop
]
tick
end
to setup-patches
;; resize the world to make it fit comfortably in the interface
resize-world 0 length-of-patch 0 length-of-patch
set-patch-size 400 / (length-of-patch)
end
to setup-agents
;; create susceptible agents
crt (total-pop - I0) [
set infected-status 0
setxy random-pxcor random-pycor
set color 55 ;; green
set size 2
]
;; create I0 infected agents
crt I0 [
set infected-status 1
setxy random-pxcor random-pycor
set color 15 ;; red
set size 2
]
end
to move-agents ;; move all the agents
ask turtles [
setxy random-pxcor random-pycor
]
end
to infect-agents
;; iterate over infected turtles
ask turtles with [infected-status = 1] [
;; check neighborhood around infected turtle for susceptible turtles...
let numNeighbors count (turtles with [infected-status = 0] in-radius infection-radius)
if (numNeighbors > 0) [ ;; there are susceptibles around, so we perform infection
ask (turtles with [infected-status = 0] in-radius infection-radius) [
let %draw (random-float 1)
if (%draw <= force-of-infection) [ ;; probability of infection
;; infect one of the neighbors
set infected-status 1
set color 15 ;; red
]
]
] ;; end of if numneighbors > 0
]
end
to recover-agents
ask turtles with [infected-status = 1] [
let %draw (random-float 1)
if (%draw <= recovery-rate) [ ;; an agent recovered
set infected-status 2
set color 105
]
]
end

Answer 1

One problem I can see is that you have: setxy random-pxcor random-pycor but you want: setxy random-xcor random-ycor
Basically you are putting all your turtles at the centre of the patch, so they are on top of each other, instead of distributing them randomly across the space. That positioning changes the distribution of possible distances between turtles.
I also changed the number of turtles to 1024 1089 and the size to sqrt 1024 (instead of 1000) to make the density match properly.
Both of those reduced the mismatch but it's unclear whether they fix the problem since I didn't do large numbers of runs.
UPDATE
Even more dimension matching is required. Changing the code so there are 1089 agents, setting length to 33 for the pred calculations, and resizing world with max of 32 appears to move the curves closer. This recognises that patch coordinates 0 to 32 actually describe a size with length 33 because NetLogo coordinates would start at -0.5 and run to 32.5 as mentioned by #Jasper