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data structures and software dependability

computer science department

brandenburg university of technology cottbus - senftenberg

Modelling epidemics

latest update: May 19, 2020, at 03:34 PM
Note: under construction.

This webpage is developed by a collaborative project between

  • Prof. David Gilbert, Brunel University London, and his team
  • Prof. Monika Heiner, BTU Cottbus, and her team.

This webpage provides a few basic models to explore how some key figures may influence an epidemic process. We favour to represent our models as Petri nets, which can be read in different ways. Here we use

  • the merely qualitative perspective (PN) and
  • the stochastic perspective (SPN).

INDEX


Form test

infect rate: (valid range: 5.0e-7 1.0e-4)
recover rate:



Disclaimer

Models are as good as the assumptions they build on.

(1) SIR model

SIR model - Looking for some background? Check wikipedia first.

There are three variables, represented as places/circles:

  • S - susceptible population
  • I - infected population
  • R - recovered population

There are two basic events, represented as transitions/boxes:

  • Infect
  • Recover

Basic assumption:

  • A recovered person will not get infected again.

(QUALITATIVE) PETRI NET (PN)


Some hints:

  • A click on the picture opens a new window with a PN, directly executable in your web brower by help of Patty; nothing needs to be installed.
  • Then, the PN can be animated by either
    • clicking on individual transitions (boxes) or
    • one of the smallish triangles in the control panel.

These model versions can be subsumed by using a constant IR (Infection Rate) in arc weights:

Note: Constants not supported yet in Patty; but you can download the PN and animate it in Snoopy; requires installation first.


STOCHASTIC PETRI NET (SPN)


Note: Animation governed by stochastic rates not supported yet in Patty; but you can download the SPN and animate it obeying the stochastic rates in Snoopy; requires installation first.

THE FOLLOWING DIAGRAMS SHALL BE GENERATED DYNAMICALLY, taking into account user-specified model parameters, read from some web form and constraint by a pre-given range.

Ideally, a few diagrams can be generated (one after the other or concurrently) and shown side by side, so one can more easily compare the impact of different rates.

  • simulation trace, k_infect=0.0000005 (5.0e-7)
  • simulation trace, k_infect=0.000001 (1.0e-6)
  • simulation trace, k_infect=0.000005 (5.0e-6)
  • simulation trace, k_infect=0.00001 (1.0e-5)

(2) SIS model

SIS model - Looking for some background? Check wikipedia first.


(QUALITATIVE) PETRI NET (PN)


. . .


STOCHASTIC PETRI NET (SPN)


. . .

(2) SCIR model


(QUALITATIVE) PETRI NET (PN)


. . .


STOCHASTIC PETRI NET (SPN)


. . .

Tools

This webpage builds on the following tools:

  • Snoopy - construction of all (S)PNs
  • Patty - web-based animation of PNs
  • Spike - simulation of SPNs; each run generates a csv file
  • Matplotlib - visualisation of the csv files, generated by Spike

References

the end

Any comments or questions are welcome. Please direct them to monika [period] heiner [snail] b-tu [period] de Privacy Policy