Population Scale Modelling

Contents

1. Summary
2. Multi-Scale integration using Cellular Automaton
3. Mathematical Modelling using Delay Differential Equations
4. Agent Based Simulation Applet

Summary

Population Modelling is concerned with the dynamics in population size as a consequence of interactions of organisms with the physical environment, with individuals of their own species, and with organisms of other species.
We designed a dynamical population model in which we simulate the behaviour of bacteria.

We want to gain insight into the dynamics of bacteriophage infection, bacteria-phage interaction essentially is a fight for survival between two populations. By adding a phage invasion in our simulated bacteria population we can simulate the whole infection process. The modelling of infectious processes is a tool which has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic (Daley & Gani, 2005). Our kamikaze construction was designed to sabotage the phage lytic cycle, but our final goal is to contend the infection at the Population Scale.
We used 3 different approaches to model the population dynamics:

1. Multi-Scale integration using Cellular Automata: Using this system we can simulate spatial interactions as movement and biomolecules diffusion. In our model spatial dynamics are of vital importance: Quorum Sensing dynamics is one of the main aspects of the Defense System, infected E.Coli will produce AHL and will warn it’s neighbours. Using the Cellular Automata we can make direct sampling from the distributions generated by the molecular simulations in real time linking the molecular and population scales.
2. Delay Differential Equations System: Deterministic models can accurately simulate the behaviour of populations when the number of individuals is big. Our experiments consists of big numbers of cells so population dynamics might be approximated using deterministic models. We want to compare the stochastic and deterministic behaviours of the population.
3. Agent based simulation:Using an agent based model implemented using the [http://ccl.northwestern.edu/netlogo | NetLogo]] platform we can see the general behaviour of our system in a nice graphical user interface. Link to Agent based simulation Applet.

References

Daley, D. J. & Gani, J. (2005). Epidemic Modeling and Introduction. NY: Cambridge University Press.
S. Goel. Stochastic Models in Biology. 2003 Istas. Mathematical Modeling for the Life Sciences.2005