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The model provided implicitly assumes that all individ- uals are potentially in contact

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[Very tough question]: The model provided implicitly assumes that all individ- uals are potentially in contact with each other. What would be a more likely scenario? What changes would have to be made to the code of the Gillespie algorithm in order to include such a scenario? If you are able to do this, do it. Then, speculate as to what could affect the results observed in the previous questions. If you feel so inclined, demonstrate it experimentally. NB: Only 10 marks have been given to this question. However, anyone managing it suc- cessfully would receive an extra 10 marks for the assignment (with the total mark capped to 100 obviously).

 

Mathematics and Computational Methods for Complex Systems

summative-assessment.pdf Prof. Luc Berthouze

The ODEs

The system is fully described by the following two ordinary differential equations:

where ẞ and are strictly positive real numbers. The first equation provides the rate of change of the number of individuals in state B and says that it is the sum of the number of individuals in state A that become B with a rate (proportional to the number of other individuals in state B) minus the number of individuals in state B that turn to state A with rate. I leave it to you to interpret the second equation. Summing both equations lead to 0 which is consistent with the fact that the total population [A] + [B] = N at all times.

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