Intermezzo+1

__**NOTE: THE INFORMATION ON THIS PAGE IS NO LONGER PART OF THE COURSE (removed from main wiki, 2014-2015)**__


 * TODO**
 * REF trade-off assumption infectivity and infection duration

=Intermezzo 1: Application of spatial hypercycle=

In a study of the evolution of pathogens, van Ballengooien and Boerlijst ([|2004]) used lessons from the spatial hypercycle system. In standard [|SIR modelling] of infections and epidemics it is often predicted that viruses should evolve to a maximum Ro (B/g). However, such killer viruses are never observed, and the question is why?

One hypothesis to explain this issue is that there is a necessary [|trade-off between infectivity (B) and infection duration (g)] (REF).

Van Ballengooien and Boerlijst ([|2004]) implemented the model in a CA and obtained the following qualitative outcomes:
 * virus dies out locally: Ro < 1
 * turbulent waves
 * semi-stable spiral waves (edge of chaos?)
 * stable spiral waves

Moreover, if they allow the parameters of the model to evolve (B and g) they find that the system always evolves to the line where B/g = 0.66. Interestingly this is also the **border of order** between stable spiral waves and chaotic waves. Then along the Ro 0.66 line, the system slowly evolves to higher infection rates.

//So why does the system evolve to the Ro=0.66 line?// Well this is where outbreak frequencies are maximized in the system!

//So what about the trade-off?// When the trade-off is imposed in the model [|a priori], evolution proceeds to where the trade-off condition intersects with the Ro=0.66 line. This means that the trade-off is enslaved within the spatial dynamics of the system, and has therefore become less relevant.

This study contributes well to our **[|paradigm] system** of CAs and the role of spiral patterns in evolutionary dynamics. As a paradigm system it shows things that might be true. Here the bottom-line is that an explicit trade-off does not need to occur and that other unforeseen processes may be more important.


 * References**
 * van Ballegooijen WM &  Boerlijst  MC** (2004) Emergent trade-offs and selection for outbreak frequency in spatial epidemics. PNAS 101: 18246-18250. [|link]