Long-Term Research Goals

3 minute read

Modelling

In my proposal (which you can view here) for my PhD research, I expressed a particular interest in updating and extending the work already done on Firefighter as a model for contagion by introducing information about agency in individuals. Specifically, I have considered attributing a kind of behavioral rating to each vertex, corresponding to how many/few details can be traced to them in the case of a revolutionary communication network or how many/few precautions and protective measures they are able to implememnt against the spread of disease. This could then be used to generate a continuous function that dictates the probability with which the fire may transfer to a given vertex. Of course, a further extension to be considered is factoring in some reproduction information in the disease spread: the base rate at which it infects, an average of how many people can be expected to contract the infection when one person has been infected. Then, we have a much more accurate understanding of the behaviour of the disease and how it can be combatted. For instance, in a Firebreak context we might allow ourselves, say the equivalent of increasing the behavioural rating of 5 people to 100%. This could mean we increase 10 people by 50%, for example or any other possible combination - our “budget” allows for a certain amount of influence and that can be spent heavily on fewer vertices or sparingly on far more vertices (or a blend of both). It would then be my goal to understand optimal strategies for this context and those where we have the equivalent of, say, 100% influence per turn in a more Firefighter-like instance. Do we focus our attention on the most well-connected vertices? Perhaps we concentrate on the lowest-rated vertices?

This extension of the original problem would be incredibly useful in understanding, for instance, how best we might distribute a very limited supply of vaccines, or a supply of vaccines that we are receiving very slowly. Of course, there are numerous ethical implications to mitiage any potential optimal strategy against. For instance, if we remain with the vaccine application, how do we ensure the most vulnerable are best protected? If we choose to focus our limited resources on the worst-rated vertices, when presumably the most vulnerable will be concentrating effort in ensuring their rating is very high, then surely we will miss them with a vaccine most of the time. Similarly, honing in on the best connected vertices will presumably not correlate to honing in on the most vulnerable, but are these strategies of protection preferable? That is, if we pursue these strategies, can we ensure the most vulnerable receive adequate protection by immunising those around them, creating a protective social layer around them? This could be explored by randomly assigning “vulnerable” status to certain vertices, not based on any other factors (such as current connections or behavioural rating). This could then also be coupled with a slight increase in rating, such as in countries during the COVID pandemic where the most clinically vulnerable were asked to ‘shield’ - that is, increase their behavioural rating. I would suggest increasing this only slightly, with some random variation, as there is no guarantee that every individual asked to follow these instructions was in a position to isolate themselves entirely and take all other relevant measures. With all this information, we have a graph where some vertices are labelled as “vulnerable” and have a higher (on average) behvaioural rating, others have entirely random behavioural ratings and numbers of neighbours (depending on the type of graph we wish to consider). Then, exploring what optimal strategies would look like against a contagion would likely be far more nuanced (and difficult) but also provide a much more informative picture of the approach policy makers should pursue in mitigating risk against contagion, both at the onset and during the spread. Perhaps another application of this could be in stopping the spread of a computer virus across a local network of computers, when the virus is not guaranteed to infect every machine and we only have so many members of staff who can protect individual machines in such a high-pressure situation. In this case, it is presumably better to protect well-connected machines (servers and the likes) but vulnerable machines (those without up-to-date antivirus software, those with sensitive information, not backed up and so on) may nonetheless have to take priority, so long as a well-connected machine is connected to machines that have a good behavioural rating, on the whole.