Anti-Gresham’s Law: Good information drives out bad

(Good information is in blue, bad information is in Red)

Read an article the other day in ScienceDaily (Faster way to replace bad info in networks) which discusses research published in a recent IEEE/ACM Transactions on Network journal (behind paywall). Luckily there was a pre-print available (Modeling and analysis of conflicting information propagation in a finite time horizon).

The article discusses information epidemics using the analogy of a virus and its antidote. This is where bad information (the virus) and good information (the antidote) circulate within a network of individuals (systems, friend networks, IOT networks, etc). Such bad information could be malware and its good information counterpart could be a system patch to fix the vulnerability. Another example would be an outright lie about some event and it’s counterpart could be the truth about the event.

The analysis in the paper makes some simplifying assumptions. That in a any single individual (network node), both the virus and the antidote cannot co-exist. That is either an individual (node) is infected by the virus or is cured by the antidote or is yet to be infected or cured.

The network is fully connected and complex. That is once an individual in a network is infected, unless an antidote is developed the infection proceeds to infect all individuals in the network. And once an antidote is created it will cure all individuals in a network over time. Some individuals in the network have more connections to other nodes in the network while different individuals have less connections to other nodes in the network.

The network functions in a bi-directional manner. That is any node, lets say RAY, can infect/cure any node it is connected to and conversely any node it is connected to can infect/cure the RAY node.

Gresham’s law, (see Wikipedia article) is a monetary principle which states bad money in circulation drives out good. Where bad money is money that is worth less than the commodity it is backed with and good money is money that’s worth more than the commodity it is backed with. In essence, good money is hoarded and people will preferentially use bad money.

My anti-Gresham’s law is that good information drives out bad. Where good information is the truth about an event, security patches, antidotes to infections, etc. and bad infrormation is falsehoods, malware, biological viruses., etc

The Susceptible Infected-Cured (SIC) model

The paper describes a SIC model that simulates the (virus and antidote) epidemic propagation process or the process whereby virus and its antidote propagates throughout a network. This assumes that once a network node is infected (at time0), during the next interval (time0+1) it infects it’s nearest neighbors (nodes that are directly connected to it) and they in turn infect their nearest neighbors during the following interval (time0+2), etc, until all nodes are infected. Similarly, once a network node is cured it will cure all it’s neighbor nodes during the next interval and these nodes will cure all of their neighbor nodes during the following interval, etc, until all nodes are cured.

What can the SIC model tell us

The model provides calculations to generate a number of statistics, such as half-life time of bad information and extinction time of bad-information. The paper discusses the SIC model across complex (irregular) network topologies as well as completely connected and star topologies and derives formulas for each type of network

In the discussion portion of the paper, the authors indicate that if you are interested in curing a population with bad information it’s best to map out the networks’ topology and focus your curation efforts on those node(s) that lie along the (most) shortest path(s) within a network.

I wrongly thought that the best way to cure a population of nodes would be to cure the nodes with the highest connectivity. While this may work and such nodes, are no doubt along at least one if not all, shortest paths, it may not be the optimum solution to reduce extinction time, especially If there are other nodes on more shortest paths in a network, target these nodes with a cure.

Applying the SIC model to COVID-19

It seems to me that if we were to model the physical social connectivity of individuals in a population (city, town, state, etc.). And we wanted to infect the highest portion of people in the shortest time we would target shortest path individuals to be infected first.

Conversely, if we wanted to slow down the infection rate of COVID-19, it would be extremely important to reduce the physical connectivity of indivduals on the shortest path in a population. Which is why social distancing, at least when broadly applied, works. It’s also why, when infected, self quarantining is the best policy. But if you wished to not apply social distancing in a broad way, perhaps targeting those individuals on the shortest path to practice social distancing could suffice.

However, there are at least two other approaches to using the SIC model to eradicate (extinguish the disease) the fastest:

  1. Now if we were able to produce an antidote, say a vaccine but one which had the property of being infectious (say a less potent strain of the COVID-19 virus). Then targeting this vaccine to those people on the shortest paths in a network would extinguish the pandemic in the shortest time. Please note, that to my knowledge, any vaccine (course), if successful, will eliminate a disease and provide antibodies for any future infections of that disease. So the time when a person is infected with a vaccine strain, is limited and would likely be much shorter than the time soemone is infected with the original disease. And most vaccines are likely to be a weakened version of an original disease may not be as infectious. So in the wild the vaccine and the original disease would compete to infect people.
  2. Another approach to using the SIC model and is to produce a normal (non-transmissible) vaccine and target vaccination to individuals on the shortest paths in a population network. As once vaccinated, these people would no longer be able to infect others and would block any infections to other individuals down network from them. One problem with this approach is if everyone is already infected. Vaccinating anyone will not slow down future infection rates.

There may be other approaches to using SIC to combat COVID-19 than the above but these seem most reasonable to me.

So, health organizations of the world, figure out your populations physical-social connectivity network (perhaps using mobile phone GPS information) and target any cure/vaccination to those individuals on the highest number of shortest paths through your network.


Photo Credit(s):

  1. Figure 2 from the Modeling and analysis of conflicting information propagation in a finite time horizon article pre-print
  2. Figure 3 from the Modeling and analysis of conflicting information propagation in a finite time horizon article pre-print
  3. COVID-19 virus micrograph, from USA CDC.

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