Background

The data frame is a network of 35 people in Mexico identified as “power elites” in the 1990s. They were deemed “powerful” for possessing political influences and high social statuses, but they were not 100% heterogeneous. Some of them had military affiliations, while others didn’t. Some of them later became presidents (grouped as “in_mpn”), while others perhaps missed the chance. There were clusters, cliques, and communities in such a small and exclusive network, which makes analyzing the spread of an infectious disease among them particularly interesting.

Aleman Valdes is the central figure in the network with 17 connections, while C. Cardenas has the least—only 2 connections.



Pandemic transmission simulations

From time 0 to time 4, the spread of COVID that starts with Trevino among the Mexican power elite is complete.



When we choose a random individual to be Patient Zero, the spread is faster by one Time.



If “Patient Zero” is Cardenas (with the lowest degree centrality), the disease takes from Time 0 to Time 4 to spread throughout the whole network.



If “Patient Zero” is Aleman Valdes (with the highest degree centrality), then the whole network is infected by Time 2.

We assume it all starts with Trevino and Madero (nodes numbered as 1 and 2). If the threshold is 0.5, none of the susceptible individuals are infected unless at least half of their contacts are at risk. Thus, higher threshold implies a longer time for the disease to spread to the whole network.



If we hold other parameters constant and change only the recovery rate from 0 (topmost) to 0.25, to 0.5, to 1, we observe that higher recovery rates correspond to a swifter recovery process, reducing the duration of infection within the network and resulting in lower peak proportions of infection.



Holding all other parameters constant, varying the transmissibility from 0.25, to 0.5, to 1 shows a faster spread of the disease, as infected individuals are more effective in transmitting the disease to others.



Out of all the diffusion models, namely SR, SIR, SIRS, SEIR, we choose SEIR model as our baseline since it best portrays a pandemic outbreak within a short period of time among a small community.

The values of the parameters are as follows:

A latency of 0.5 means that it takes two days to become infectious. Our recovery assumption of 0.25 indicates that it takes 4 days to recover. For a comparatively short period of time like an outbreak, we chose a very low value for waning and assumed that there would hardly be time for immunity from either getting sick or vaccinated to wane. The seeds are still Trevino and Madero by default. The peak of the proportion of infected is at around two weeks.



Hypothesis testing

Hypothesis 1: Having a military affiliation (having been in the military before) means better immunity systems against the disease.

To test that, we add an attribute of threshold = 5 to people with a military affiliation, meaning they’re less likely (it takes more contacts) to get infected; and threshold = 1 to those without a military background for contrast.



The top panel assumes people with military background are less susceptible since they are more disciplined and healthier than average people. Thus, we prove that elites with military affiliations are less likely to be infected and the spread of the disease is slower with their presence.



Hypothesis 2: Vaccination is effective.

If we have a group of people, for example the most elite group (those who became future presidents, marked as “in_mpn”) in the network vaccinated, the transmission rate will slow down, compared with everyone having zero immunity. We use the parameter immune = 1 to indicate vaccination.



Our simulations prove that vaccination strategies work well to stop an infectious disease. In the first plot where some are vaccinated, no infections occur, and thus, halting an epidemic. Of course, in the real world, who should get vaccinated first remains a critical matter of equity and awaits further discussion.

Knowledge transfer for pandemic prevention

The diffusion model also applies to spreading pandemic prevention information or good practices via influential nodes like cores or clique bridges.

Piggybacking on the transmission analysis on the spread of the virus, information on health protocols spreads fastest through Aleman Valdes, the most central and least constrained person in the network, based on node constraint scores (indicated by node sizes).