In an earlier post I mentioned that agent-based models provide a substantially different way of approaching the problem of pandemic modeling. ABM models are generative simulations of processes that work incrementally through the behavior of discrete agents; so modeling an epidemic using this approach is a natural application.
In an important recent research effort Gianluca Manzo and Arnout van de Rijt have undertaken to provide an empirically calibrated ABM model of the pandemic in France that pays attention to the properties of the social networks that are found in France. They note that traditional approaches to the modeling of epidemic diseases often work on the basis of average population statistics. (The draft paper is posted on ArXiv; link; they have updated the manuscript since posting). They note, however, that diseases travel through social networks, and individuals within a society differ substantially in terms of the number of contacts they have in a typical day or week. This implies intuitively that the transmission of a disease through a population should be expected to be influenced by the social networks found within that population and the variations that exist across individuals in terms of the number of social contacts that they have in a given time period. Manzo and van de Rijt believe that this feature of disease-spread through a community is crucial to consider when attempting to model the progression of the disease. But more importantly, they believe that consideration of contact variation across a population suggests public health strategies that might be successful in reducing the spread of a disease at lower social and public cost.
Manzo offers a general framework for this approach in “Complex Social Networks are Missing in the Dominant COVID-19 Epidemic Models,” published last month in Sociologica (link). Here is the abstract for this article:
In the COVID-19 crisis, compartmental models have been largely used to predict the macroscopic dynamics of infections and deaths and to assess different non-pharmaceutical interventions aimed to contain the microscopic dynamics of person-to-person contagions. Evidence shows that the predictions of these models are affected by high levels of uncertainty. However, the link between predictions and interventions is rarely questioned and a critical scrutiny of the dependency of interventions on model assumptions is missing in public debate. In this article, I have examined the building blocks of compartmental epidemic models so influential in the current crisis. A close look suggests that these models can only lead to one type of intervention, i.e., interventions that indifferently concern large subsets of the population or even the overall population. This is because they look at virus diffusion without modelling the topology of social interactions. Therefore, they cannot assess any targeted interventions that could surgically isolate specific individuals and/or cutting particular person-to-person transmission paths. If complex social networks are seriously considered, more sophisticated interventions can be explored that apply to specific categories or sets of individuals with expected collective benefits. In the last section of the article, I sketch a research agenda to promote a new generation of network-driven epidemic models. (31)
Manzo’s central concern about what he calls compartmental models (SIR models) is that “the variants of SIR models used in the current crisis context address virus diffusion without modelling the topology of social interactions realistically” (33).
Manzo offers an interesting illustration of why a generic SIR model has trouble reproducing the dynamics of an epidemic of infectious disease by comparing this situation to the problem of traffic congestion:
It is as if we pretended realistically to model car flows at a country level, and potentially associated traffic jams, without also modelling the networks of streets, routes, and freeways. Could this type of models go beyond recommendations advising everyone not to use the car or allowing only specific fractions of the population to take the route at specific times and days? I suspect they could not. One may also anticipate that many drivers would be highly dissatisfied with such generic and undifferentiated instructions. SIR models currently in use put each of us in a similar situation. The lack of route infrastructure within my fictive traffic model corresponds to the absence of the structure of social interactions with dominant SIR models. (42)
The key innovation in the models constructed by Manzo and van de Rijt is the use of detailed data on contact patterns in France. They make highly pertinent use of a study of close-range contacts that was done in France in 2012 and published in 2015 (Béraud et al link). This study allows for estimation of the frequency of contacts possessed by French adults and children and the extensive variation that exists across individuals. Here is a graph illustrating the dispersion that exists in number of contacts for individuals in the study:
This graph demonstrates the very wide variance that exists among individuals when it comes to “number of contacts”; and this variation in turn is highly relevant to the spread of an infectious disease.
Manzo and van de Rijt make use of the data provided in this COMES-F study to empirically calibrate their agent-based model of the diffusion of the disease, and to estimate the effects of several different strategies designed to slow down the spread of the disease following relaxation of extreme social distancing measures.
The most important takeaway from this article is the strategy that it suggests for managing the reopening of social interaction after the peak of the epidemic. Key to transmission is frequency of close contact, and these models show that a small number of individuals have disproportionate effect on the spread of an infectious disease because of the high number of contacts they have. Manzo and van de Rijt ask the hypothetical question: are there strategies for management of an epidemic that could be designed by selecting a relatively small number of individuals for immunization? (Immunization might take the form of an effective but scarce vaccine, or it might take the form of testing, isolation, and intensive contact tracing.) But how would it be possible to identify the “high contact” individuals? M&R consider two strategies and then represent these strategies within their base model of the epidemic. Both strategies show dramatic improvement in the number of infected individuals over time. The baseline strategy “NO-TARGET” is one in which a certain number of individuals are chosen at random for immunization, and then the process of infection plays out. The “CONTACT-TARGET” strategy is designed to select the same number of individuals for immunization, but using a process that makes it more likely that the selected individuals will have higher-than-average contacts. The way this is done is to select a random group of individuals from the population and then ask those individuals to nominate one of their contacts for immunization. It is demonstrable that this procedure will arrive at a group of individuals for immunization who have higher-than-average numbers of contacts. The third strategy, HUB-TARGET, involves selecting the same number of individuals for treatment from occupations that have high levels of contacts.
The simulation is run multiple times for each of the three treatment strategies, using four different “budgets” that determine the number of individuals to be treated on each scenario. The results are presented here, and they are dramatic. Both contact-sensitive strategies of treatment result in substantial reduction in the total number of individuals infect over the course of 50, 100, and 150 days. And this in turn translates into substantial reduction of the number of ICU beds required on each strategy.
Here is how Manzo and van de Rijt summarize their findings:
As countries exit the Covid-19 lockdown many have limited capacity to prevent flare-ups of the coronavirus. With medical, technological, and financial resources to prevent infection of only a fraction of its population, which individuals should countries target for testing and tracking? Together, our results suggest that targeting individuals characterized by high frequencies of short-range contacts dramatically improves the effectiveness of interventions. An additional known advantage of targeting hubs with medical testing specifically is that they serve as an early-warning device that can detect impending or unfolding outbreaks (Christakis & Fowler 2010; Kitsak et al. 2010).
This conclusion is reached by moving away from the standard compartmental models that rely on random mixing assumptions toward a network-based modeling framework that can accommodate person-to-person differences in infection risks stemming from differential connectedness. The framework allows us to model rather than average out the high variability of close-contact frequencies across individuals observed in contact survey data. Simulation results show that consideration of realistic close-contact distributions with high skew strongly impacts the expected impact of targeted versus general interventions, in favor of the former.
If these simulation results are indeed descriptive of the corresponding dynamics of spread of this disease through a population of socially connected people, then the research seems to provide an important hint about how public health authorities can effectively manage disease spread in a post-COVID without recourse to the complete shut-down of economic and social life that was necessary in the first half of 2020 in many parts of the world.
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Here is a very interesting set of simulations by Grant Sanderson of the spread of infectious disease on YouTube (link). The video is presented with truly fantastic graphics allowing sophisticated visualization of the dynamics of the disease under different population assumptions. Sanderson doesn’t explain the nature of the simulation, but it appears to be an agent-based model with parameters representing probability of infection through proximity. It is very interesting to look at this simulation through the eyes of the Manzo-van de Rijt critique: this model ignores exactly the factor that Manzo and van de Rijt take to be crucial — differences across agents in number of contacts and the networks and hubs through which agents interact. This is reflected in the fact that every agent is moving randomly across space and every agent has the same average probability of passing on infection to those he/she encounters.