Social contact networks and the spread of Covid-19

Epidemiology is much to the fore at the moment and the curves that feature in the epidemiological modelling are to be seen in TV, newsprint and many a social media post. The models used vary according to the biological characteristics of the relevant bug and there is a good summary of a number of their various types here, where a general reader’s scan of the list will suffice to give a flavour: https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model

They work via analysis of the interplay between variables that are defined by medical states, linked via a system of differential equations, which may be deterministic or stochastic. The chief negative feedback mechanism is from the number of people who have been infected (N) – one of the medical state-variables (one of the ‘compartments’ or boxes) – to the rate of new infections. The more people that have been infected, the fewer in number are those who remain susceptible to infection (S). The strength of the feedback pressure tends to gather force over time, becoming greatest in the later stages,

There is also a positive feedback loop which is dominant early on – the more people that are infected the greater the infection rate (because the number of those doing the infecting expands). The changing balance between these two pressures determines the shapes of the contagion’s curves.

Looking at this picture, a social scientist will naturally ask: where are the social variables (where the word ‘social’ is to be construed broadly to include, for example, the settlement and movement patterns studied in human geography)? The bug is invading a highly complex, socially-ordered network of encounters between individual members of society. These encounters are very far from being random in general, though they may be in individual instances.

So, consider one the important parameters to be found in epidemiological models, the number of close (physical) contacts (CCs) that an infected person might have with others. This directly affects the basic transmission rate of the virus (i.e. Ro the number of infections of others that an individual might cause in circumstances where all contacts are with others who are susceptible to the disease), and we can expect that basic number to vary significantly from one individual to another, in reflection of the heterogeneity of the circumstances in which individuals come into close contact with one another.

Let me at this point, make a shift from epidemiological jargon to economic jargon and rename Ro as the ‘propensity to infect’ (PI). An average PI (API) can be calculated for the population as a whole, and it is such an average that is used when people talk about seeking to acquire ‘herd immunity’ by getting to a point where Ro < 1, in consequence of the negative feedback mechanism of a falling number of Ss.

What is often missing from the epidemiological models, however, are the correlations between variables which can arise from the existence of the social structures. Let me look at just one such correlation (since the aim of this note is to encourage thinking about the contagion in a different way, not to expound any new comprehensive view of it). It is that the close contacts (CCs) of many with high propensities to infect (PIs) will not be random, but will be tilted toward CCs with other high PI people, because of the social networks in which they move.

This could be true for professionals who work and socialise with other professionals (and they do tend to network quite a lot), or for inhabitants of multi-occupancy buildings in socially deprived areas. An immediate implication is that the early stages of a contagion will ‘naturally’ select for people at each end of a particular transmission who are both high PI individuals, and hence that the early spread could be very rapid.

What taking this type of social factor into account requires is the addition of new equations to the differential equation system of an epidemiological model. That will obviously affect the solutions of the equations: in this particular case what the additional correlation implies is the introduction of another, negative feedback loop/mechanism (additional to the negative feedback that comes from a reduction in S as more and more people are infected). Once the contagion gets going, it immediately starts to thin out those who are high transmitters of the disease.

To illustrate let’s take an extreme, hypothetical, ‘teaching’ simplification, which introduces social differentiation in a very limited way: in effect, it divides the population into two types of people with identical, intra-type characteristics (and goes no further than that). There are ‘Highs’, with a PI of 5 and who make up 30% of the population, and there are ‘Lows’, with a PI of 0.8 and who make up 70% of the population. The API(Ro) for the population as a whole is 2.06 (5*0.3+0.8*0.7). It is assumed that the Highs and Lows never have inter-type close contacts. How in this case does the infection go?

Not very far is the answer, if the virus only has a foothold among the Lows. It peters out almost immediately. Given a foothold among the Highs, however, it will progress very rapidly at first and then slow as the number of Highs who are still susceptible to the disease decreases (because increasing numbers have been infected).

To track infections in the latter case it is necessary to solve out for the differential equations for the High part of the population, but it is easy to see that infection of 80% of the Highs would be more than sufficient to bring their API down to API (Ro) = 1. The feedback loop from the reduced number of High Ss would also be in play, so the number of infections required for API =1 (among Highs) can be expected to be lower than that. If it were, say, 80% of 80% = 64% of Highs, that would translate into an infection rate for the population as a whole of 19.2%.

This illustrates an important point, which has major implications for policy trade-offs: The early ‘selection’ of high API individuals clearly assists the bug in moving swiftly in its first stages, but it comes at a price (for the bug): the spread may peter out when infections reach only a modest fraction of the total population (like say 19.4%). The rapid early progress is bought at the price of not reaching an otherwise potentially large fraction of the population at a later stage.

The problem for the bug is that the ‘selection out’ of high PI transmitters is, at least with the kinds of numbers assumed in the illustrative hypothetical, such a powerful factor in reducing the API. In terms of whole population averages, when 10% of the whole population in the example has been infected, the API will have fallen from 2.06 to 1.56 as a result of this feedback pressure alone. At 20% infected, that becomes an API of 1.06.

Setting the crude simplification aside, the more general point is that there is a ‘social-contact selection’ process at work:  particularly in the contagion’s early stages, in a social setting the natural selection of the biology picks out high API victims. But, as it does so it has the immediate and direct effect of reducing the population API, which occurs with none of the slowness associated with the negative feedback pressures that build from the reduction in the number of susceptibles (S).

What I think is best called ‘community resistance’ – which is the combined effect of all the negative feedback loops in play (two in the illustrate example, more in practice) – will then be determined not only by the aggregate numbers of those infected and those still susceptible (the prime focus of the epidemiological work) – but by the social characteristics of the heterogeneous individuals who make up the numbers. Who are they? Where do they live? What are their living conditions? Where do they work? What do their social (physical contact) networks look like? And so on. Without some knowledge of those things, it is, I think, impossible to understand the contagion in any detail. We are left to play guessing games.

A second general point that follows from all this is a classic health warning, given by all good advisors to politicians contemplating a perturbation to a social system: beware of unintended effects/consequences. In the case of Covid-19, it is easy to see that the social distancing effects of a general lockdown are bound to have a negative direct (all other things being equal) effect on the rate of spread of the virus. At least in its less mitigated forms, however, it is an undiscriminating, one-size-fits-all policy and, as such, it hinders the ‘natural’ selection process that, at least arguably, has done most to inhibit the spread of the virus.

Whether such a policy will, in the end, actually reduce the cumulative deaths attributable to the contagion is, therefore, very much an open question at the time of writing:  it cannot safely be presumed.  If a bug’s eye view of things suggests that finding its way quickly to the infection of high transmitters is good for it in the short term, but not so good for it in the longer term, that intelligence might be useful information for humans contemplating how best to counter the harms it brings.

Finally, to repeat a sentiment expressed above, this short piece is directed at encouraging policymakers to look at the issues in a different light, a light that illuminates the social factors that are involved in the contagion. Man is a social animal embedded in a highly complex social ecology, not a herd animal, still less like those atoms in the kinetic theory of gases that move about randomly, bumping into others as they do so. We should not lose sight of that.

Author: gypoliticaleconomyblog

Lifetime student of political economy, retired academic and regulator.

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