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:

They work via analysis of the interplay between variables that are defined by medical states, linked via a system of differential equations that 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.  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 (Ro) 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.

Starting from Ro, the ‘effective transmission/reproduction rate’,  R (the number of people that an individual can be expected to infect at any given, later time)  changes over time as the number of susceptibles falls.

Let me at this point, make a shift from epidemiological jargon to economic jargon and rename Ro as the ‘ basic propensity to infect’ and likewise rename R  as simply 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 getting to a point where the API or R < 1, in consequence of the negative feedback mechanism of a falling number of susceptibles (S).

What is often missing from the epidemiological models, however, are adequate examinations of the interactions between medical variables which can arise from the existence of social structures and from the social conduct that occurs within them.  This neglect has occurred despite an epidemiological  ‘recognition in the abstract’ of their relevance.  Thus, if the Wikipedia entry for ‘Basic Reproduction Rate’ is looked up, there it can be read that “Ro is not a biological constant for a pathogen as it is also affected by other factors such as environmental conditions and the behaviour of the infected population [my emphasis].”

The behaviour of members of a society is, of course, what social scientists study and it is a feature of the current situation that their contribution to an understanding of the contagion has been notable chiefly by its absence.

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 contact 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, or for London commuters using its mass transit systems (who mix closely with one another on a daily basis). 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 can be very rapid indeed.

To get a feel for the numbers, imagine the first person infected among those who regularly used London Transport in, say, mid February.  The average Ro for the UK might by 2.5, but what might it be for the community of London commuters. If ‘infectee one’ makes a tw0-legged commute twice a day, that would, in effect, amount to participation in 20 super-spreading events in a working week.  Ro could be a 100 or more, and at that rate the daily infections rise very, very quickly.

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.  What the tendency for there to be high PIs at both ends of a transmission implies is required for analytical purposes is a socially structured disaggregation of the familiar negative feedback loop that reflects decreases in the number of susceptibles among close contacts.  One differential equation needs to become a set of several equations.

Once the contagion gets going, then, it immediately starts rapidly to thin out infections characterised as being between high PI individuals, and this can radically affect the dynamics.

To illustrate let’s take an extreme, hypothetical, ‘teaching’ simplification, which introduces social differentiation in a very limited way.  Suppose there are two types of people with identical, intra-type characteristics (e.g. London mass transit commuters and everyone else). There are ‘Highs’ with a PI of 10 and who make up 20% of the population, and there are ‘Lows’, with a PI of 0.8 and who make up 80% of the population.  It is assumed (and its the crudest of the simplifying assumptions) that the Highs and Lows never have inter-type close contacts. There are ‘two nations’.  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. 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 90% of the Highs would be sufficient to bring their API down to 1.  Nine of ten people who would be infected if susceptible, would no longer be infected:  only one would be, and hence the spread would no longer be advancing.

This illustrates an important point that  has major implications for policy trade-offs: The early ‘selection’ of high PI individuals clearly assists the virus  in moving swiftly in its first stages, but it comes at a price (for the virus): the spread may peter out when infections reach only a modest fraction of the total population, in this case 18% (which would reduce further in the event of the existence of sources of innate immunity such as T cell activity or cross-immunity from other coronaviruses:  if innate immunity were, say, at 30%, the contagion would stop advancing at a whole population infection level of 12%). The rapid early progress is bought at the price of the virus being less able to find powerful allies later in the process.

Setting the crude simplification aside, the more general point is that there is a social-contact, natural selection process at work, particularly prominent in the contagion’s early stages.  In a social setting the natural selection of the biology picks out high PI victims. But, as it does so it has the immediate and direct effect of reducing the population API much faster than would be the case if all humans led similar social lives.

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 a fully developed model), will be determined not only by the aggregate numbers of those infected and those still susceptible (the prime focus of the epidemiological work), but  also 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 are their preferred lifestyles? 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 playing 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, does most to inhibit the spread of the virus.  Under such a general lockdown, everyone is treated the same, irrespective of social characteristics.

It is easy to see that there might be political reasons for doing that, but it should be recognised that they come with a cost:  ‘Covid-management policies can be expected to be less effective.

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 virus’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.  Will extended lockdown simply be good for reducing transmission in the shorter-term, but bad for reducing transmission later, when it is relaxed?

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. Homo Sapiens is a highly 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 other atoms 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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