Making contagion social: Epidemiology,calculus,and the theory of happenings

Abstract

The beginnings of formal epidemiology are conventionally marked by the introduction of mathematical modelling in the early 20th century. However, Ronald Ross, colonial medical officer and 1902 Nobel laureate for his proof of the insect vector of malaria, envisioned the future of mathematical epidemiology as a much more expansive project, one that would eventually exceed the remit of a medical science. This article introduces and analyses Ross’ theory of happenings as an attempt to generalise the concept of contagion as a non-material form of social organisation. To contextualise this approach, I explore the parallels and the common references between the mathematical method of epidemiologist Ronald Ross, and the work of sociologist Gabriel Tarde, who wrote Laws of Imitation (1890), to establish a relative and universal sociology. Both conceptualisations of contagion disregard a meaningful boundary between the natural and social world, they focus on affect and affectedness to embrace a radical plasticity in the human subject, both champion a philosophy of the infinitesimal to reject simplistic causes for social processes and to analyse large occurrences by focus on the vanishingly small. These parallels provide an opportunity to challenge assertions of a schism between the social sciences and the project of formal epidemiology, and to instead consider the contours of a different kind of social theory at the heart of the modern epidemiological project.

Introduction

Society, we now know, consists in the exchange of reflections. Mutually to ape one another, and by dint of accumulated apings diversely combined to create an originality is the important thing. (Tarde, 1905: 52)

In his short novella Underground Man, published in English in 1905, ¹ the French sociologist and criminologist Gabriel Tarde delivered a fable to chime with a then-fashionable anxiety about the sudden extinction of modern life: a future in which the sun imploded, humanity had to retract to a system of caves and catacombs, and society had to be reinvented from a void. Having escaped the pressure of relating to, relying on, or overcoming the constraints of nature in the underground, the social has become a pure experiment: what determines the underground society need no longer be defined by ‘certain sophists, who were called economists’ (Tarde, 1905: 52). Tarde's modernist sociability – which has its most utopian expression in this late literary work – posits social bonds instead as the mere ‘exchange of reflections’, as a society shaped by laws of imitation, rather than one structured by the exchange of goods, services, and deeds. Imitation, replication, or ‘aping’, so Tarde argued, were in fact not synonymous with the downfall of individual freedom, rationality, and consciousness, but rather enabled a novel, improved social order (Tarde, 2013). ² According to the British novelist H. G. Wells, Tarde had delivered nothing short of a radical ‘new conception of human intercourse’ (Wells, in Tarde, 1905: 11).

In the same year Tarde's novella was published in English, the British colonial medical officer Ronald Ross, Nobel laureate for proving Patrick Manson's theory of a mosquito vector for malaria, grappled with a similar question, although under very different terms. Ignorant of Tarde's work, Ross sought to provide a ‘logical basis’ for mosquito population reduction, by venturing beyond the empirical constraints of the material world. It was impossible to measure the density of mosquitos in each area or region, and so his mathematical approach set off from a hypothetical ‘country of indefinite extent, every point of which is equally favourable to gnats’. While Ross admitted that such a country does not exist, he required its proposition to develop a mathematical analysis, which in turn provided estimates about the ‘influx, efflux and varying density of mosquitos’; a logical basis that was supposed to inform any experiment on mosquito reduction (Ross, 1905: 699). While Tarde's artificial and ahistorical world of pure social contagiousness in the Underground Man constituted the culmination of the sociologist's theorising of imitation and suggestibility, Ross’ proposition of a virtual country was one of his first crucial steps towards developing a generalised epidemic theory with an increasingly expansive focus on happenings, affect, and susceptibility.

How do laws of imitation, conceptualised so sharply in the fin de siècle sociology of Gabriel Tarde relate to the rules of contagion formalised by Ronald Ross? This question will be the leading line of inquiry for the following pages. Why did Ross advance his mathematical pondering so far beyond the scope of his previous work, which used to focused on one specific infectious vector-borne disease? What led Ross to apply his epidemic theory not only to a class of infectious diseases or even just to a wider range of medical phenomena, but to everything that affects humans in their social life?

My argument breaks with the common assumption that Ross's generalisation of epidemic theory was unique in its time or that he was particularly original in thinking contagiously about the social. ³ On the contrary, matters need to be considered in reverse: the ambition of Ronald Ross to develop a generalised theory of contagion formalised popular beliefs at a time when moral contagions, psychic epidemics, and the fear that they were both causes and effects of ‘degeneration’ were commonplaces in politics as well as in the human and life sciences.

Second, the development of formal epidemiology is too often associated with a critical reduction of the field's involvement with the social sciences (Amsterdamska, 2005; Hardy, 1993; Krieger, 2011; Magnello, 2002; Morabia, 2013). Mathematical formulas and the design of theoretical and simulated epidemics are accused to have lost the granular detail of social analysis and to have weakened the causal power of sociological arguments in the name of public health. Instead, formal epidemiology supposedly advanced a mechanistic and reductionist view of epidemics as the abstracted interplay of population and pathogen, mitigated by a few selected and exchangeable factors. In most popular accounts, Ross’ theory of happenings has come to exemplify this apparent shift from concerns about sanitary status, population fitness, or bacterial virulence towards a system of opaque interdependent functions and factors, which are expressed in the neutral and abstract language of equations. However, while this shift may well have been motivated by the rejection of simplistic causal theories – such as blaming epidemics on infected immigrants – the turn to a priori theories did not come out of thin air. In a critical reversal of much of the common complaints about epidemiology's formalisation, this article explores how Ross’ epidemiology did indeed advance the sociological compass into epidemiological reasoning, while, however, yielding to a different kind of social theory.

Ross mobilised a set of consequential considerations, whose impact on modern thought is best acknowledged when considered as a tandem history with developments in sociological thought in France. ⁴ Ross mathematical forays into epidemic theory refuted a growing trend among his contemporaries to fix causal explanations for social dynamics in biological factors; a trend too often associated with a deeply held pessimism about the fate of democracies and liberal societies (Trotter, 1917). Tarde, similarly, rejected the ‘absurd idea’ that for example concepts of race would be the cause, rather than the obvious outcome of social facts (Tarde, 2013[1890]: 20). Ross’ theory of happenings was also designed to contradict the more pessimistic social contagion arguments at the time. Just like Tarde's laws of imitation, Ross theory was not conceived to enable moral judgement on a presumed pathological nature of spreading social issues: because something spread contagiously did not mean for it to be a problem.

The wider consequence of these assumptions at the origin of modern, formal epidemiology are astonishing. Not only did his theory mobilise epidemiological reasoning far beyond the realm of infectious disease, but Ross’ formulaic work rejected the idea that pathogens exist as natural kinds. He did not of course conspire against the all-too-real threat of infectious diseases. Instead, he theorised pathogenicity not as the inherent characteristic of some specific microbes, but as a contextually emerging effect when multiple conditions align. ⁵ Or, as Tarde put it, ‘Parasites also have their parasites’ (Tarde, 2015: 42).

Both projects, Ross’ epidemiology and Tarde's sociology, embraced a new, transformative way of mathematical reasoning that sought to explain large issues with a focus on the smallest of processes. Both welcomed the opportunity of differential calculus to be applied to an infinite range of problems, while enabling an analytical lens to move across the radical commensurability of social and natural domains. ⁶ That which constituted a universal sociology for Tarde, reaching in its application from cells to stars, re-appeared in Ross’ epidemiology, framed as a generalised theory of happenings that extrapolated from infectious diseases to marriages, political sects, and the accrual of wealth.

To develop this tandem history, I will first consider the prevalence of social contagion ideas in European social thought at the end of the 19th century. Second, I turn to Ronald Ross to sketch out the development of his theory of happenings. Third, I contrast the work of Ross to that of Tarde and their design of epidemiology (Ross) and sociology (Tarde) as modern scientific enterprises. This, I will conclude, offers a new way to map Tarde's social order onto the history of formal epidemiology and to revise common assumptions about its lost social conscience.

Psychic epidemics, moral contagion, and fear of degeneration

Theories of contagion without microbes were popular at the turn of the century within sociology, early psychology, and a range of associated fields such as criminology and anthropology, particularly on continental Europe. Across the 19th century and stretching from Russia to the United States, social contagion theories flourished to explain the behaviour of social groups, the dynamics of the masses and the distribution of views, movements, and resistances within populations. ⁷ In France, Gustave Le Bon wrote his influential thesis on the dynamics of crowds in 1895 (Le Bon, 1896), psychologists such as Georges Dumas sought to theorise the spatial patterning of psychiatric conditions in 1911 as contagious issues, while German psychologists like Wilhelm Wundt turned to hypnotism and suggestion as elements of social cohesion (Dumas, 1911; Hoche, 1910; Wundt, 1892). Motivated by eugenic sentiments to govern population betterment or to understand and contain prevailing images of degeneration, concepts of social contagion were astonishingly popular. Concerned as they were with suggestibility and patterns of imitation, fuelled by evolutionary anxieties about the decline of races and peoples, contagion theories provided a useful shortcut to paint alarming pictures of threatened institutions and tradition.

To capture social phenomena, and particularly those less desired, as ‘psychic epidemics’ or as mental or moral contagion, was, according to Jan Goldstein, ‘becoming a commonplace in fin-de-siècle France’ (Goldstein, 1984). First, the rhetoric of moral contagion allowed expression of an ‘antidemocratic animus’, bringing a language of uncontrollable disorder to bear on the crowd as a fragile foundation of democratic order. The mass was not to be trusted. Even the most integral member of society risked being corrupted when participating in or becoming subsumed by the crowd. Second, so Goldstein argues, moral contagion advanced the formation of the social sciences in France, particularly criminology, sociology, and social psychology (ibid.: 183). Third, and finally, the French concern with imitations and suspicions about crowds would not have yielded to such political weight without the introduction of the notion of Freud's unconscious. Here, the process of contagion could be readily conceptualised as a valid concern below the level of conscious decisions and self-awareness, introducing suggestibility, imagination, and ‘somnambulism’ (Tarde, 2013[1890]) into the language of politics. ⁸

This popularity of social, emotional, and moral contagion cannot exclusively be attributed to the psychological – or psychoanalytic – deconstruction of human agency. Importantly, the distribution of social theories about contagion should be understood in relation, rather than in opposition, to ongoing materialisation of infection in the bacteriological laboratory. By means of comparison to the transmission of pathogens – visible as pathogens could be in the laboratory – theories of social contagion could suddenly lend credibility and status to often spurious arguments about social phenomena through their reliance on biological science. ‘These theories’, Daniel Beer argues with regards to moral contagion discourses in imperial Russia, ‘gave scientific authority to social fears and moral panics and lent respectability to theories of social transformation’ (Beer, 2007: 534 f.). However, as many historians of infectious disease can attest to, the laboratory never succeeded to clarify the meaning of contagion into a ‘hard fact’, to which one might contrast the ‘soft facts’ of social phenomena (Amsterdamska, 2005; Engelmann, 2021b; Latour, 1988; Mendelsohn, 1996, 2002). Moral panics and social fears were as much part and parcel of the science of infectious disease as they may have motivated the emergence of new explanatory frameworks for a range of social phenomena.

In Britain, things are often understood to have developed slightly different. In her now-classic account of the history of the social sciences in England, Reba Soffer diagnoses the late-Victorian English elite to have remained somewhat indifferent to ideas of social degeneration. British social sciences, with some notable exceptions, managed to stay largely clear of the melancholy and moral panic of their European counterparts. Instead, they advanced a transformative spirit in the study of poverty, crime, and disease. For Soffer, confidence in individual and social regeneration remained the leitmotif for much of the British social sciences. In the absence of ‘Prussian military might, virulent Austrian and French anti-Semitism, anarchistic Balkan and Italian nationalism’, the project of British social science was able to maintain a primary commitment to social reform as a shared value, imbricated in the ‘rational will and conscience of the great majority of people’ (Soffer, 1978: 2).

The relative absence of a rhetoric of contagion in the British reflection of turn-of-the-century social issues supports Soffer's diagnosis. However, the insignificance of moral contagion or psychic epidemics to explain social transformation in England should not be mistaken for an abundant optimism among social scientists in a nation of industrial destitution and sustained sanitary and epidemic crisis. Soffer herself offers a useful distinction: on the one hand there were revolutionaries, who structured their social scientific project as a fulcrum to advance the cause of the people, to abandon tradition, and to overthrow established ways of thinking. On the other side, revisionists, who – like their European colleagues – grew suspicious about the liberal foundation of democracy. In turn-of-the-century England, the revisionist school of thought was assembled around the emerging field of social psychology. William McDougall, in his introduction to social psychology from 1906, raised a systematic concern about the manipulative forces that individuals so readily gave in to. Concerned as he was with the ‘gregarious instinct’, an instinct that brings people to follow the ‘baneful attraction’ of the ‘vast human herd’, he grew particularly suspicious of the ever-growing towns and cities (McDougall, 1906: 303). As an elitist research programme, social psychology was also championed by the surgeon and neurologist Wilfred Trotter. He advanced social science as a ‘political polemic’, utilising fragments of evolutionary theory to protect established social hierarchies, while shaping the mass into a source of trouble, driven by an uncontrolled ‘tyranneous [sic] power of the social instinct’ (Laffey, 1985; Soffer, 1978: 218; Trotter, 1917).

McDougall and Trotter were widely read in early 20th-century circles of British science. Social psychology provided context and explanation to growing fears about the potent irrationality of democratic policy. Furthermore, their work, just like the contributions of their contemporary Martin Conway, forged the emergence of the crowd as an ‘unpredictable and antidemocratic entity’ (Soffer, 1978: 230). Stopping short of a rhetoric of contagion, it was suggestibility that the social psychologists elevated into a scientific concept. Not only was suggestibility, as a threat to rationality and conscious morality – conditions of political choice and democratic process – the hallmark of spontaneous crowd behaviour, but the position of the individual in the social world of the crowd (symbolised in urban density) became the model of a pessimistic social science, in which the crowd would be positioned as the antithesis to liberal democracy.

While the height of the British discourse may have evaded the melancholy of the European fears of moral contagion, there was another site associated with Britain where such metaphors sprawled: the colonies. As Anjuli Fatima Raza Kolb has elegantly argued, the justification of British rule over India has been sharply characterised by a growing epidemiological rhetoric. ‘Insurgents’, so Kolb argues, ‘were described as passive, wave-like, meteorological, miasmatic’ phenomena, to contrast them with the agency and rationality attributed to their colonizing opponents (Kolb, 2021: 39). At least since the 1857 Mutiny, the language of contagion shaped British fear of and respect for the threat of rebellion. Tethering threats of disease to the framing of rebellion as naturalised, unpredictable but spreading danger, allowed writers – in prose and poetry – to emphasise the infectiousness of ideas of resistance, while disqualifying their followers as unthinking, suggestible subjects. In Rudyard Kipling's ‘Kim’, one of the ‘most-widely read colonial novels’, published in 1901, the plague of mutiny remains a key motive. This is especially relevant to the question at stake in this article, as Kipling was, so Edward Said, one of the first ‘novelists to portray the logical alliance between Western science and political power at work in the colonies’. Kim, the novel's protagonist, assumes critical agency in the service of British imperial mappings and military surveyorship. ⁹

It is in this scene of the integration of Western science with political power in the colonies, supported by a chorus of European social pessimism amid growing concern about the public's suggestibility, where Ronald Ross first developed his mathematical approach to epidemics (see contributions by Mendelsohn and Corteel, this issue). Bringing his theory of happenings into conversation with prevailing approaches to social and moral contagion, to social psychology, psychic epidemics, suggestibility, and affect, I suggest a different historiographical framework that allows an embrace of this history of social contagion as a contagious history: a history where the thinking of and with contagion was always subjugated to processes of transmission, distribution, and contagion across and between disciplines, fields of knowledge, and colonial geographies.

A theory of happenings

Ronald Ross always suffered from a sense of being misunderstood and undervalued. ¹⁰ In 1931, looking back on his legacy, he penned a small unpublished manuscript entitled ‘A Priori Epidemiology’, which was likely produced in the context of republishing his mathematical papers as a book (Ross and Hudson, 1931). The opening lines clarify that although his name had ‘long been recognized even among the general British public as that of a man who largely verified Manson's mosquito theory of malaria’, his true legacy can instead be found elsewhere: ‘In my own opinion my principal work has been to establish the general laws of epidemics.’ ¹¹ These laws were general in the sense of their independence from statistical facts, but conceived to improve the analysis of a great variety of epidemics. But Ross’ laws of epidemics were also general in a second sense: not only did they disregard the specificity of diseases and outbreaks, but his theory was so sweeping in its applicability that it circumscribed a theory of human's social and natural organisation. The acquisition of wealth, marriages, slight accidents, or membership in the Royal Society were examples Ross mobilised for epidemic distribution dynamics just as much as he referred to measles, smallpox, or malaria.

There are three steps to consider in Ross’ mathematical construction of what he called a theory of happenings: First, he moved from the more common a posteriori to an a priori approach. Instead of fitting his equations to empirical data from mortality statistics he aimed to define the premise, constants, and parameters within which epidemic dynamics could be ascertained on logical grounds. This shift was – as Corteel (2025) has argued – largely motivated by practical problems in Ross’ research field of malaria. Ross found it impossible to ‘state the exact number of mosquitos to the square mile or yard’. Rather than to invest in exhausting and pointless efforts to produce reliable data, he sought to ‘deploy strict logical deduction from ascertained premises’ (Ross, 1905: 690) such as the reproduction rate of mosquitos to build theoretical models of hypothetical epidemics.

Second, his mathematical language shifted roughly around 1911 from finite differences to infinitesimals, expressed in the deployment of differential calculus in his publications. While finite calculus might have been sufficient to express the problems occurring in malaria research, he found the differential calculus allowed him to move beyond a thinking in discrete steps of time, while also allowing for more flexibility in covering a larger variety of scenarios. The differential calculus was useful to Ross, as it ‘enables us to consider continuous variation in the functions’ (Ross, 1911a: 676; original emphasis). Even if one were to begin from the simple assumption that the introduction of an infection into a fixed population would lead to a variation of infected, diseased, and recovered individuals, it was obvious to Ross that these variations ‘will not remain fixed, but will vary from time to time and from place to place’ (Ross, 1911b: 466). There were further factors that needed to be considered: Infection was not the same as sickness, the capacity to infect was not a given in infected individuals, cases of reinfection or reversal to susceptibility needed to be taken on board, and prevention measures, medical treatment, and unexpected immunity would skew the picture further. It was cumbersome to express these parallel and interdependent processes that structure epidemic phenomena with traditional methods and to describe them in writing, whereas the differential calculus allowed Ross to calculate variations impacting on variables so to present epidemics as continuous, interdependent processes. These processes – or rates of change such as the increase or decrease of individuals becoming infected – could be expressed in differential calculus elegantly as depending on another rate of change, such as the rate of mosquito reproduction or the rate of recovery from disease in the population.

Third, even though Ross had framed his mathematical approach to epidemics as a pathometry – in analogy to nosometry – the principal object of his studies shifted from disease to that of so-called happenings. ¹² His theoretical engagement with epidemiological mathematics moved away from the variables that might govern a specific disease, such as malaria, but he was also no longer concerned with the characteristic dynamics of infectious diseases. He ventured instead to classify dynamics of distribution; dynamics that included infectious diseases or chronic conditions such as cancer, but it also considered social phenomena such as party politics or the accrual of wealth. In part, this expansion of the analytical gaze was motivated by Ross’ conviction that dynamics of epidemics should be explained by the variable organisation of population and not with regards to specific biological factors that would make pathogens inherently more or less likely to cause epidemics. In part, it was also the affordances of differential calculus that implied a notation and set of definitions designed to capture the dynamics of a population's affectedness in the broadest and most general terms possible.

While Ross developed his theory of happenings from 1899 onwards, he brought it to a wider audience over a series of publications between 1904 and 1916. The second edition of his Prevention of Malaria in 1911 was graced with a lengthy addendum, in which he sketched out most elements of his approach, however still in the notation of the finite calculus. He indicated here, in the preamble to his mathematical study, that the following equations would consider ‘time-to-time variations not only of malaria, but of all disease, and not only of diseases of man, but those of any living organisms. Still further as infection is only one of many kinds of events which may happen to such organisms, we shall deal with happenings in general’ (Ross, 1911a: 655). In following articles for Nature and the BMJ, he argued that quantitative and a priori approaches to epidemics required to be expressed in the most general terms possible, and that the event of an infection ought be treated as about the same as the events of ‘accident, death, marriage, bankruptcy, receipt of bequests, insect-bite, that happen to parts of a population’ (Ross, 1911b: 466). However, not all of these events would follow similar dynamics. The infection with a pathogen or the occurrence of a household accident could occur on multiple occasions and might happen to individuals more than once, while other factors, such as immunity (from vaccination) or marriage, should be contemplated as the ‘continuance of the event in the individual’, which in turn might govern whether an infection or a divorce could affect that individual. This approach allowed him in 1911 to develop a preliminary set of rules showing that malaria or yellow fever pose very little threat if a critical threshold of mosquito density is maintained, while just a comparably small growth in mosquitos beyond that threshold would lead to a critical outbreak affecting swiftly half of the susceptible population.

From the development of these analytical tools to advance public health in a specific case (malaria), Ross sought to comprehensively progress his theory in the language of the differential calculus and to present it as a sweeping mathematical reinvention of epidemiology. Somewhat delayed by the beginnings of the First World War, he submitted his mathematical magnum opus in 1916 to the Royal Society. His first part was authored by himself, but the second and third part were co-authored with the capable mathematician Hilda Hudson, whom Ross was able to employ on a grant from the Royal Society (Barrow-Green, 2023; Ross 1916; Ross and Hudson, 1917a, 1917b). It was here, in the series of these publications, where Ross first began to bring his theory of happenings to bear on an ever-expanding set of phenomena, and where he offered a few eclectic statements and definitions to further elucidate the purpose of his increasingly complex maths.

In the first article, he began the Prefatory with a discussion of the different dynamics of diseases. Some, such as leprosy and tuberculosis, may be characterised by a low frequency of fluctuation months to months, others – such as malaria or measles – seem to flare up while maintaining a low persistence all year round, and some of the grand epidemics, such as plague or cholera, seem to disappear completely. Ross then returns to first principles and asks: ‘Why, indeed, should epidemics occur at all, and why should not all infectious diseases belong to the first group and always remain at an almost flat rate?’ (Ross, 1916: 205) The purpose of the following liturgy of equations was to answer this question in one important way: the differential dynamics of these epidemics were, Ross was convinced, neither an effect of the variable infectivity of their ‘causative agents’, ¹³ nor should they be attributed to dramatic shifts in the environment. Instead, so Ross argued, the causes should be identified through the analysis of happenings, that is, the differential rate at which a proportion of a population can be affected by a happening and the rate at which it returns to an unaffected status. To ascertain these causes, Ross relied on mathematical approaches that have been shown to be effective in ‘astronomy, physics, and mechanics’ (Ross, 1916), and which gave ground to a theory that would cover pathological issues as much as ‘statistics, demography, public health, the theory of evolution, and even commerce, politics, and statesmanship’ (ibid.: 208).

It will be crucial to understand the foundational elements, the constants ¹⁴ of Ross mathematical theory, to appreciate how and why his work now ventured towards generalisation. Ross provided the reader with five definitions. First, he set population as P, which was divided into a proportion of Z for those affected and A for those not affected. Second, a key aspect of his theory was to allow for variations (v,V) within both the affected and the unaffected populations to be computed with reactions to different kind of happenings. Ross took these variation elements, namely birth (n,N), mortality (m,M), immigration (i,I), and emigration (e,E), to argue that each of these might be differently affected. ¹⁵ ‘Mild maladies, enlistments in civil professions, conversions to religious or political parties, entries into unlimited societies or trades-union’ (Ross, 1916: 209) should not affect any difference between these rates in the affected or the unaffected population (v = V). However, most diseases as well as military enlistment would lead to a higher birth rate in the unaffected population (N < n) and a higher mortality rate in the affected parts (M > m). Notably, some ‘alarming epidemics’ might yield to the immigration of affected populations to be significantly lower than in the unaffected population (I < i), whereas the emigration would present as the reversed state (E > e). Computed in this manner, Ross believed his theory could be adapted to commercial application, where the variation elements could be translated to manufacture (n,N), waste (m,M), exportation (e,E), and importation (i,I).

The third definition concerned r, the element of reversion. This could be either understood to relate to the loss of immunity after an infection, leaving the population vulnerable to reinfection, or it could be conceptualised as the way in which a divorce enables capacity for marriage, or how ‘discharge in certain employments’ leads to potential re-employment. It would be important, so Ross, to consider how such rates of reversion are either high – such as ‘possibly in nasal catarrh’ or in ‘controversial political parties due to rational divergence of opinion’ and where such rates are low, such as in leprosy, organic diseases, and ‘ordinary party-politics’ (Ross, 1916: 210).

Fourth, Ross defined h, the happening element itself. While the happening element is given as the factor that transforms the unaffected proportion of a population within a period of time into an affected proportion, Ross concedes that it will have to be taken into account that the happening happens to all parts of the population to the same extent, while having an effect only on those not already affected (A). However, this left the definition of the frequency of new cases (F) rather vague and led Ross to develop his fifth, perhaps most distinguished definition. He separated happenings in two different classes: one in which the frequency of happenings can be treated independently of the proportion of individuals already affected, and the other where the frequency of happenings is a direct consequence of this proportion. Hence, the class of independent happenings would refer to ‘accidents and non-infectious diseases due to causes which operate, so to speak, from outside’, with h or F being defined as a constant (Ross, 1916: 211). The other class of dependent happenings applied to cases such as ‘infectious diseases, membership of societies and sects with propagandas, trade-unions, political parties, etc., due to propagation from within, that is, from individual to individual’ (ibid.) and assumed h or F not to be a constant, but to be a function of Z (the affected population).

Ross did not leave us with any explicit reasoning about why he would generalise his theory beyond infectious or any diseases, nor did he state any interest in a theory of social contagion to explain vexing sociological questions. It would be tempting to attribute this shift in gear as consequence of his application of differential calculus. In his appreciation of Ross’ theory of happenings, the mathematician Paul Fine certainly attributes significant weight to a transition from ‘simple arithmetic product expression; to difference equations; to differential equations’ in Ross’ work (Fine, 1975). Rather unhelpfully, Ross stated merely the matter of fact that his work advanced from one style of mathematical reasoning to another: ‘The Differential Calculus concerns itself with infinitesimally small differences, while, my previous work had dealt with Finite Differences.’ ¹⁶ But rather than attribute significant transformative power to a thinking in infinitesimals, we might do better to ask to what extent differential calculus offered an opportunity to address challenges Ross sought to overcome. Uncovering some of his implicit motivations might help to rationalise this radical expansion of the scope of his theoretical framework while also elucidating the purpose and advantage of a reasoning based in differential calculus.

First, it is important to stress how useful this extension of reference was to Ross’ ambition to refute causal explanations for epidemics that were overly focused on the biological capacities of pathogens. In the ongoing quarrels between bacteriologists and epidemiologists at the time, Ross fell clearly on the side of explaining epidemics through population dynamics (Amsterdamska, 2005; Mendelsohn, 1998). He referred with scepticism to Farr's inferences about declining epidemic curves because of diminishing infectiveness (Ross, 1916: 206) and his entire mathematical corpus treats infectiveness instead as a constant. Further, he remained disinterested in simplistic assumptions about presumed weakness or strength of populations – as his contemporary eugenicists would have argued. Instead, Ross established the event of infection as the exclusive category to classify population as either affected or non-affected.

With this analytical starting point, Ross shifted the question of what makes an epidemic to become epidemic away from the internal dimensions of specific pathogens or populations and towards a distinction of different infectious dynamics. To focus on the classification of these dynamics, he rendered any intrinsic characteristics of that which might cause an infection entirely irrelevant. In that way the pathogen could become comparable to a political idea, and the status of infectedness could became identical to membership in a royal society. How individuals might end up in a political party, how fast an infectious disease assumes the status of a pandemic, or for how long one might remain within a royal society was, so Ross’ maths implies, not a question of the intrinsic quality of political ideas, the biological properties of the pathogen or the reputation of the royal society, but merely a question of the rate of susceptible individuals ready to be affected by transmissible factors. The implied consequence is a notion of susceptibility that seemed to over-emphasise the effect of contagious dynamics, while undermining notions of individualism or the rationality of political choice, and to refuse any engagement with the ontology of a discernible cause.

In the following sections of the first and throughout the second and third parts of Ross and Hudson's publications in the Proceedings, they presented then a series of modifications of the original equation to integrate all known epidemic dynamics into the theory of happenings. They concluded, ‘The rise and fall of epidemics as far as we see at present can be explained by the general laws of happenings, as studied in this paper’ (Ross and Hudson, 1917b: 239). ¹⁷ Ross and Hudson's theory of happenings revolved around the question of affection and susceptibility not to shed new light on questions of consciousness and rationality, but to produce an apparatus that would enable the identification and classification of contagious processes across multiple domains of modern society and beyond a boundary of natural and social organisation. Their differential equations afforded Ross and Hudson a mathematical language to redress the epidemiological approach into one in which all causes were already known: ‘We assume a knowledge of the causes, construct our differential equations on that supposition, follow up the logical consequences’ (Ross, 1916: 205). As a result, the theory of happenings was no longer beholden to pathological and undesirable phenomena, but could describe contagion as an ever-present constructive and productive dynamic of social and natural organisation.

Susceptibility, suggestibility, and the infinitesimal

Ross’ formal revision of epidemiological science resonates with the conceptual delineation of social contagion sentiment, as emerged in the late 19th century. It affirms a popular trope of the time rather than to offer an innovative departure from common sense. It would have been preposterous to argue in 1916 that only infectious diseases would follow contagious dynamics, that the idea of contagion was conclusively materialised in the distribution of microbiological specimens.

However, the prevalent discourse among psychologists, sociologists, and other commentators on the contagiousness of social processes was concerned with unwanted, threatening, and disturbing phenomena, dynamics that, like an epidemic of an infectious disease, risked undermining the health and prosperity of society. For Gustave Le Bon, contagion was a phenomenon of the ‘hypnotic order’, synonymous with a pessimistic dissolution of individual interests in the favour of collective mania (Weingart, 2008). Le Bon placed the conscious mind, the capacity to enact individual agency, in radical opposition to the individual affected by contagious thoughts, ideas and fashions: ‘The individual forming part of a crowd … is no longer himself, but has become an automaton who has ceased to be guided by his will’ (Le Bon, 1896: 13). The crowd was an antagonism to reason and liberal freedom. Crowds at that time were, as Borch recalls, imagined to be ‘endowed with characteristics of suggestibility, femininity, immaturity, in short, irrationality’ (Borch, 2006: 84). As a ‘diagnostic category’ the crowd offered its analyst an approach to the ‘dark side of modern society; to something which is intrinsic to the edifice of this social order’ (Borch, 2012: 16). ¹⁸

Ross’ maths did not partake in such moral judgements; nor was his theory meant to help purge society of its unwanted social developments. He freely admitted that the title pathometry might have derived from a desire to introduce mathematical analysis into the study of epidemics, but for him, the term also retained a misguiding orientation towards the pathological (Ross, 1916: 206). It would be wrong to assume that Ross’ mathematical advancement of a theory of social contagion merely offered a sophisticated naturalisation of unwanted, problematic, and concerning social behaviours at the time, simply because Ross had previously worked on epidemics of infectious diseases. Instead, his maths enabled him to circumscribe a different kind of social order. In this order, the delineation between social and natural phenomena ceased to make much sense; nor were finite causes – such as infected immigrants as a cause of epidemics – important any longer. It is in this rejection of simplistic causes, the refusal of maintaining a meaningful boundary between the social and the natural, and in the projection of contagion as a moral-free category, where Ross’ theory of happenings converges in unsuspected ways with the work of another French contemporary: the sociologist Gabriel Tarde.

Tarde shared a concern about the dynamics of the crowd with Le Bon. He did not, however, view crowd behaviour as a pathological degeneration of conscious individuality, but rather as an intensified state of social relations that characterised all of society. Sven Opitz argues that Tarde's writing shifted the semantics of contagion so that it could shed its association with impending crisis and threatened order, and instead assume a foundational position in sociological terminology to describe an order of contagion (Opitz, 2015). This different kind of order has been usually positioned in contrast to the work of Durkheim, who also emerged in the 1890s as a fierce critic of Tarde. Durkheim saw in Tarde an ‘imprecise and speculating psychologist’, whose work had little utility for the project of a social science (Tonkonoff, 2017: 25). The sociological project, so Durkheim stated, had to be concerned with the causal powers of structures to shape individual actions – structures that could be identified beyond the realm of minute social interactions, such as economic upheaval in Durkheim's paradigmatic study of suicide – which was designed partly as a rebuttal to Tarde (Borch, 2012: 65; Durkheim, 1897). These structures – or finite causes – gave according to Durkheim the social sciences their exclusive object, which in turn allowed them to emulate a scientific model from the natural sciences to join the ranks of the positivist enterprise. In this polemical dichotomy, Tarde's approach was largely disqualified and misunderstood as a concern for and with social pathologies as well as the more fringe phenomena of imitation in the context of hypnosis and somnambulism. ¹⁹

Imitation sat at the heart of Tarde's work on contagion. His book Laws of Imitation, first published in 1890, described how imitation entangles organic, symbolic, and affective registers (Tarde, 2013[1890]). But rather than focus on specific instances and oddities of imitation, Tarde asked to what extent imitation might be elevated to a general principle of social organisation. He conceptualised a contagious process, in which the individual assumed a relational position towards others. A social thing, contrary to Durkheim, was for Tarde not a universal or structural force beyond the direct interaction of individuals, but something deeply embedded within modern sociability: ‘Every social thing, that is to say, every invention or discovery, tends to expand in its social environment, an environment which itself, I might add, tends to self-expansion, since it is essentially composed of like things, all of which have infinite ambitions’ (ibid.: 17).

This idea of imitation, however, did not fit neatly into the categories used by the emerging social psychologists at the time. For Tarde, suggestibility was neither merely an unconscious trait of human sociality, nor a symptom of the weakness of individual rationality. He insisted that embodied reactions, for example by fascination or fanatism, were essential to incorporate the kind of contagion he had in mind. Characteristically, Tarde rejected the distinction between conscious and unconscious states, or voluntary and unvoluntary acts as unscientific, and described his interest with yet another powerful metaphor of the late 19th century: ‘[Imitation] consists of a quasi-photographic reproduction of a cerebral image upon the sensitive plate of another brain.… By imitation I mean every impression of an inter-psychical photography, so to speak, willed or not willed, passive or active’ (Tarde, 2013[1890]: xiv). As Opitz underlines in his reading of Tarde, this contagionism emphasised the pre-cognitive dimension of social communicability and would culminate in the projection of the social individual as an ‘affective relais’, equipped with the capacity to be affected or to affect others (Opitz, 2015: 133).

But the epistemological implications of Tarde's sociology did not stop there. Extrapolating from his work on imitation – outlined explicitly in his novella quoted above – he saw the crowd not as a social pathology, but rather as a phenomenon that exemplifies the social in its purest and least mediated form. Crowds were a function of modern society, and society was built on imitation; indeed, ‘society is imitation’ (Tarde, 2013[1890]: 74). It follows that social order was no longer the result of rule adherence and normative superstructures but was the sedimented result of multiple series of accidents, events, and innovations that had cascaded through a myriad of imitations. This equivalence implied that ‘throughout science the normal appears to originate from the accidental’. ²⁰ In a brilliant essay, Ruth Leys captured the lasting impact of Tarde's work on early American sociology to propose Tarde's theory as a powerful rejection of the notion of individualism, which challenged boundaries between self and other to establish instead ‘a highly plastic notion of the human subject’ (Leys, 1993: 281).

Tarde's conceptual plasticity expanded far beyond the human subject. Following Leibniz, Tarde's sociology proposed a world comprised of infinitesimal monads (Candea, 2015; Milet, 1970). His thinking followed the Leibnizian verdict that the true actions and agents that ‘constitute the world are to be found at the level of the infinitely small’ (Tonkonoff, 2017). In an essay on ‘Monadism and Sociology’, published in 1893, Tarde argued for a radical and universal sociology; one that stretches from the study of nations to the society of cells or stars. To exemplify the already ongoing transformative effects of thinking with the infinitesimal in and across the scientific discourse at his time, Tarde choose no other example but Pasteur's microbes. Whereas ‘ancient doctors used to treat [illness] as a person’, the idea of disease had since exploded into ‘infinitesimal disorders of histological elements’. Pasteur had introduced to the question of illness the ‘internal conflicts of tiny organisms’, but as ‘parasites also have their parasites’ (Tarde, 2015: 42), the principal cause of illness was no longer a finite category; rather, illness itself was the result of an infinite chain of events and conflicts that reach from an invisibly small event to those apparent in bodily symptoms. Thinking with monads meant for Tarde to reject a distinction of mind and matter, therefore ‘every thing is a society, and every phenomenon a social fact’ (ibid.: 43). ‘Every specific type is’, according to Tarde, resolvable in mathematical forms as an ‘integer of innumerable differences’. The place where mind and matter coalesce into an indistinguishable movement is the ‘infinitely small, the imperceptible’ (ibid.: 33), a place in which neither the distinction of mind and matter nor any separation of biological and social domains would prove particularly useful.

When the sociologist Tarde stated in the Laws of Imitation that political or religious ‘sects are the yeast of crowds’ (Borch, 2012: 53), therefore, he did not propose to use the political as metaphor for a natural process or vice versa. Similarly, when the epidemiologist Ross grouped the spread of ideas in political sects with highly contagious pathogens, he did not intend to disqualify the implied political process as a disastrous epidemic. Both grappled in their own disciplinary language with a way of thinking about contagion and epidemics as integral elements of the modern human constitution.

On closer inspection, Ross’ focus on happenings aligns neatly with Tarde's concept of imitation. For Ross, a happening described a moment of interaction, in which an idea, a pathogen, or a kind of behaviour was transmitted. This could either be the adoption of a political view, infection with a transmissible disease or an insect bite; in either case the happening implied that the transmission was coupled with a transformation in the susceptible individual, which acquired a shared trait. In that sense, any happening – regardless of it being cultural or biological – was first and foremost defined by a social condition. Like imitation for Tarde, happening was Ross’ synonym for ongoing ordering of society structured by an infinite cascade of distributed ideas, concepts, and disease rather than individual conscious rationality. As Matei Candea points out in his reading of Tarde, such a projection of society implies a position of the subject that always and often involuntarily finds itself acting upon others while being acted upon (Candea, 2015). Suggestibility and susceptibility were neither exception nor weakness but a constitutive element of any society (or population).

By turning to differential calculus, Ross adapted a kind of reasoning in which large-scale transformation could be explained through a focus on the infinitesimal small. His mathematical reasoning on epidemics begins with the absence of finite causes, or rather, with the rejection of structural determinants to impact on the waxing and waning of epidemics. For Tarde, infinitesimal calculus, as introduced to him by the French mathematician Augustin Cournot, offered a methodological way to construe a radical concept of society made up by a myriad of infinitesimal small elements (Milet, 1970). For both, the mathematical reason of differential calculus offered a rigorous method to marry a thinking of sedimented laws with the radical contingency in contagious processes by introducing open-ended temporal dynamics into their designs of the social. And finally, the prominence of differential calculus and the deep imprint that the infinitesimal had left on chemistry, physics, and astronomy brought scientific credentials to a sociology of contagion as well as to an epidemiology of the social.

Without attributing the concept of the infinitesimal with the power of a force majeure that has shifted the understanding of natural and social worlds, it makes sense to appreciate the leverage with which differential calculus advanced a different kind of reasoning across the scientific landscape. Ever since Galileo, Wallis, and the Newtonians had championed the infinitesimal in their mathematics, it was associated with the proposition of a ‘more pluralistic and flexible order’, as Amir Alexander writes (Alexander, 2014). Whether it is possible to speak of an infinitesimal revolution at the end of the 19th century is a different question, but some – like Tarde and Ross – would certainly share the ‘firm conviction that infinitesimal calculus has provoked a conceptual transformation in the mode of thinking of mathematics’, as Tonkonoff argues. Both believed they were part of a larger scientific movement, where the concept of the infinitesimal would ‘produce an analogous mutation in the mode of thinking tout court’ (Tonkonoff, 2017: 13).

The philosopher Henri Bergson captured the spirit that united the otherwise disjointed projects of Tarde's universal sociology and Ross’ theory of happenings in their commitment to the transformational power of differential calculus. ‘Modern mathematics’, Bergson wrote in his introduction to metaphysics, The Creative Mind, ‘is precisely an effort to substitute for the ready-made what is in process of becoming, to follow the growth of magnitudes, to seize movement no longer from outside and in its manifest result, but from within and in its tendency towards change, in short, to adopt of the mobile continuity of the pattern of things’ (Bergson, 2010: 161; Tonkonoff, 2017: 23).

Bruno Latour, in his reading of Tarde's relationship to maths and quantification, notes in a footnote how Tarde's disruption of fin de siècle sociology mimicked much of the impact Pasteur had on thinking about infectious diseases a few decades earlier. While Pasteur had contributed to a shift in the notion of miasma towards a theory of infection that relied directly on material transmission of a pathogen between persons, Tarde had rejected the popular cloud of vague collective qualities and inherent social laws to reshape the notion of the social as one structured by direct transmission via imitation from person to person (Latour, 2015: 199). Much in the same way, had Ross taken the impulse of the infinitesimal to reshape the notion of the epidemic as one that had always been social, with or without Pasteur's microbes.

Conclusion

As far as is known, Tarde was not aware of Ross's work. His writing remained refreshingly ignorant of the emerging field of epidemiology and except for a few notes here and there, Tarde's fascination for the natural sciences focused on evolution rather than microbiology. Ross, likewise, made no explicit reference to Tarde's work in his own. Due to the insightful work by Emilie Taylor-Pirie on the literary ambitions of Ross, we know of Ross’ admiration for H. G. Wells, who, in turn, prefaced Underground Man, Tarde's science fiction novella quoted at the beginning of this article (Taylor-Pirie, 2022). As the novel was widely available in English from 1904, there was a chance that Ross noticed it and perhaps it became one of the many literary sources he consulted for his work.

But how to make sense of the relationship between these two contributions to social and epidemiological theory in the early 20th century? This is not quite a transfer of knowledge between two adjacent fields, as captured in the programmatic literature in history of science. The resonance between Ross’ epidemiology and Tarde's sociology does not qualify as a shared practice culminating in a material space of translation (Secord, 2004); nor can one project the ubiquity of contagion as the ‘flow of a cognitive good’ between Paris and Liverpool, as their work shares very little common references (Bod et al., 2019). It would also be a stretch to position contagion as a boundary object, as the concept of contagion hardly maintains a common identity across sites and scholarly communities (Griesemer and Star, 1989).

One could speculate on the contagiousness of ideas of social contagion at the time, and the European melancholy sketched out above certainly provided the mindset for both sides of this tandem history to flourish. But such a view would potentially miss the important nuance that both Tarde and Ross embraced popular imaginations of contagion but brushed them against the prevailing mindset of social pessimism and degeneration. Whatever the connection may have been, the parallel histories told above reveal a shared embrace of modernity in two disjointed disciplinary and geographical efforts. Here prompted by the refusal to disavow the crowd as a failure of rationality (Tarde) and there motivated by the unwillingness to consider epidemics of infectious disease as exceptional crises (Ross). Both projects sought to conceptualise a social order that integrate, rather than purge uncontrolled, dependent social dynamics from the modern scientific project. Both Tarde and Ross rejected the coupling of contagion and pathology, both focused on suggestibility and susceptibility as functions, not failures, of modern sociability, and both turned to the infinitesimally small to explain large, defining phenomena in society without falling for the microbe as the absolute cause of crisis.

Ross’ mathematical advances are commonly seen as a point of origin for the formalisation of epidemiological reasoning. An epidemiological science grounded in maths stayed clear, so argued its advocates, of the overt politics found in sanitary science or eugenics. While this distinction may be justified, the tandem history here provides an opportunity to unpack the implicit understanding of the social and natural world that Ross coded in his equations. Drawing on similarities to Tarde's sociology exposes significant assumptions about the plasticity of the human subject in Ross’ idea of a population. But, more importantly, it clarifies that Ross’ vision of epidemiology did not only exceed the realm of infectious diseases, but was supposed to claim relevance in a much wider range of social, cultural, economic, and political subjects. In the historical legends of epidemiological modelling, this might have been noted as a curious development (Kucharski, 2020). Instead, the breadth of Ross’ theory of happenings requires a reorientation of the field's historiography. The epidemiological consideration of population as a set of interchangeable compartments has long been more than just a conceptual crutch to navigate epidemic crisis, and it will be vital to scrutinise how formal concepts of infection and susceptibility have sustained their dependence on social theories of affection and suggestibility and remain anchored in the assumption of a radical plasticity in the human subject.

Reading Tarde in the context of Ross’ epidemiology raises a different set of questions for the social theorising that has followed in the footsteps of the French sociologist. The consequence of asserting a modernist social consciousness at the heart of formal epidemiology invokes an epidemiological unconsciousness in the social sciences. Unpacking the epidemiological category of susceptibility perhaps offers ways to rethink suggestibility as a social category, and differential calculus offers new and imaginative ways to theorise affect (Z), recursion (r), and the happening (h) not as compartmental descriptors of epidemic crisis, but as interdependent conditions of the modern condition as an epidemiological order.