Exploring the Ontology of Pandemic

Abstract

Pandemics do take place. When exactly they begin and end, and why, is harder to determine, as also demonstrated in early 2020 at the start of the Covid pandemic and the many debates in 2022 on calling it over. To determine these points, one has to know which criteria have to be satisfied and which not, respectively. This requires a clear definition of what a pandemic is, with at least its necessary and suficient characteristics. There is no such crisp and clear definition, neither in the expert documentation nor in domain ontologies. In this paper, we assess mentions of 'pandemic' in domain ontologies, evaluate the argument that foundational ontologies may provide guidance, and examine the characteristics that domain experts have put forward for pandemics. The guidance from foundational ontologies is underwhelming when taken together, but tooling greatly simplified the alignment. The assessment of characteristics show that pandemic is not bearer of them all but they are of attendant entities, elucidates which ones are dependent and which essential, and it demonstrates why one may compute more than one unique start and end of a pandemic. Considering the complexities, it may be of use to develop an ontology of pandemics.

Keywords

• eol>Pandemic
• Foundational Ontology
• Ontology comparison
• Covid-19

1. Introduction

Pandemics have taken place throughout the millennia

[ 1 ] and they have been investigated by scientists in many disciplines, but not ontology. Pandemics somehow start and end; e.g., the 1918 influenza pandemic ended in 1920. This raises the questions as to what the criteria are such that something is an instance of Pandemic and which criteria would have to be not met to determine the end of the pandemic. And, practically at present: how does it apply to the current Covid-19 pandemic?

They are simple questions without easy answers. The informal short description of ‘pandemic’ is that it is a large epidemic [ 2 ] and, by the WHO’s guidelines, the pandemic is over when it is alike a seasonal influenza epidemic (“post-pandemic phase 6”)1. While the former is easy to communicate to the public and the latter is operationally clear, scientifically, it is an unsatisfying answer. The key issues are that, ontologically, there is no clear definition of pandemic in such a way as to unambiguously classify something as being a pandemic or not being a pandemic. This holds for both the scientific literature of the subject domain and, as we shall see, the domain ontologies that have ‘pandemic’ in their vocabulary. In this unclear situation, foundational ontologies (FOs) should be able to be of assistance somehow, to help determine at least the category that a domain entity such as ‘pandemic’ is. There is only limited published independent practical alignment guidance for two of the multitude of the FOs [ 3, 4 ], in the sense of not having to rely on human services [ 5 ] to accomplish the task.

In taking steps toward the ontology of pandemic, we are guided by the following questions. What is a pandemic, ontologically? What properties does it have? To which entity in a FO should it be aligned or categorised into, and as part of that: how to align and how to know one has done that alignment correctly? Methodologically, we first examine related work with the 9 relevant domain ontologies and summarise the key advances from the domain experts. We then proceed toward an ontological characterisation, by, first, assessing 7 FOs and seek to align pandemic to it, and subsequently we examine the asserted characteristics of pandemics (notably [ 2 ], but also [ 6 ]) as an ongoing process of modelling refinements.

The tooling support for FO alignment was found to be very helpful and increased confidence that the alignment is as precise as it can be. The assessment of asserted characteristics of pandemics are, in some cases, actually properties of intricately related entities (e.g., the disease), some turned out to be dependent or implied, others are essential. Crucial for classifying something as (not) a pandemic, is that several properties are vague and thus there can be multiple start and end points for a single pandemic. To be able to classify things as a pandemic, a separate ontology of pandemics may be needed and perhaps a rule-based decision table as well.

In the remainder of the paper, the related work is presented in Section 2 and the assessment with FOs (Section 3) and pandemic’s claimed characteristics (Section 4) follow afterward. We discuss in Section 5 and conclude in Section 6.

2. Related work

collectives, aggregates) of individuals, be they processes or objects, are categorically diferent kind of entities from We consider first the domain ontologies that contain ‘pan- single individuals and from the individuals that are memdemic’ and subsequently summarise domain literature ber of it—both ontologically (e.g., [ 7 ]) and in FOs such as that, overall, have it ill-defined as well. BFO with its object aggregate (and, in BFO v1, process aggregate)—but epidemic and pandemic are not categor2.1. Domain ontologies ically diferent kinds of things. There is a fiat boundary between an epidemic evolving into becoming a pandemic Domain ontologies that have something to do with pan- and then subsiding into one or more epidemics, as the demics were collected by means of a BioPortal search recent IDO documentation also indicates (see figure 4 using the search string “pandemic” (without quotation in [8]). A secondary issue that the IDO approach faces marks), which returned 17 hits2. Of those, 9 refer to the in particular, is how to determine the boundary of one entity (of which 3 with the same IDO entry), 1 is a list epidemic from another (of the same disease with same rather than an ontology (the ELD) once it was added as causative agent) to be able to construct a collective, if it a top category afterthought (in LOINC), once as instance indeed is one, and, more fundamentally, what the respecfor just the pandemic in 1918 (in OMIT), and once the tive identities of those co-occurring epidemics are. This organism (in SNOMED CT), rather, and 4 hits are related is unclear; among others: is it one epidemic in two places things, such as ‘Product delay due to pandemic’ in MED- that it jumped to—e.g., from Italy to South Africa—or do DRA. The 9 were analysed further and their respective they count as two? How to count two purportedly sepkey points are summarised in Table 1. We shall discuss arate ones when they touch: do they merge to become each in turn, on i) how pandemic relates to epidemic (and one large one or are they presumed to be overlapping outbreak), ii) what its parent is within the subject domain distinct entities (that may not be identifiable as such)? A scope, and iii) what its domain-independent ancestor is third issue, and minor for the current scope, is the defwithin the realm of top-level entities typically in FOs. inition for epidemic in the ontology’s annotation field,

Regarding how pandemic relates to epidemic, a key mentioning “statistically significant increase in the indiference across the 9 ontologies is to have it either as fectious disease incidence” as determiner, but actually it subsumption, the same, or sibling, which cannot be all is based on a threshold that is based on a moving epicorrect. The subsumption rationale is based on the notion demic method that relies on historic data for the country that a pandemic is a large epidemic, having spread over [9], for influenza at least. If epidemic and pandemic are more or larger regions and afecting more people, i.e., siblings rather than the former subsuming the latter, a that that is an extra feature meriting the subsumption. better argument has to be put forward. At this stage

The sibling approach of the IDO and its related on- of the analysis, the argument for subsumption is more tologies is based on the premise that a pandemic is an plausible. aggregate or collection of “multiple infectious disease Regarding pandemic’s parent in the subject domain epidemics”, as indicated by the natural language defini- of the selected ontologies (see Table 1), it cannot be eitions in the ontology (it lacks an axiomatisation). There ther of them. In particular, public health in MeSH and are three problems with this approach. The first, and key, medicine in CRISP are merely intended as broad groupproblem is the ‘collection’ of epidemics: collections (i.e., ings of context, not ontologically a superclass, despite that the ontology formally asserts the latter. The infec2https://bioportal.bioontology.org/; last checked d.d. 2-3-2022 tion in AURA and IOBC and disease or disorder in NCI country regularly calculates it by comparing it to their are all more specific as superclass than the previous two, own historical data over the preceding years [9]3. Inbut are attendant topics, rather. A particular infection, an formally, an epidemic is an occurrence where there are instance of a disease (or disease course in an organism) or multiple instances of an infectious disease in organisms, disorder each are a single thing, as an intrinsic whole, in for a limited duration of time, and that afects a commuan individual organism, whereas from outbreaks onward nity of said organisms living in a region, and the number to pandemic, there are multiple related infections in mul- organisms it afects exceeds the agreed-upon threshold tiple organisms in at least one region. Pandemics need compared to average historical data for that region. infections to happen, but that does not make them infec- Also within the WHO there used to be a lot of debate tions. Similarly, there is a disease that causes a pandemic, about defining and describing a pandemic [ 11, 6, 2 ], and but that does not make the pandemic a disease. several national centres of (infectious) diseases made at

Lastly, the top-level category, for those that had one. tempts as well. The lowest common denominator, and The IOBC category ‘Biological phenomenon, process, and oft-repeated phrase, is still that it is a large epidemic. state’ is too imprecise for ontological analysis, although it Minor additions or refinements of features include that it does provide a general indication that pandemic is some- is spread over the world, or at least multiple regions and thing that is happening, or occurring or perduring, in continents, and that it usually afects many people 4, that ontological terms. For the others, the key distinction be- it has to involve a new disease5, and that there are out-oftween process and event—however it may be formalised season infections [ 6 ]. Morens, Folkers and Fauci’s literain one’s preferred logic—is that processes, at least in the- ture review on pandemics [ 2 ] resulted in a list of eight ory, can go on forever whereas events necessarily have characteristics, which are: wide geographic extension, both start and an end, i.e., they have a limited duration by disease movement, high attack rates and explosiveness; definition whereas processes do not. We know from his- minimal population immunity, novelty, infectiousness, tory that pandemics indeed do have an end, even though contagiousness, and, with some caution since it is not it may not be trivial to determine and have fiat bound- often added explicitly, also severity. We shall analyse aries. them further in Section 4.

In sum, the domain ontologies have been mostly help- Overall, there is a tendency to oversimplify the definiful in indicating what a pandemic is not, and a possible tion of a pandemic for the wider population—as a large avenue for the direction for FO alignment. epidemic—and leave it for the experts to debate the features, which features really count most, and at least for 2.2. Domain literature some of them, what a threshold would be for declaring something an outbreak or an epidemic, and to keep it Domain experts have had multiple debates about defining that way to avoid public confusion [ 2 ]. This approach of what a pandemic is and they assessed it from multiple an- outward underspecification seems to have carried over to gles, including infectious diseases, immunology, epidemi- the domain ontologies. While an underspecification may ology, and health policy. In the literature, most debate sufice for some tasks, e.g., literature annotation, to be occurred from around 2009 during the H1N1 influenza able to determine whether we have a pandemic at hand, pandemic (‘swine flu’) to about 2011. when a pandemic can be called over, and to compare

WHO’s eventual pandemic phases document consists pandemics, a higher level of precision is required. of descriptions of the phases, but steers clear of a definition of pandemic (see fn. 1). Its first phase is where an animal influenza circulates but is not reported to jump 3. Categorising Pandemic over to humans and it goes up to phase 6 (where we still are with Covid-19 at the time of writing), where Before assessing the possible characteristic properties there are sustained community outbreaks in two or more of a pandemic, it first has to be established what sort of countries in one region and at least one other country generic entity it is. Two FOs have an assistive method in another WHO region. It also has a “post-peak” phase to categorise an entity, therewith contributing to filling that is still pandemic but the worst is deemed to be over, the tool gap in the ontology-as-a-service approach [ 5 ], and a “post-pandemic” phase when there are “levels seen which we therefore commence with. Afterward, we will for seasonal influenza in most countries with adequate surveillance”, revealing also that these phases were specified either with the expectation that the next pandemic would be an influenza pandemic or on the basis that seasonal influenza is acceptable loss. Seasonal influenza surveillance is well-established and, knowing that those values vary by country for a range of reasons [10], each 3The interested reader may consult such a surveillance report for an impression, e.g., https://www.nicd.ac.za/wp-content/ uploads/2022/02/NICD-Private-Consultations-Surveillance-Epidemic-Threshold-Report-Week-5-2022.pdf

4https://www.cdc.gov/csels/dsepd/ss1978/lesson1/section11. html 5https://www.healthdirect.gov.au/what-is-a-pandemic consider a selection of other FOs to examine whether it will shed any further light on the matter. a perdurant and bfo:occurrent aligns to dolce:perdurant [15].

3.2. Other FOs

3.1. FOs with decision diagrams: DOLCE and BFO

A recent inclusive survey lists 37 resources as FOs and

There is a “D3” decision diagram to guide entity align- candidate top-level categorisations [16]. We created a sement [ 3 ] to DOLCE [12]. The question trail is as follows: lection based on the following considerations: commonly • Is [pandemic] something that is happening or oc- considered foundational or top-level, ample documentacurring? Yes (perdurant). tion, ideally there is also a file to inspect with the formali• Are you able to be present or participate in [a pan- sation, diverse in ontological commitments, and the final demic]? Yes (event). selection represents a wide geographic distribution just • Is [a pandemic] atomic, i.e., has no subdivisions of in case that matters. This reduced the selection to BORO, it and has a definite end point? No (accomplish- GFO, SUMO, UFO, and Yamato, which will be discussed ment). in alphabetical order. The outcomes are summarised in From the viewpoint of the afected population, it may be Table 2. unpleasant to state that pandemic is an accomplishment, but it is one from the perspective of the infectious agent. BORO The Business Objects Reference Ontology [17] Regardless, it confirms that a pandemic unfolds in time has the distinguishing metaphysical commitment of perand is a temporal entity with a limited lifespan. It will durantism. Since Type is the most specific for types, it cease to be a pandemic at some point in time and evolve does not reveal any category for Pandemic. BORO may back to epidemic6. This does not help determining when be more useful for representing a pandemic’s components it starts or ends, just that it does. or stages that have boundaries and parts, such as a wave

We developed the BFO Classifier 7 [ 4 ] for BFO v2 [14], of infections with a variant or a flare-up of infections due as a tool wrapping around the new decision diagram. to lapsing prevention measures.

Pandemic is a process, as follows: • Does [pandemic] persist in time or unfold in time? GFO The General Formal Ontology [18] diferentiates

Unfold in time (occurrent). between universals and individuals, where the Individual • What is [pandemic]’s relation to the universal spa- branch is where universals are placed for representing tiotemporal region? Inhabits (occurrent, still) instances. By elimination of options, Pandemic has to be • Does [pandemic] have a proper temporal part? Yes a Concrete and among those subclasses, an Occurrent (process) that has temporal parts. Based on the descriptions in • Is [pandemic] the sum of the totality of processes the ontology, in the documentation, and knowledge of in a material entity’s spatiotemporal region? No pandemic, it is not possible to be certain of the appro(process, still) priateness of Occurrent’s subclasses, partially because 1) • Is [pandemic] a collection of disjoint part-processes? the descriptions are not easily accessible to casual users,

None of the above (remains a process) in turn partially due to the incomplete characterisation Regarding the last question, which is optional since ‘pro- in the OWL file and partially because the documentacess’ may be a leaf category (or: its subclasses are not tion is out of lockstep with the content of the ontology, exhaustive): a pandemic is not a collection of disjoint part- and 2) Pandemic meets several criteria among the sibprocesses if the part-processes all have to be instances of lings. Notably, Actions “are occurents which are caused diferent types of processes. BFO’s process need not have by some presential (the agent) at every (inner and outer) an end, however, whereas pandemics do. So one may ar- time-boundary of the chronoid framing the occurent.”: gue that bfo:process is not as precise as could be for a gen- there is an agent (the SARS-CoV-2 virus), so it may fit. eral high-level category. For now, most relevant is that And processes “are a special kind of occurrent. Processes pandemic is in the occurrent branch of BFO, which is in are directly in time, they have characteristics which canagreement with DOLCE since dolce:accomplishment is not be captured by a collection of time boundaries.”, and where discrete processes “are made up of alternating sequences of extrinsic changes and states or continuous processes”, which does not sound necessarily inapplicable either. Process and Action are not declared disjoint, so a multiple inheritance is permitted if needed. An argument in favour of action is that it has that agent for the duration of the action that the process does not have 6It might be that it evolves from pandemic to endemic, but even then it is expected to evolve via epidemic. Pandemic to endemic has not happened with any of the previous pandemics. HIV/AIDS is still categorised as a pandemic [13], not endemic. To not overcomplicate the analysis, any possible endemicity of an infectious disease after a pandemic is assumed to occur via an epidemic stage.

7https://bfo-classifier.github.io/ explicitly, and so it may capture pandemic somewhat ticular configuration of a part of reality which can be more precisely. understood as a whole and in which entities stand in re

The reference article for GFO [18] also includes event, lations.”) and the gUFO does not have Perdurant. There which “is a right boundary of a process”, rather, and thus is gufo:Event that is a “A gufo:ConcreteIndividual that inapplicable. ’occurs’ or ’happens’ in time. They may be instantaneous or long-running.”, without the baggage of dispositions.

SUMO The Suggested Upper Merged Ontology [19] Regarding pandemic, then: 1) they clearly also exist would have pandemic to be at least a process, which may in the now and not only in the past, and they will occur be of the continuing variety and those with a sure end in the future, thus it cannot be a perdurant, 2) if indeed to it (i.e., events). Process has 10 direct subclasses and the “nature of events as manifestations of objects’ disfurther subclasses, and it may satisfy more than one of positions” [20] holds, then it is not at all certain that them. For instance, the subclass causing unhappiness pandemics would be events, since there is no inherent “Any Process whose result is that the patient of the pro- disposition in an infectious agent of ‘pandemic-causing’ cess is unhappy.”: if ‘patient’ includes the infected organ- to be manifesting itself. Perhaps a population of organisms, pandemics surely qualify, but Natural process as isms, under the assumption it would be an individual, “A Process that take place in nature spontanously.” fits may have a disposition of, say, ‘propensity to sufer from as well. These sibling classes are not declared disjoint. a pandemic’ that is being manifested. On dispositions, Biological process sounds potentially applicable too, but two papers from 2016 by the main proposers of UFO are it is a subclass of internal process that happens within referenced, that in turn pass the bucket of clarification to a single object, which is not the case with a pandemic a book by Molnar and Powers from 2006, at which time I that happens to many organisms simultaneously. Regard- categorised this line to be a dead end. ing natural process’s subclasses, there are electrical and Two more directions were pursued. First, contrary mechanical processes and resonance, neither of which to other FOs where Walk is an example of process or applies to pandemic, and so it remains at being a natural event, it is a Mode in UFO (which is the parent of Disprocess as best fit among the options in the ontology. position), which is a Moment that is an Endurant [21]. Moment in the documentation is gufo:Aspect, and the match to the mode is gufo:IntrinsicMode that is described as “A gufo:IntrinsicAspect that is not measurable.”, which does not rhyme with the Walk, and so this direction was abandoned as well. Second, pandemic as a Situation may be plausible, and the slight diferences across the sources do not fundamentally contradict Situation in [20], cf gUFO:Situation, above (that is disjoint from Event and Endurant); it is mentioned in [21] but not used in any formalisation. What the disposition and atomic event are is to be determined. Having roughly checked the Situation axioms in [20], which are richer than in gUFO, it does not seem to contradict. There is no example in either [20] or gufo.owl as a way to further check understanding. In conclusion, if something had to be chosen for alignment of pandemic, it might be Situation in UFO-B.

UFO The Unified Foundational Ontology has several

versions. We consider its OWL version gUFO and both the UFO-B for events [20] and the recent UFO overview [21]. These recent key sources are not in agreement with each other, which hampers alignment of pandemic to something; a selection follows.

The latest UFO reference paper [21] describes very little about UFO-B. Presumably, Pandemic would be a Perdurant and UFO-B slotted in there, but it cannot. “Perdurants are individuals that unfold in time accumulating temporal parts. They are manifestations of dispositions and only exist in the past.” [21] where a disposition “inheresIn a unique ConcreteIndividual” [20]. That contradicts with gUFO:Situation that is not a manifestation of a disposition (“A gufo:ConcreteIndividual that is a parYAMATO Lastly, the Yet Another More Advanced Top- modelling style [23]. They are presented and discussed in level Ontology [22], with YAMATO20120714.owl. It is the remainder of this section in the sequence they were definitely an event, since it mentions the start and end presented in Morens et al.’s article. and has unity and wholeness. Among that, it is an ordinary_event (cf. instant), but any more precise is dif- 1. Wide geographic extension This refers to the geifcult to determine at this stage, with its subclasses in- ographic region where the organisms that are infected trinsic_accomplishment and extrinsic_accomplishment. with the disease-causing infectious agent are living. ‘Wide’ For the extrinsic one, there is a process and start and end, is vague, which may be fuzzy in the mathematical sense with as example ‘a walk in the park’; the intrinsic one or be estimated by other means. It is the statement that “is an accomplishment by itself alone”, such as ‘a confer- indicates there is no crisp threshold when ‘wide’ starts ence, a game, or a trip’. If we were to know whether a (1/yes) or ends (0/no), but either with a gradual mempandemic always ends by itself or that that is superseded bership function between 0 and 1 or there are ranges of by humans deciding it is over, we would be able to say values based on some arbitrary scale. This could be prefor certain which of the two it is. Either way, for sure cisiated by consensus at least in theory, but practically pandemic is an ordinary_event in YAMATO. will still run into issues. For instance, ‘if on 1 continent, then Localised’, ‘if 2 continents, then Wide’, and ‘if all

In closing, without any aid to help aligning or cate- or -1 continents, then Global’: not all continents are gorising a subject domain entity to a FO, it is nontrivial equal in size and population density (hence, disruptive to do so and that with less certainty, largely due to insufi- efects of a growing epidemic), such rules are yet to be cient detail that may not be consistent across the sources. defined, and there are several diferent continent models, For the alignments themselves, they are split along a di- counting between 4 and 7 continents on earth. If there vide of either something that possibly can go on forever is scientific consensus on those aspects as well, then the (process) where there is no entity in the ontology that has vagueness can be eliminated. something that unfolds and with an end to it, and ones For an ontology, three possible short-hand representathat do have such type of entity (event, accomplishment). tions for the wide geographic extent are as a binary, say, Whether it is an intentional act of omission of the former geo_extent ↦→ Pandemic × {local, wide, global}, where group (at least: BFO, GFO, and SUMO), is unknown; their that range consists of either classes or values, or an obdocumentation does not indicate intentional exclusion. ject property geographic region and a suitable cardinality constraint, such as ≥ 4 for the 6 or 7-continent model. 4. Further domain analysis Alternatively, one may opt for including all components of the complex property—inclusive of the species, disease, and causative agent—for which we first need to address some of the other characteristics, further below.

Kelly’s “out of season” feature [ 6 ] implies wide geographic extension and may be more useful than simply counting continents. Kelly focussed on influenza, which is seasonal, and many infectious diseases are seasonal [24], but it does not imply that any pandemic-causing infectious agent would otherwise be seasonal. A more accurate term may be nonseasonal; either way, this is a clear yes/no attribute of the disease. This is illustrated with the COVID-19 pandemic, where countries record infections throughout the year and have waves in multiple seasons.

So far, based on domain and foundational ontologies, pandemic is a subtype of epidemic, and it an occurrent (perdurant) that unfolds in time and, if available in the foundational ontology, an event or accomplishment. This is still at a very high level. In this section, we zoom in on what the properties of pandemic are claimed to be, what they may be ontologically, and to assess how, if at all, it may assist refining the ontological status of pandemic to determine when some thing is one or not.

The pandemic feature most often mentioned is the ‘large’. Etymologically, the ‘pan-’ in pandemic means ‘all’, in that it is happening across the world or, practically, at least multiple regions and continents. For this to happen, it suggests that there must be an almost simultaneous transmission taking place, which entails that infections are happening out of season. Other proposed features include that it usually afects many people and that it has to involve a new disease. Morens, Folkers and Fauci collated eight characteristics of pandemics [ 2 ] and it is, to date, still the most comprehensive list. From an ontological and modelling viewpoint, ‘characteristics’ is to be understood informally, since there are multiple ways to represent them in an ontology, depending on the 2. Disease movement This means that there is transmission from one place to another place and it can be traced. This implies a comparison of geographic extents across time points, which has a known solution in information systems. Ontologically, at the type (TBox) level, however, it is computationally costly to represent and reason with temporal and spatial information. Depending on the purpose of the ontology, one could choose to represent those details nonetheless, e.g., using the DOL framework to tie in a first order predicate logic [ 25], or an inherently fuzzy feature without crisp boundaries to delegate that to an external system to merely record other than the two extremes of 100% immunity and 0% yes/no disease movement with a data property and a where no-one is, which is the case when the agent is so Boolean data type, or refine that into a categorical vari- novel that not even partial cross-immunity—i.e., the imable or with ranges how slow or fast it moves for more munity to another agent protects at least a little from the detailed analysis, where a ‘yes’ sufices for pandemic. Dis- novel one—applies. To add this to a data model, one again ease moment may not be an essential primary property of can take the ‘easy’ way by introducing, e.g., a categorical pandemics, but rather a secondary one related to arriving variable alike a populationImmunity with possible valat, and maintaining, a wide geographic distribution. ues {minimal,partial,high,full}. Also this property can be unpacked to bring it more into the realm of 3. High attack rates and explosiveness Many peo- ontologies. As a minimum, population, organism, and inple are afected in a short amount of time. The notions of fectious agent are involved and, second, an agreed-upon ‘many’, ‘short’, and ‘high’ all indicate vagueness, which definition of population immunity [27] is needed that, in can be made specific in diferent ways either with a turn relies on the 0 estimate (and thus relates to the membership function or thresholds by consensus. A attackRate). A higher 0 entails a higher population shortcut with an attribute attackRate ↦→ Pandemic × immunity threshold, as do imperfect vaccines when they {low,medium,high} (or, noncommittal, to anyType) do not prevent against infection [27]. While this latter is useful for information systems, but not a scientific on- aspect is less relevant for declaring a pandemic—minimal tology. Attack rate relies on components to determine immunity is easy to determine—it is more relevant for the rate, such as that there is a disease, an infectious when to declare a pandemic over, because it requires a agent, and the reproduction (R) number of the agent. certain adjustable level of immunity. The R number with all its variants, in turn, uses notions such as population, susceptibility to infection (or: level of immunity; see below), social dynamics of a population (i.e., how people behave), ability to measure infections and mortality figures, and a dispersion parameter (how (un)evenly an infected organisms passes on the agent to other individuals in the population)8. 5. Novelty The species’ immune system has never been exposed to it or, in the case of a localised epidemic, a subset of the population of a species has not been exposed to the infectious agent. This can be a yes/no attribute in its simplest form. One maybe could add ‘partial’ to make it three-valued, either in the sense of those subpopulations or a strain may be new but not the disease 4. Minimal population immunity Immunity to an more broadly (as with influenza and SARS). This relates infectious agent is relative, in that an organism has it to to immunity insofar as that novelty implies that there will a degree to some or all of the variants of the infectious be minimal population immunity. Entities underpinning agent, and likewise for the whole population. This is also novelty are that it is a property of the infectious agent in relation to the organisms of the species it infects, and 8A brief overview about the R number and in the context of therewith it is only secondary to pandemic itself. COVID-19 and the pandemic can be found in [26]. 6. Infectiousness It has to involve an infectious dis- WHO’s Pandemic Influenza Severity Assessment uses ease and thus excludes non-infectious states, disorders, as attendant properties the transmissibility, impact (e.g., or diseases such as obesity, heart attacks, and smoking. efect on hospitalisations), and disease severity as input Thus, there has to be an infectious agent that causes the to compute severity [28], which has been successfully disease, excluding all non-communicable diseases. This adapted to Covid-19 recently as well (e.g., [29]). The may be a straight-forward notion for which a ‘yes’ is es- details are actively being investigated and therefore an sential to pandemics, alike infectiousness ↦→ Pandemic attempt to formally characterise it would be part of ongo× {yes} as a shortcut. Whose property it really is, is less ing research rather than only a representation challenge straight-forward, however: a pandemic is not infectious, for ontologies, and thus, as temporary representation, a but the causative agent of the infectious disease that, in single property with an output value may be the leastturn, gets a species into a pandemic, is the one that bears worst option. the infectiousness property, i.e., a chain of relations from, e.g., Pandemic ⊑ ∃causedBy.InfectiousDisease to Infec- In sum, there seem to be nine properties, of which six tiousDisease ⊑ ∃causedBy.InfectiousAgent and only are at least mandatory, if not also the necessary and sufthen InfectiousAgent ≡ Agent ⊓ ∃infects.Organism, un- ficient conditions for something to be a pandemic. They der the assumption of clear definitions of causation and are summarised in Table 3. There are indeed vague propinfection and an agreement on whether the ‘∃’ over in- erties because either humans have not determined the fects should really be a ‘some’ (or an ‘only’ or ‘at most boundaries or it is inherently dificult to measure. This 1’) or the converse. will make it practically dificult to determine when some thing is a pandemic, especially because the fuzzy proper7. Contagiousness This refers to the transmission ties may generate multiple optima/minima under which process, i.e., how it is being spread, and thus entails the a certain situation is classified as being a pandemic or not. infectiousness property. Only a limited set of options of For SARS-CoV-2 and Covid-19, for instance, at least early transmission are possible. For humans, it can be from in 2020, it easily ticked all those boxes and so a pandemic person to person (i.e., contagious) or through some other ontology with a suitable automated reasoner would have medium, such as an animal intermediary (e.g., fleas, rats) classified the situation we were in, as a pandemic. But or the environment (e.g., water, as with cholera), and now, in early 2022 after the first omicron variants of conamong human-human, there are, touch, droplets, and air- cern? Of those properties, numbers 4 and 8 much less borne. While it is relevant to know from a scientific and so, and number 5, on whether there will be worse novel health policy viewpoint which of the possible values it ‘variants of concern’ to come, is a key question to answer. is, it is irrelevant for calling something a pandemic [ 1 ] or There are still out-of-season infections as well. calling an end to a pandemic. That makes this an optional property for classifying something as a pandemic. 5. Discussion 8. Severity While Morens et al. note that severity is Based on the analysis, the guiding questions posed in the not always included, they also observed that, historically, Introduction can be answered at least partially. Regarding the term ‘pandemic’ has been applied more often for dis- what a pandemic is and what properties it has, this has eases that are severe or that have relatively high fatality been made specific to some extent, but for as long as some rates, such as HIV/AIDS (a pandemic since 1981 [13]) of the key characteristics are imprecise due to incomplete and the three recent influenza pandemics of the past cen- data and knowledge by the domain experts, it is not tury, than for milder ones. As such, it would be only an going to be resolved with more ontological analysis. It optional property of the pandemic as a whole, or, more may be possible still to capture some of it with fuzzy precisely, of the disease, not be part of the set of necessary representation [30] and reasoning [31] if one were to be and suficient conditions. However, regarding assessing willing to use data properties in an ontology. An informal and representing this property, first, what is deemed se- visualisation summarising pandemic, attendant entities, vere and what not is subjective, and thus it will be either and vagueness is included in Fig. 1. There is a multitude fuzzy or some thresholds can be set, alike mild, interme- of ways to formalise it, be it according to a particular diate, severe, and very severe, or to WHO’s [28] set of modelling style [23] or ontology ecosystem like the OBO values for influenza ( {below seasonal threshold, Foundry [32], and choice of logic to not only capture the low,moderate,high,Extraordinary}). crisp, declarative, static knowledge, but also the fuzzy

Second, while severity is a property of the disease and and temporal constraints. The temporal constraints in whose value depends on, among others, number infec- Fig. 1 were taken from the TREND language that uses tions, case fatality rates, and treatment options, it is also the ℒℛ Description Logic as foundation [33]. a compound property of a pandemic. More precisely, e.g., Concerning alignment to a FO, it appeared that the two with guidance were at least as good as the many As future work, it would be useful to develop a sohours spent trying to understand the other FOs and their called application ontology that then can drive a simudocumentation. The little tooling support [ 3, 4 ] reduced lator to model the interactions between the parameters the time to categorise pandemic to 1-2 minutes. Assess- to gain more insight and therewith improve the specifiing more FOs did not help gain more insight, other than cation of what a pandemic is. It also would be useful if solidifying the divide between process vs. event. In ad- domain experts could precisiate the vague properties. dition, the absence of guidance entails a lack of quality control mechanisms to ascertain correctness of the alignment, which does not induce confidence in the process References compared to answering questions in a decision tree. This is exacerbated by the observation that for some FOs, multiple points of alignment were defensible. A ‘contact the authors’ guideline is undesirable as a general strategy for domain entity alignment. As also noted in [ 34, 5 ], FO tooling is needed for use and quality and, indeed, should be considered as a service to potential and actual FO users.

6. Conclusions

The assessment of domain and foundational ontologies and literature revealed that pandemic is an event (likely also an accomplishment) that unfolds in time. To be classified as a pandemic, there are a number of features from mostly attendant universals, such as the infectious agent and the disease it causes, that have to be satisfied. They are not all crisp properties and those imprecise boundaries have not all been defined. This hampers defining pandemic. Consequently, it suggests why it is dificult to determine when exactly a pandemic starts and ends. [8] S. Babcock, J. Beverley, L. Cowell, et al., The infec- [22] R. Mizoguchi, YAMATO: Yet Another More Adtious disease ontology in the age of COVID-19, J. vanced Top-level Ontology, in: Proceedings of of Biomedidal Semantics 12 (2021) 13. the Sixth Australasian Ontology Workshop, Con[9] T. Vega, J. E. Lozano, T. Meerhof, R. Snacken, ferences in Research and Practice in Information, J. Mott, R. Ortiz de Lejarazu, B. Nunes, In- CRPIT, 2010, pp. 1–16. Sydney : ACS. lfuenza surveillance in Europe: establishing epi- [23] P. R. Fillottrani, C. M. Keet, Dimensions afecting demic thresholds by the moving epidemic method, representation styles in ontologies, in: Proc. of Influenza and Other Respiratory Viruses 7 (2013) KGSWC’19, volume 1029 of CCIS, Springer, 2019, 546–558. pp. 186–200. [10] D. Fleming, M. Zambon, A. Bartelds, J. de Jong, The [24] M. E. Martinez, The calendar of epidemics: Seasonal duration and magnitude of influenza epidemics: a cycles of infectious diseases, PLOS Pathogens 14 study of surveillance data from sentinel general (2018) e1007327. practices in England, Wales and the Netherlands, [25] T. Mossakowski, M. Codescu, F. Neuhaus, O. Kutz, European J. of Epidemiology 15 (199) 467–473. The Road to Universal Logic–Festschrift for 50th [11] P. Doshi, The elusive definition of pandemic in- birthday of Jean-Yves Beziau, Volume II, Studies in lfuenza, Bulletin of the WHO 89 (2011) 532–538. Universal Logic, Birkhäuser, 2015. [12] C. Masolo, S. Borgo, A. Gangemi, N. Guar- [26] D. Adam, A guide to R – the pandemic’s misunderino, A. Oltramari, Ontology library, Wonder- stood metric, Nature 583 (2020) 346–348. Web Deliverable D18 (ver. 1.0, 31-12-2003)., 2003. [27] P. Fine, K. Eames, D. L. Heymann, “herd immunity”: Http://wonderweb.semanticweb.org. a rough guide, Clinical infectious diseases 52 (2011) [13] C. Beyrer, A pandemic anniversary: 40 years of 911–916.

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