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Dept. of Information Engineering - University of Padova 1 Corresponding author: M. Falda, Dept. of Information Engineering, v. Gradenigo 6 – 35131 Padova (Italy). Email: marco.falda@unipd.it Abstract. No matter how prepared a population may be, bioterrorism cannot beprevented: the first clues will always be given by ill people. Temporal analysisapplied to this type of scenarios could be an additional tool for limiting disrup-tion among civilians allowing for recognizing typical temporal progression andduration of symptoms in first infected people. We propose the application of afuzzy temporal reasoning system we have developed for biomedical temporaldata analysis in different scenarios after a hypothetical attack. The system is ableto handle both qualitative and metric temporal knowledge affected by vaguenessand uncertainty, taking into account in this way the vagueness of patients reportsexpressed in natural language.
In case of biological attacks, the effects of a deliberate release will be obvious if a largenumber of troops become ill with similar symptoms at the same time. It may be lessclear in a civilian population [1], supposed to be in a period of peace. For this reasonestablishing a diagnosis is critical to the public health response to a bioterrorism-relatedepidemic, since the diagnosis will guide the use of vaccinations, medications, and otherinterventions [2]. Moreover, new or reemerging infectious diseases have relevant im-plications: during the past 20 years, over 30 new lethal pathogens have been identified;for example the emergence of Severe Acute Respiratory Syndrome (SARS) in South-east Asia rapidly spread to 29 countries in less than 90 days [3]. Emerging diseaseoutbreaks may be difficult to distinguish from the intentional introduction of infectiousdiseases for nefarious purposes, when considering that Genetic Engineering of biologi-cal warfare agents can alter their pathogenicity, incubation periods, or even the clinicalsyndromes they cause. For this reason, it is important to develop automatic SyndromicSurveillance Systems [2] able to notify as soon as possible the early manifestations ofbioterrorism-related diseases from population monitoring. A preliminary step towardsthe design of a component of such a System could be based on the use of temporalreasoning techniques in order to identify typical temporal progression of diseases.
Taking into account that medical data relative to temporal evolution of diseases are often affected by vagueness and uncertainty, the temporal reasoning model that seems to be more adequate for such real application could be the Fuzzy Temporal ReasoningSystem (FTR in the following) that we developed in a previous research [4].
The system is based on the integration of temporal information both qualitative and metric represented as fuzzy constraints in a network and extends a previously proposedsystem [5] that dealt with fuzzy qualitative temporal reasoning. We have applied ourSystem in several diagnostic problems. In [6], we applied it for discriminating exan-thematic diseases from temporal patterns of patient symptoms and in [7] we studiedhow our system could represent temporal evolutions of symptoms in different patientsaffected by SARS, thus making possible to deduce characteristic periods of a new dis-ease.
Dealing with the study of biological warfare, we address the problem of the auto- mated analysis of temporal medical data in order to obtain information useful for earlydetection of biological attacks. In particular, we will start from the temporal evolutionof five NIAID (National Institute of Allergy and Infectious Diseases) diseases repre-sented as fuzzy constraint temporal networks. Then we will check the consistency oftemporal data relative to a set of ten patients reports [8] with respect to the previouslyconsidered diseases; we will use the algorithmic methodologies for checking temporalconsistency offered by the FTR system. Two are the main objectives: – to find the most plausible disease and, once found it,– to exploit the information in order to infer the possible contagion.
The paper is organized as follows. Section 2 describes the problem of identifying bio-logical attacks while Section 3 is dedicated to a brief presentation of the FTR System.
In Section 4 the considered diseases are summarized and in Section 5 the results abouttemporal analysis of patients data is shown.
Early symptoms of disease induced by a biological warfare agent may be non-specificor difficult to recognize, for example a simple febrile illness; the disease itself couldaffect individuals living in widely dispersed areas, who may then present to severaldifferent healthcare providers [1]; once the disease has been diagnosed, appropriateprophylaxis, treatment, and other measures to decrease spreading, such as quarantine(for a contagious illness) would be adopted.
As said before, many diseases caused by bioterrorism present with relatively com- mon features, such as fever or headache, but there are several considerations that canease the identification of a Bioterrorism-related scenario [9]: symptoms: a number of patients that abruptly present to care providers or emergency rooms manifesting similar and unexpected symptoms; zoonoses: most of the agents used in biological warfare are diseases that affect animals, for this reasons sudden deaths between animals can anticipate diffusion amonghumans; unexplained factors: whenever an unusual pattern is detected a biological attack may be suspected: unexplained deaths for an usually mild disease, unusual exposureroutes for a pathogen, for a geographical area, for a season; diffusion patterns: higher symptoms manifestations in certain areas, for example build- ings, or in short time periods. The abrupt onset and single peak of cases wouldimplicate a point-source exposure without secondary transmission [10].
In this paper only considerations about time will be taken into account.
In the present section we will summarize the main characteristics of the FTR System(for a more detailed description cfr. [4]).
In Allen’s Interval Algebra [11] the temporal qualitative knowledge is represented as a binary relation between a pair of intervals in terms of atomic relations: where each rel i is one of the 13 mutually exclusive atomic relations that may exist between two intervals (such as equal, before, meets etc.).
To deal with vague and uncertain temporal information Allen’s Interval Algebra has been extended in [5] with the Possibility Theory by assigning to every atomic relationrel i a degree αi, which indicates the preference degree of the corresponding assignmentamong the others I1 R I2 with R = (rel 1[α1], . . . , rel 13[α13]) where αi is the preference degree of rel i (i = 1, . . . , 13); preferences can be defined in the interval [0, 1]. If we take the set {0, 1} the classic approach is obtained.
Intervals are interpreted as ordered pairs (x, y) : x ≤ y of 2 × 2 in such a way that the pairs of intervals that are in relation rel k have membership degree αk.
Temporal metric constraints have been extended to the fuzzy case starting from the traditional TCSPs [12] in many ways [13,14,15]. To represent fuzzy temporal metricconstraints we adopt trapezoidal distributions [4], since they seem enough expressiveand computationally less expensive than general semi-convex functions [16].
Each trapezoid is represented by a 4-tuple of values describing its four characteristic points plus a degree of consistency αi denoting its height.
is either ( or [ and
is either ) or ]. The points bk and ck determine the interval of those temporal values
which are likely, whereas ak and dk determine the interval out of which the values are
absolutely impossible. The generalized definition of trapezoid extreme increases the
expressiveness of the language.
As far as integration is concerned, we have defined the fuzzy extensions P Afuz, P Ifuz, IP fuz and IAfuz of the corresponding classical algebras P A, P I, IP andIA referring to point-point, point-interval, interval-point and interval-interval relations [17,4,5], we have extended the composition operation and the transitivity table [18]. Inthe integrated framework we can manage temporal networks where nodes can representboth points and intervals, and where edges are accordingly labeled by qualitative andquantitative fuzzy temporal constraints.
Path-Consistency and Branch & Bound algorithms have been generalized to the fuzzy case adding some relevant refinements that improve their efficiency. Path-consi-stency has a polynomial computing time and it is used to prune the search space inthe Branch & Bound algorithm; however for real world applications tractable subsetsof relations such as those belonging to the Convex Pointizable Algebra SAc should beused, since in that case Path-consistency is sufficient to find the minimal network [19].
Before presenting the application of the Temporal Reasoning system it is useful tobriefly describe the biological agents that will be considered.
NIAID (National Institute of Allergy and Infectious Diseases) is the primary Institute atNIH, the US National Institute of Health, for emerging infectious diseases research, in-cluding research on agents of bioterrorism. This institute has grouped biological agentsin three categories according to their ease of use for a biological attack; the most dan-gerous are in Category A (Table 1) and are agents that can be easily disseminated ortransmitted person to person, that have high mortality and can cause public panic andsocial disruption, therefore needing special action for public preparedness.
• Bacillus anthracis (Anthrax)• Clostridium botulinum toxin (Botulism)• Yersinia pestis (Plague)• Variola major (Smallpox) and other pox viruses• Francisella tularensis (Tularemia)• Viral hemorrhagic fevers (VHF) We have considered the timelines of five diseases: Anthrax, Tularemia, Smallpox, Plague and Ebola. These timelines can be obtained from temporal characteristics of thediseases themselves and are reported in Figure 1. In the following just Anthrax andPlague are described.
Anthrax (Bacillus anthracis) Anthrax is one of the most serious diseases: when in-haled it can be quite lethal [9].
Most of the early symptoms of inhalation Anthrax are similar to those for other in- fectious diseases, making a differential diagnosis difficult during flu season, for example Fig. 1. Timelines for the considered diseases; for each disease the incubation period, the worsen-ing period and the death have been represented (in days).
[20]. The distribution of the incubation period for inhalational Anthrax can be relativelybroad as observed in Sverdlovsk (2-43 days); in any case, it does not extend more than60 days. The clinical presentation has been described as a 2-phases illness: the nonspe-cific prodrome for Anthrax may last from several hours to several days [2]. The secondphase develops abruptly, with sudden fever, dyspnea, diaphoresis, and shock.
Case fatality rates of 80% or more, with nearly half of all deaths occurring within 24 to 48 hours, is highly likely to be Anthrax or pneumonic plague. A temporal constraintnetwork for modelling Anthrax can be composed by four vertices: the contagion (1),the first symptom (2), the worsening phase (3) and the death or recovery.
The constraints, deduced from the previous description, are expressed in hours.
– Incubation lasts no more than 60 days: 1 {(−∞, −∞, 1440, 1440]} 2– First phase lasts from several hours to several days: 2 {(6, 12, 24, 96)} 3– Death occurs within 24 to 48 hours: 3{(12, 24, 48, 60)} 4 Plague (Yersinia pestis) Plague is of great concern in a biological attack scenario,since it is available around the world, it is easy to produce and disseminate it throughaerosolization; moreover, it causes high fatality rates and can rapidly spread during anepidemic [21]. Vaccine has limited efficacy following aerosol dispersion [9].
A pneumonic plague outbreak would result with symptoms initially resembling those of other severe respiratory illnesses. Exposure to aerosolized Y. pestis results inpneumonic plague, which has a typical incubation period of 2 to 4 days (range 1-6days).
The fatality rate of patients with pneumonic plague when treatment is not com- menced within 24 hours of symptoms onset is extremely high [21]. In modelling plague constraint network notice that second phase is almost immediate, therefore, assumingthat the same vertices are used for all diseases, the constraint between vertex 3 and 4could be: Notice that in the description of Anthrax fuzzy metric constraints were used, while here also a qualitative fuzzy temporal constraint has been specified. This shows that auser can represent the temporal knowledge as it is available.
To develop a general framework for automated temporal analysis of biological warfaredata different aspects can be considered. Here first we apply the solver to match tempo-ral data coming from patients with the typical evolution of the five diseases previouslycited in order to identify the most plausible disease. Second, when the disease has beenselected its characteristic development is used to infer the contagion period.
We consider a set of medical dataconcerning 10 patients reports [8].
These descriptions contain tempo-ral information that can be mod-elled using a temporal constraintnetwork according to the FTR rep-resentation system.
tients is shown in Figure 2. In thefollowing we report as a detailedexample the description and themodelling of the first patient.
Patient 1 On October 2, 2001,a 63-year-old Caucasian personawoke early with nausea, vom-iting, and confusion and wastaken to a local emergency room Fig. 2. Timelines for patients (S = first symp- tom, H = hospitalization, W = worsening, D = characterized by malaise, fatigue,fever, chills, anorexia and sweats.
[.] On hospital day 2, penicillin G, levofloxacin, and clindamycin were begun. He re-mained febrile and became unresponsive to deep stimuli. His condition progressivelydeteriorated, with hypotension and worsening renal insufficiency. The patient died onOctober 5.
A temporal constraint network for modelling, for instance, Patient1 can be com- 5. death / discharge from hospital (D).
The constraints, deduced from the previous reports and expressed in hours from Jan • 1 [6456, 6456, 6480, 6480] 2 (on Sep 27)• 1 [6576, 6576, 6600, 6600] 4 (on Oct 2)• 1 [6624, 6624, 6648, 6648] 3 (on Oct 4)• 1 [6648, 6648, 6672, 6672] 5 (on Oct 5) Now, to find the most plausible disease we combine the patients networks with the network of each agent. In this way, by means of a consistency analysis, we can have anidea of the disease that has the highest compatibility with the considered scenario andthen infer the contagion period.
Assuming that the outbreak is located in a single source, all patients should become ill within the incubation period. Applying the FTR system it results that Anthrax is theonly disease among the 5 considered which is consistent with all patients; for examplethe Plague incubation period is too short to fully accommodate a range of 1 monthbetween the appearing of the symptoms in the patients. This inference confirms thehypothesis about Anthrax found by laboratory tests [8].
Then, taking into account that Anthrax incubation lasts no more than 60 days and that symptoms in all patients appeared from September 24 to October 26, the FTRsystem can deduce that contagion of all these patients could have occurred from the endof July to few days before September 22.
In this paper we have studied how to develop a Temporal Reasoner for an automaticSyndromic Surveillance System able to notify as soon as possible the early manifes-tations of bioterrorism-related diseases from population monitoring. To this aim thedetection of temporal characteristic features become an important aspect that we haveaddressed using the Fuzzy Temporal Reasoning System. This system has allowed in-ferring information about possible contagion period in an Anthrax attack scenario hap-pened in U.S. in 2001.
As future directions are concerned, we intend to enrich the analysis capabilities of the FTR system for example to identifying clusters in contagion dynamics. In this waywe aim to develop a more sophisticated system to face this global threat.
1. Beeching, N.J., Dance, D.A.B., Miller, A.R.O., Spencer, R.C.: Biological warfare and bioter- 2. Buehler, J.W., Berkelman, R.L., Hartley, D.M., Peters, C.J.: Syndromic surveillance and bioterrorism-related epidemics. Emerg Infect Dis. 9 (2003) 1197–1204 3. Kortepeter, M., Christopher, G., Cieslak, T., Culpepper, R., Darling, R.: USAMRIID’s Med- ical Management of Biological Casualties Handbook. 6th edn. U.S. Army Medical ResearchInstitute of Infectious Diseases (2005) 4. Badaloni, S., Falda, M., Giacomin, M.: Integrating quantitative and qualitative constraints in fuzzy temporal networks. AI Communications 17 (2004) 183–272 5. Badaloni, S., Giacomin, M.: The algebra IAfuz: a framework for qualitative fuzzy temporal reasoning. Artificial Intelligence 170 (2006) 872–908 6. Badaloni, S., Falda, M.: Discriminating exanthematic diseases from temporal patterns of patient symptoms. In: Proc. of the 10th Conference of Artificial Intelligence in Medicine(AIME 2005), Aberdeen, Scotland (2005) 33–42 7. Badaloni, S., Falda, M.: Temporal characterization of ill-known diseases. In: Proc. of of the International Workshop on Intelligent Data Analysis in Biomedicine and Pharmacology,Verona, Italy (2006) 17–22 8. Jernigan, J.A., Stephens, D.S., Ashford, D.A., C., O., Topiel, M.S., M., G., M., T., Fisk, T.L., Zaki, S., Popovic, T., Meyer, R.F., Quinn, C.P., Harper, S.A., Fridkin, S.K., Sejvar, J.J.,Shepard, C.W., McConnell, M., Guarner, J., Shieh, W.J., Malecki, J.M., Gerberding, J.L.,Hughes, J.M., Perkins, B.A.: Bioterrorism investigation team. bioterrorism-related inhala-tional anthrax: the first 10 cases reported in the united states. Emerg Infect Dis. 7 (2001)933–944 9. Bellamy, R.J., Freedman, A.R.: Bioterrorism. QJ Med. 94 (2001) 227–234 10. Dennis, D.T., Inglesby, T.V., Henderson, D.A., et al.: Tularemia as a biological weapon: medical and public health management. Journal of American Medical Association (JAMA)285 (2001) 2763–2773 11. Allen, J.F.: Maintaining knowledge about temporal intervals. Communications of the ACM 12. Dechter, R., Meiri, I., Pearl, J.: Temporal constraint networks. Artificial Intelligence 49 13. Dubois, D., Lang, J., Prade, H.: Timed possibilistic logic. Fundamenta Informaticae 15 14. Marín, R., Cárdenas, M.A., Balsa, M., Sanchez, J.L.: Obtaining solutions in fuzzy constraint network. International Journal of Approximate Reasoning 16 (1997) 261–288 15. Godo, L., Vila, L.: Possibilistic temporal reasoning based on fuzzy temporal constraints. In: 16. Khatib, L., Morris, P.H., Morris, R.A., Rossi, F.: Temporal constraint reasoning with prefer- ences. In: Proc. IJCAI 2001, Seattle, WA (2001) 322–327 17. Badaloni, S., Giacomin, M.: Fuzzy extension of interval-based temporal sub-algebras. In: Proc. of IPMU 2002, Annecy, France (2002) 1119–1126 18. Meiri, I.: Combining qualitative and quantitative constraints in temporal reasoning. Artificial 19. van Beek, P., Cohen, R.: Exact and approximate reasoning about temporal relations. Com- putational Intelligence 6 (1990) 132–144 20. Wilkening, D.A.: Sverdlovsk revisited: Modeling human inhalation anthrax. In: Proc. of the National Academy of Sciences (PNAS). Volume 102 (20). (2006) 7589–7594 21. Inglesby, T.V., Dennis, D.T., A., H.D., et al.: Plague as a biological weapon: medical and public health management. Journal of American Medical Association (JAMA) 283 (2000)2281–2290

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