A Meta-ontology Framework for Parameter Concepts of Disease Spread

Simulation Models

Le Nguyen and Deborah Stacey

School of Computer Science, University of Guelph, Guelph, Ontario, Canada

Keywords:

Meta-ontology, Parameters, Animal Disease Spread, Simulation Models, Transformation, Parameters

Assessment.

Abstract:

This work reports on an ontological organization (framework) that separates domain knowledge from knowl-

edge of speciﬁc views and formalizes conceptual relationships by linking to the meta-ontology structure. We

use parameters of animal disease spread simulation models as an example, although all concepts presented

could apply to human disease spread simulation as well. A meta-ontology is created to document parameter

concepts in different comparable simulation models. It formalizes relationships between parameter concepts.

This offers several advantages such as allowing explicit domain knowledge representation and provenance,

allowing for the assessment of parameters with respect to domain knowledge, and assisting in usage and eval-

uation of the models. The meta-ontology allows views about parameter concepts to be captured. This is

important because it establishes a neutral view point which allows the assessment of parameter semantics in

respect to documented domain knowledge. While this work uses the domain of animal disease spread, the

principles of ontological representation of model parameters is applicable to a wide range of domains.

1 INTRODUCTION

Today, we live in an era of global markets. Products

and livestock are shipped from one part of the globe

to another. While globalization might have beneﬁts to

the world economy, the world is facing greater risks

of transmission of infectious (including zoonotic) dis-

eases than ever before. It is imperative and impor-

tant that a country is well prepared to deal with these

risks. Simulation models for the spread of diseases

are popular tools to study the spread of diseases and to

evaluate the effectiveness of control strategies. Over

the last decades, several simulation models for ani-

mal disease spread have been developed and achieved

several objectives such as to mimic the outbreak of

animal diseases, to study the aspects of animal dis-

ease transmission, to develop support decision sys-

tems, to support preparedness planning, and to assess

economic impacts, etc. These agent-based simulation

models are characterized by large numbers of parame-

ters. Because of the large numbers of parameters, it is

challenging to make these models work together and

to share the knowledge of a model (as expressed in its

parameters) to others or to compare them. This often

https://orcid.org/0000-0002-2019-9905

contributes to high costs and is time consuming. One

of the reasons for this problem is that the semantics

of these parameters are often overlooked by the mod-

els. The semantics of these parameters are determined

by the reality that the modeller wish to emulate. This

has a great implication because emulation of the same

reality can be different based on the views of the mod-

ellers, e.g. views with different semantics, views with

different granularity, and views in different contexts,

etc. It is often done implicitly. Because of this im-

plicit representation of the parameters, there are sev-

eral disadvantages of the current models. This paper

explores the use of a meta-ontology framework to rep-

resent explicitly the semantics of agent based simula-

tion model parameters to address some shortcomings

of the current models such as knowledge representa-

tion, knowledge sharing, and assessment of domain

knowledge (as expressed in the parameters) allowing

a means to share information across simulation mod-

els and to assist usage and comparison of these mod-

els.

Nguyen, L. and Stacey, D.

A Meta-ontology Framework for Parameter Concepts of Disease Spread Simulation Models.

DOI: 10.5220/0010299302230233

In Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2021) - Volume 5: HEALTHINF, pages 223-233

ISBN: 978-989-758-490-9

223

2 RESEARCH CONTEXT

Parameter-based simulation models are characterized

by large numbers of parameters and processes that

model the behaviours of phenomena. In this con-

text, we examine parameters of the animal disease

spread models for Foot and Mouth Disease (FMD)

such as the North American Animal Disease Spread

(NAADSM) and InterSpread Plus models. The dis-

ease spread simulation models’ parameters are used

to describe animal units, farm locations, movement

of animal units, spread mechanisms and courses of

infection. Without disease control mechanisms, a dis-

ease spread in an animal population is a result of com-

bination of the farm network, the movement of herds,

herd infectiousness (the course of an infection), and

disease spread mechanisms. Regardless of how well

a model is built, it always is an approximate version

of reality. There always exist uncertainties associated

with simulation models. There are two types of un-

certainty associated with simulation models:

• Model structural uncertainty: “the imperfect rep-

resentation of processes within a model” (MA

et al., 2013)(Kennedy and Hagan, 2001)(Arendt

et al., 2012).

• Model parameter uncertainty: “the imperfect

knowledge of the values of parameters” (bi-

ological parameters, model parameters, and

model artifacts) associated with modelling pro-

cesses (Kennedy and Hagan, 2001)(MA et al.,

2013)(Arendt et al., 2012).

For users, the ease of use and interpretation of pa-

rameters are key requirements for simulation model

builders. In order to evaluate simulation models, we

ﬁrst must agree on parameters and their semantics be-

fore an evaluation can take place. They should reﬂect

the intended meaning with respect to the simulation

models and the related domain knowledge. It is chal-

lenging because there exist many implicit facts that

relate to simulation models. It is a result of the mod-

ellers’ views on how they wish simulation models to

be perceived. The progression of the simulation mod-

els through time (life cycle) also contributes to the

changing of parameters (and especially the changing

of their semantics) that makes them harder to use, to

maintain and to evaluate.

Figure 1: Traditional disease spread parameters setting and

ontology approach for comparing models.

3 OUR APPROACH

3.1 Design Scope and Restrictions

The scope of our ontology is to capture core concepts

of simulation models’ parameters and related domain

knowledge. Our study uses:

• Concepts related to the parameters of the

NAADSM, InterSpread Plus models and the re-

lated FMD domain knowledge for an FMD course

of infection, i.e., we use animal disease spread do-

main as our example. Restrictions within this do-

main include:

– For the duration of a state in the FMD infection,

the distribution is assumed to be a normal dis-

tribution and a Poisson distribution is used as

an example

– A single production type (type of animal) is

used for both models

– Parameters for farm/herd information in

NAADSM and InterSpread Plus models are

used

– The farm network is not included in this study

– Spread mechanism is not included in this study

3.2 Overview of Our System

An overview of our system is depicted in Figure 2.

There are two (2) basis components in our approach:

• Knowledge Representation

– A domain meta-ontology is used to capture

core concepts of parameters related to the FMD

course of infection as reﬂected in the FMD do-

main literature and simulation models. It pro-

vides vocabularies to describe parameter con-

cepts of simulation models and related FMD

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domain knowledge for an FMD course of in-

fection.

– Conceptual descriptions of model parameters.

They are descriptions of simulation model pa-

rameter settings and the related FMD domain

knowledge.

• Semantic Engine

– A semantic engine is used to examine and to

assess the parameter concepts and perform pa-

rameter transformation from one model to an-

other.

Figure 2: Our system overview.

3.3 Knowledge Representation

3.3.1 Ontology Architecture

A two-layered architecture for our ontology is pro-

posed. It is shown in Figure 3. There are two lay-

ers associated with our ontology. In the ﬁrst layer,

the domain meta-ontology has concepts shared by

the simulation models and the related FMD domain

knowledge. It provides shared vocabularies to de-

scribe parameter concepts and the related FMD do-

main knowledge. The second layer describes the con-

ceptual descriptions of models’ parameter settings for

the FMD simulation models and related FMD domain

knowledge. The shared vocabularies permit parame-

ter descriptions of new models since new model con-

cepts are generally taken from the domain knowledge.

Thus, it provides a scalable way to describe the con-

ceptual descriptions of simulation models’ parame-

ters.

Figure 3: Ontology architecture.

3.4 Knowledge Acquisition

We adopted the method from Uschold and Gruninger

(Fox and Gruninger., 1995) by capturing the do-

main in natural language. Other automatic and semi-

automatic knowledge extraction techniques may be

used, however, most of these methods are fairly prim-

itive and do not work well on a large and complex do-

main. We acquired domain knowledge by examining

a number of literature works as follows:

• Foot and mouth disease papers (G., 2001)(Mar-

dones et al., 2010)(C. et al., 2016)(Sanson,

1993)(S. et al., 2003)(P. et al., 2006)(R. et al.,

2009)(K. et al., 2007)(JM. et al., 2012)(M. et al.,

2009)(van Roermund H. et al., 2010)

• NAADSM papers (Harvey et al., 2007) and re-

lated papers (Harvey and Reeves, 2012)

• InterSpread Plus papers (MA et al., 2013) and re-

lated papers (team, 2018)

We used the above literature to acquire knowledge

and case study scenarios to aid in building our on-

tology.

3.5 Ontology Speciﬁcation

Our ontology speciﬁcation provides the core vocabu-

laries or concepts to describe the parameter concep-

tual model of animal disease spread simulation mod-

els such as NAADSM and InterSpread Plus models,

and related FMD domain knowledge for an FMD

course of infection. There are two components of

this speciﬁcation. The ﬁrst component is the do-

main meta-ontology component. It provides the core

concepts to describe the parameter conceptual mod-

els. The second component is the conceptual de-

scriptions of FMD simulation models’ parameters.

These are the descriptions of the parameter models for

NAADSM, Interspread Plus, and knowledge domain.

Among these models, they share the same fundamen-

tal parameter concepts related to an FMD course of

infection. However, with respect to each concept, the

parameters of each model might be set differently.

This reﬂects the complexity and the differences in

semantics in choosing the parameter settings for the

models. In this section, we construct a series of ques-

tions that the domain meta-ontology must be able to

answers. These serve as a basis of our speciﬁcation. It

is important to note that our competency questions are

to check whether the domain meta-ontology answers

to these questions at the terminological level.

A Meta-ontology Framework for Parameter Concepts of Disease Spread Simulation Models

225

3.5.1 Domain Meta-ontology

Our domain meta-ontology is only about the con-

ceptual description of an FMD course of infection

(i.e. we do not consider the containment or control

of the spread). The following questions and answers

are to address core concepts that are captured in our

ontology (only a small selection are presented here).

Who are the Users of Ontology?

• The users of the ontology are FMD experts and

FMD simulation modellers.

What Does the Ontology need to Describe?

• The ontology is to describe parameters and their

semantics related to an FMD course of infection

for NAADSM and InterSpread Plus simulation

models and related FMD domain knowledge.

What is a State?

• A state is a basic unit of a state transition models.

It indicates a disease state of an animal unit. A

state has following properties:

– State name

– State order

– State duration

What is a State Duration?

• A state duration is the amount of time (usually,

days) that an animal unit is in a state.

• It can be speciﬁed by the users, e.g. modelled as a

probability density function.

A Course of FMD Infection might have following

States:

• Infected State

– Latent State

– Subclinical Infectious State

– Clinical Infectious State

– Clinical Non-infectious State

– Immune State or Naturally Immune State

– Incubation State

– Infectious State

• Noninfected State

– Susceptible State

In the domain meta-ontology, we built the core con-

cepts that are needed to describe the semantics of pa-

rameter settings of simulation models and the related

FMD domain knowledge. Our emphasis is on the

states’ concepts and other concepts related to an FMD

course of infection. We create and use the ontology

structure of the states to ﬁnd and to reason about the

incubation state, infected states, non-infected states,

infectious states, and non-infectious states related to

the simulation models’ parameter settings. It can be

further developed to work with the states of many

other diseases.

3.5.2 Conceptual Descriptions of Simulation

Models’ Parameter Settings

In this section, we discuss the usage of the domain

meta-ontology for the description of FMD simulation

models’ parameters settings and highlight differences

between the simulation model concepts. First, we ex-

amined some examples of FMD courses of infection.

We show the states of an FMD course infection and

their deﬁnitions which aims to clarify the semantics

of the states of simulation models. Second, from the

examples, we construct a list of competency questions

that the ontology needs to answer. Normally, an an-

imal or an animal unit that associated with an FMD

course of infection goes through a number of states

as the disease progresses. In essence, we want to de-

scribe these concepts as reﬂected by a model’s param-

eter settings. To show how domain meta-ontology

can be used to describe the FMD course of infec-

tion, we examine the following cases: the descrip-

tion of an FMD course of infection for FMD domain,

NAADSM model, and InterSpread Plus model. The

concepts of parameter settings are depicted in Figure

4, 5, and 6.

Figure 4: An example of FMD domain course of infection.

It is taken and modiﬁed from (C. et al., 2016).

In Figure 4, 5, and 6, we provide the state con-

cepts, and their descriptions related to the models’

parameter settings. We note that there are differ-

ences in the description of the states and state names

as shown in the ﬁgures. For example, in NAADSM

model, clinical state means clinical infectious state

whereas in FMD domain, clinical state might have

different meaning. The ﬁgures show that there are dif-

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Figure 5: An example of NAADSM model’s FMD course

of infection. It is modiﬁed from (Harvey et al., 2007).

Figure 6: An example of InterSpread Plus FMD course of

infection.

ferent states if we compare the FMD course of infec-

tion between the NAADSM model, the InterSpread

Plus model and the FMD domain knowledge. In

the NAADSM model, states are modelled in differ-

ent granularity as compared to the InterSpread Plus

model. Given the conceptual models of the parameter

presented by the ﬁgures, we want to use our domain

meta-ontology to describe the parameters setting. We

want to answer the following questions:

• What are states that associated with an FMD sim-

ulation model parameter settings?

• What are concepts related to an FMD model pa-

rameter setting?

• What is a duration of a state?

• What types of infectious states are associated with

an FMD simulation model?

• Which models have an incubation state?

• Which models have a clinical non-infectious

state?

In section 3.6, we formally provide a discussion

on FMD state relations and descriptions of an FMD

course of infection.

3.6 Formal Knowledge Representation

In this section, we present the core part of the formal

knowledge representation of our ontology. A com-

plete ontology can be accessed via the link provided

in (Nguyen, 2020). There are two parts of the on-

tology: the terminological components, and the as-

sertion components. We present only core termino-

logical components. The assertion component can be

accessed via the previous link. We use Manchester

OWL syntax and Prot

e (Musen, 2015) for our for-

mal knowledge representation.

3.6.1 Terminological Components

They are used to describe an FMD course of infection

in the FMD domain, and NAADSM and InterSpread

Plus models. In this section, we discuss core compo-

nents of our ontology. The generic components are

vocabularies that can be used to construct an FMD

course of infection. State concepts are key compo-

nents of our ontology. The domain meta-ontology

state relations are depicted in Figure 7. In this ﬁg-

ure, it shows the relationship between the primitive

classes and deﬁned classes.

Figure 7: Domain meta-ontology state relation.

In Figure 7, primitive classes are depicted in light

yellow ovals. The deﬁned classes or named classes

are depicted in orange ovals. We can use the named

classes for reasoning purpose. We can use primitive

classes to deﬁne more named classes to ﬁt the ontol-

ogy requirements.

A Description of an FMD Course of Infection.

The description of an FMD course of infection is gen-

erally deﬁned in the ProductionType subclass. It oc-

curs here since a course of infection is speciﬁc to the

animal in which it occurs, i.e. the production type

since these models are restricted to agricultural an-

imal species. It uses concepts in the Generic class

component to describe the concepts related to an

A Meta-ontology Framework for Parameter Concepts of Disease Spread Simulation Models

227

FMD course of infection. We will examine the FMD-

ContextSingleProductionType, NAADSMSinglePro-

ductionType, and InterSpreadPlusSingleProduction-

Type classes.

1. FMD Course of Infection: This is the FMD do-

main course of infection. It is reﬂected in the

deﬁnition of the FMDContextSingleProduction-

Type class. In this class, a cover axiom is used

to ensure only necessary concepts are used to de-

scribe FMDContext. The description of FMD-

ContextSingleProductionType has an object prop-

erty hasModelState. It is used to establish a re-

lation between the production type and a state.

In this class, each production type has several

states with exactly 1 LatentState, Subclinical-

InfectiousState,ClinicalInfectiousState, Clinical-

NonInfectiousState, and NaturallyImmuneState.

Class: PO:FMDContextSingleProductionType

SubClassOf:

PO:ProductionType,

PO:hasModelState only

(PO:ClinicalInfectiousState

or PO:ClinicalNonInfectiousState

or PO:LatentState

or PO:NaturallyImmuneState

or PO:SubclinicalInfectiousState),

PO:hasModelState exactly

1 PO:ClinicalInfectiousState,

PO:hasModelState exactly

1 PO:ClinicalNonInfectiousState,

PO:hasModelState exactly

1 PO:LatentState,

PO:hasModelState exactly

1 PO:NaturallyImmuneState,

PO:hasModelState exactly

1 PO:SubclinicalInfectiousState

2. An FMD course of infection in NAADSM model:

It is deﬁned in the NAADSMSingleProduction-

Type class.

Class: PO:NAADSMSingleProductionType

SubClassOf:

PO:ProductionType,

PO:isProductionTypeOf some PO:UnitOfNAADSM,

PO:hasModelState only

(PO:ClinicalInfectiousState

or PO:LatentState

or PO:NaturallyImmuneState

or PO:SubclinicalInfectiousState

or PO:SusceptibleState),

PO:hasModelState exactly

1 PO:ClinicalInfectiousState,

PO:hasModelState exactly

1 PO:LatentState,

PO:hasModelState exactly

1 PO:NaturallyImmuneState,

PO:hasModelState exactly

1 PO:SubclinicalInfectiousState,

PO:hasModelState exactly

1 PO:SusceptibleState

3. An FMD course of infection in InterSpread Plus

model: It is deﬁned in the InterSpreadPlusSin-

gleProductionType class.

Class: PO:InterSpreadPlusSingleProduction-

Type

SubClassOf:

PO:ProductionType,

PO:hasModelState only

(PO:IncubationState

or PO:InfectiousState

or PO:NaturallyImmuneState

or PO:SusceptibleState),

PO:hasModelState exactly

1 PO:IncubationState,

PO:hasModelState exactly

1 PO:InfectiousState,

PO:hasModelState exactly

1 PO:NaturallyImmuneState,

PO:hasModelState exactly

1 PO:SusceptibleState

Similar to the FMD course of infection for

the FMD domain knowledge, descriptions of FMD

courses of infection for NAADSM and InterSpread

Plus are formally presented. They use the same vo-

cabularies to describe the states related to the FMD

course of infection. These models are different in the

way that the FMD course of infection is deﬁned as

discussed previously. The concepts of these models

are reﬂected via parameter settings aligned with the

FMD domain knowledge. Thus, we can leverage the

ontology structure to share and infer new knowledge

associated with the models.

3.7 Domain Meta-ontology Queries

There are nine competency question (CQ) queries

which are used to ask about classes associated with

animal unit states, production type, animal unit and

duration that are related to the states. They are pre-

sented in the section 3.7.1. In this table, we present

the CQs and the corresponding queries for domain

meta-ontology. The translations for the CQs are very

straight forward. Most of the time, they are self-

explanatory. In query 7, we ﬁlter other subclass

based on the super class DiscreteProbabilityDistribu-

tion since we use Poisson distribution as an example

for all duration of the states. We use the ﬁlter clause to

remove owl:Nothing from the set of answers because

owl:Nothing is a subclass of any class expression.

3.7.1 Domain Meta-ontology CQ’s and Queries

1. What all states do an FMD course of infection

have?

SELECT ?x WHERE {

?x rdfs:subClassOf po:ModelState .

FILTER(?x !=owl:Nothing)}

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2. What are subclasses of Incubation State?

SELECT ?x WHERE {

?x rdfs:subClassOf po:IncubationState .

FILTER(?x !=owl:Nothing)}

3. What are subclasses of InfectiousState?

SELECT ?x WHERE {

?x rdfs:subClassOf po:InfectiousState .

FILTER(?x !=owl:Nothing)}

4. What are subclasses of NonInfectiousState?

SELECT ?x WHERE {

?x rdfs:subClassOf po:NonInfectiousState .

FILTER(?x !=owl:Nothing)}

5. What are substates of InfectedState?

SELECT ?x WHERE {

?x rdfs:subClassOf po:InfectedState .

FILTER(?x !=owl:Nothing)}

6. What production types are captured in the ontol-

ogy?

SELECT DISTINCT ?x WHERE {

?x rdfs:subClassOf po:ProductionType .

FILTER(?x !=owl:Nothing)}

7. What durations are associated with a state?

SELECT DISTINCT ?t WHERE{

?x rdf:type po:ModelState .

?x po:hasMathematicalFunction ?y .

?y rdf:type ?t .

?t rdfs:subClassOf ?super .

?otherSub rdfs:subClassOf ?super .

?t rdfs:subClassOf ?otherSub .

FILTER (?otherSub != ?t)

FILTER (?super =

po:DiscreteProbabilityDistribution)}

8. What animal species concepts are captured?

SELECT DISTINCT ?x WHERE {

?x rdfs:subClassOf po:AnimalSpecies .

FILTER(?x !=owl:Nothing)}

9. What animal units are captured?

SELECT DISTINCT ?x WHERE {

?x rdfs:subClassOf po:Unit .

FILTER(?x !=owl:Nothing)}

3.8 Application of Meta-ontology

Queries

The queries related to the application of the meta-

ontology are to further test the meta-ontology, and its

objectives. We would like to be able to answer the

questions shown in section 3.8.1. We show queries

related to the NAADSM model. Similar queries work

with the InterSpread Plus model and the FMD domain

knowledge conceptual model. We include the com-

plete queries in the link previously provided.

3.8.1 NAADSM Application of Meta-ontology:

Competency Questions and Queries

1. What are individual states of NAADSM model?

PO:NAADSMModel(?m) ˆ PO:hasUnit(?m, ?u)

ˆ PO:hasProductionType(?u, ?pt)

ˆ PO:hasModelState(?pt, ?s)->

sqwrl:select(?s)

2. What is incubation state of NAADSM model?

PO:NAADSMModel(?m)

ˆ ParameterOntology:hasUnit(?m, ?u)

ˆ PO:hasProductionType(?u, ?pt)

ˆ PO:hasModelState(?pt, ?s)

ˆ PO:IncubationState(?s)->sqwrl:select(?s)

3. What is incubation durations means and variance

of a NAADSM model?

PO:NAADSMModel(?m1)

ˆ PO:hasUnit(?m1, ?u1)

ˆ PO:hasProductionType(?u1, ?pt1)

ˆ PO:hasModelState(?pt1, ?s1)

ˆ PO:IncubationState(?s1)

ˆ PO:hasMathematicalFunction(?s1, ?pd1)

ˆ PO:hasMeanValue(?pd1, ?mean1)

ˆ PO:hasVarianceValue(?pd1, ?variance1)

-> sqwrl:sum(?mean1)ˆsqwrl:sum(?variance1)

4. What are state concept differences between

NAADSM and Interspread Plus models?

PO:NAADSMModel(?m1)

ˆ PO:hasUnit(?m1, ?u1)

ˆ PO:hasProductionType(?u1, ?pt1)

ˆ PO:hasModelState(?pt1, ?ms1)

ˆ abox:caa(?class1, ?ms1)

. sqwrl:makeSet(?set1, ?class1)

. sqwrl:size(?size1, ?set1)

ˆ PO:InterSpreadPlusModel(?m2)

ˆ PO:hasUnit(?m2, ?u2)

ˆ PO:hasProductionType(?u2, ?pt2)

ˆ PO:hasModelState(?pt2, ?ms2)

ˆ abox:caa(?class2, ?ms2)

ˆ sqwrl:makeSet(?set2, ?class2)

ˆ sqwrl:size(?size2, ?set2)

ˆ sqwrl:difference(?set3, ?set1, ?set2)

ˆ sqwrl:size(?size3, ?set3)

ˆ sqwrl:element(?e3, ?set3)

-> sqwrl:select(?class1, ?size1,

?class2, ?size2, ?size3, ?e3)

3.9 Semantic Engine

The semantic engine is responsible for performing the

following two tasks:

• Parameter assessment

• Transformation of parameters from one model to

another

A Meta-ontology Framework for Parameter Concepts of Disease Spread Simulation Models

229

The parameter assessment and transformation can

be performed by leveraging the meta-ontology struc-

ture. Queries can be used to extract and evaluate con-

cepts with evidence in domain knowledge and other

models. These tasks can be machine driven. How-

ever, in the complex scenario, we can use an external

framework to assist with these tasks. For example,

we can use statistical framework to analyse the statis-

tical distribution related to the duration of a state. We

have constructed a small framework to illustrate these

tasks but will concentrate here in showing how we

use queries and rules to perform required tasks. Fur-

thermore, to demonstrate these tasks, we restrict our-

selves to state concepts of an FMD course of infection

to show the parameter assessment and transformation

tasks.

3.9.1 Parameters Assessment

To perform the parameter assessment, we need to per-

form the assessment of the state concepts of the sim-

ulation models with respect to the concepts of the

FMD domain knowledge model. We use the follow-

ing steps:

• Get state concepts that are aligned between pa-

rameters of the simulation models and the FMD

domain knowledge.

• Get the instances of the state concepts. Compare

the state instances or individuals of FMD domain

knowledge to those of the simulation model.

• Do the same for other aligned concepts.

The parameter assessment allows us to know the dif-

ference in parameter settings between the parameters

of the simulation models and the FMD domain knowl-

edge. We examined two cases:

• Case 1: NAADSM parameter assessment

– Assessment of latent state

– Assessment of sub-clinical infectious state

– Assessment of clinical infectious state

– Assessment of naturally immune state

• Case 2: InterSpread Plus parameter assessment

– Assessment of incubation state

– Assessment of infectious state

– Assessment of naturally immune state.

Given the knowledge base, we want to answer the

queries that are related to the assessment of param-

eters concepts related to simulation models.

• Simulation model parameter assessment queries

– Given the asserted state concepts individuals of

a simulation model and FMD domain knowl-

edge, can we ﬁnd the aligned concepts of the

two models?

– Can we infer and assess the duration of the state

concepts with respect to FMD domain knowl-

edge given the asserted individuals of the two

models?

3.9.2 Transformation of Parameters from One

Model to Another

To show how the transformation works for an FMD

course of infection, we need to discuss some concepts

in FMD domain knowledge that are used to describe

an FMD course of infection. An FMD course of infec-

tion description is based on primitive classes, deﬁned

classes and attributes. The primitive classes are used

to construct the deﬁned class. The deﬁned classes,

incubation, and infectious states, are deﬁned as:

• Incubation state is a state from infection to onset

infectiousness. It is a union of latent state and sub-

clinical infectious state.

• Infectious state is a state of infectiousness. It is a

union of sub-clinical infectious state and clinical

infectious state.

Without a disease control mechanism, an FMD

course of infection is related to the disease state con-

cepts. Because the NAADSM and InterSpread Plus

models are designed differently, the incubation, in-

fectious, and infected states are set differently. In

the NAADSM simulation model, there are explicit

states such as latent state, subclinical infectious state,

clinical infectious state and naturally immune state as

compared to the InterSpread Plus model’s states such

as susceptible and infected states (incubation state, in-

fectious state, immune state are explicit, and latent

state, subclinical infectious state, clinical infectious

state, and immune states may be implicit states). To

show how the domain meta-ontology can be used in

the parameter transformation of simulation models,

we examine how a parameter setting can be expressed

or transformed in terms of another model.

We examine the following case:

• Given a parameter set for the NAADSM model,

can we generate a semantically equivalent param-

eter set for the InterSpread Plus model or vice

versa?

In order to perform the transformation, we need to

deﬁne the transformation criteria and transformation

procedure.

Deﬁnition of Transformation Criteria.

Typically, a transformation criterion for parameters is

a number of concepts that are reﬂected in the simula-

tion models’ parameters. These concepts must exist

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in both source and destination simulation models for

a transformation to take place. If there are missing

concepts in the simulation models, the transformation

is not possible or might be possible with high uncer-

tainty due to the conceptual heterogeneity existing in

the simulation models.

Transformation Procedure.

There are two transformation procedures: Concepts-

based transformation procedure and missing concept

procedure.

1. Concepts-based transformation procedure:

• Get the concepts of source models.

• From the concepts, we can generate required

correspondent criteria concept parameters for

the destination simulation model’s parameters

with respect to source concepts.

2. Concepts-based transformation procedure with

missing concepts:

• Perform the concepts-based transformation for

aligned concepts of models as described above.

• With missing concepts, we can estimate or infer

missing concepts based on the concepts from

the source model’s parameters if it is possi-

ble to infer or estimate the destination settings.

With random estimation, these parameter set-

tings may have high uncertainty because of our

lack of knowledge, and it must then be left

for the users to decide if they wish to pro-

ceed with this level of uncertainty. We can use

FMD course of infection domain knowledge

that aligned with the source model to assist in

the transformation.

We examine the following cases for parameter

transformation:

Case 1: Parameter Transformation from

NAADSM Model to InterSpread Plus Model.

Let us set the criteria for the transformation as:

• Farm unit related concepts

• State concepts: Incubation state, infectious state,

immune state.

The NAADSM model can infer the incubation state,

infectious state, and naturally immune state from its

basic states.

• Incubation state can be obtained from latent state

and subclinical infectious state.

• Infectious state can be obtained from subclinical

infectious state and clinical infectious state.

• Naturally immune state can be obtained from its

state.

The incubation, infectiousness state, and naturally

immune state exist in InterSpread Plus. Thus, we can

transform from NAADSM to InterSpread Plus in this

case.

Case 2: Parameter Transformation from

InterSpread Plus to NAADSM. Using the same

criterion as in the previous case, however, the state

concepts are latent, subclinical infectious, clinical

infectious, and naturally immune states. In the In-

terSpread Plus model we can set the incubation state

and the infectiousness state of the FMD course of

infection by specifying these states in the following

forms:

• With infectiousness state, incubation state, im-

mune state.

• With user deﬁned latent state, infectious state, in-

cubation state, immune state and implicit clinical

infectious state and subclinical infectious state.

Figure 8: Disease state transition models for NAADSM and

InterSpread Plus without control measures.

The challenge in transformation from InterSpread

Plus to NAADSM is the missing concepts (latent,

sub-clinical, and clinical states) that are required in

the NAADSM model. This is depicted in Figure 8.

We examine the following cases:

• Case 2a: With latent state, and incubation state,

infectious state and naturally immune state it is

possible to transform into NAADSM parameter

setting because we can obtain the needed concepts

to construct NAADM’s parameters:

– Subclinical infectious state can be estimated

from incubation and latent states

– Clinical infectious state state can be estimated

with subclinical state and infectious state.

– Naturally immune state can be obtained from

the immune state

• Case 2b: With only infectiousness state and in-

cubation state, a transformation is not possible

A Meta-ontology Framework for Parameter Concepts of Disease Spread Simulation Models

231

because we cannot obtain the latent, subclinical

infectious, and clinical infectious states from in-

cubation and infectious states. Although we can

randomly generate the latent and sub-clinical du-

rations to match the incubation duration and the

sub-clinical and clinical durations to match the

infectious duration in InterSpread Plus, this will

generate high uncertainty due to lack of knowl-

edge.

In summary, the deﬁnition of criteria for parame-

ter transformation is dependent on a number of con-

cepts that are reﬂected in the parameters’ settings.

• Concepts must exist in both models. It is a condi-

tion for a transformation to take place.

• With missing concepts, we can perform the pa-

rameter transformation as described in a transfor-

mation procedure with uncertainty.

4 CONCLUSIONS

In this paper, we propose the use of a meta-ontology

framework to capture the semantics of parameters and

related domain knowledge associated with an FMD

course of infection in animal disease spread simula-

tion models. It permits parameter knowledge sharing,

parameter assessment and parameter transformation

between models. Our motivation for this approach

is to minimize the ambiguity that exists in parame-

ter settings and allow a standard way to describe pa-

rameter settings and the related domain knowledge.

It promotes the interoperability between simulation

models, and the ability to assess domain knowledge.

By explicitly describing parameter knowledge and es-

tablishing the linkage between parameters and doc-

umented domain knowledge, this allows us to have

an understanding of the differences between different

models’ parameters and views of the domain knowl-

edge. It strives to provide a basis for a new way to

understand and assess parameter and related views of

domain knowledge. The central piece of this work is

the focus on the meta-ontology framework construc-

tion in capturing the semantics of the parameters, the

related FMD course of infection domain concepts and

assisting in the assessment and the transformation of

parameters between models. This work reports on a

novel ontological organization that separates domain

knowledge from the knowledge about the parameters

in different comparable simulation models and for-

malizes a relationship between parameters by linking

to the domain knowledge part of the ontological struc-

ture. It allows explicit knowledge representation, a

means to compare animal disease spread simulation

models and a means to evaluate views (as expressed

in parameters) related to simulation models and do-

main knowledge. This work also acknowledges the

limitations in ontology creation. It is a time consum-

ing process that requires great effort and collaboration

of a number of experts in different domains. In gen-

eral, without experts’ assistance, parameter settings

alone are not sufﬁcient to account for the differences

between the models’ parameters due to differences in

parameter representation of the models and their as-

sumptions. The introduction of an ontology provides

a standard means to document and describe the views

of simulation models and views of the domain knowl-

edge. These views are built from ontological concepts

that are reﬂected by the parameters, their semantics

and related domain knowledge. The ability to cap-

ture conceptual relations, properties and the ability

to verify the consistency of the ontology allows facts

related to parameter settings to be assessed not only

with other simulation models but also to the related

domain knowledge.

In future work, we hope to extend our ontological

concepts to other domains and to extend the number

and types of tasks that our semantic engine can per-

form including validation of requirements, compari-

son of concepts between related ontologies, and the

transformation of concepts and values between on-

tologies. We anticipate that these extensions will ﬁnd

use in many domains where there is a need to compare

and reconcile competing ontologies.

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