POPH90271: Infectious Disease Modelling and SARS Outbreaks Report

This report critically evaluates two academic studies, Gumel et al. (2004) and Chowell et al. (2003), which employed infectious disease modeling to understand and control SARS outbreaks. The report explores the primary questions addressed by both papers, focusing on the impact of patient isolation and quarantine as mitigation strategies. It delves into the use of deterministic models in predicting disease outcomes and the importance of incorporating factors like patient demographics and biological parameters. The report compares the models' approaches to incorporating current disease knowledge, including the role of zoonotic origins and transmission modes. Similarities and differences in the studies' literature reviews and model designs are highlighted, along with the limitations of each model, such as the absence of detailed stochastic models and complete diagnostic information. The analysis concludes by summarizing the main purposes and findings of each study, emphasizing how they complement each other in advancing the understanding of SARS and informing public health interventions.

Running head: INFECTIOUS DISEASE MODELLING
INFECTIOUS DISEASE MODELLING
Name of the Student:
Name of the University:
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Introduction
The process of ‘Infectious Disease Modeling’ implies the usage of mathematical steps of
process as an attempt to predict the most probable functions underlying the outbreak of a disease
outbreak or epidemic (Briggs et al., 2016). An epidemiological model for infectious diseases
assists in the development of public health interventions and educational strategies for the
purpose of alerting the public as well as health professionals on the prevention and management
of future outbreaks of the same (Rousseau et al., 2016). The following paper will hence aim to
critically explore and evaluate the underlying components of the infectious disease models
utilized by two academic studies – that by Gumel et al., (2004) and Chowell et al., (2003),
respectively.
Discussion
Background and Purpose
Primary Question: Upon evaluating the studies by Gumel et al., (2004) and Chowell et
al., (2003), it is evident that both papers are seeking to define mechanisms of transmission and
associated demographics of the affected population which acted as the key determinants
underlying the rapid outbreak of SARS across numerous countries. Thus taking insights from the
same, it can be stated that the specific primary question addressed by both papers include an
understanding of the impact of isolation of patients as a key mitigation strategy aimed at
controlling outbreaks of SARS in 2003 (Chowel et al., 2003; Gumel et al., 2004). However, the
research by Gumel et al., (2004), also specifically evaluates the impact of quarantine, in addition
to isolation for controlling SARS outbreaks respectively.

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As discussed by Salcedo and De Lara, (2019), the purpose of mathematical models of
infectious diseases, comprises of development of predictive models which not only pave the way
for formulation of future public heath interventions but also allow concise and objective
identification and inclusion of a large amount of data on individual risk and symptomatic factors
determining a disease outbreak. Thus, as evidenced by Andrianakis et al., (2017), a mathematical
model is required to answer the identified primary question considering its ability to design
future preventive public health interventions which are holistic, comprehensive and take into
consideration multiple patient demographic factors.
The paper by Gumel et al., (2004) seeks to address the dynamics underlying the
transmission of SARS and its role in the outbreak as well as prevention of disease across diverse
individual factors, such as individuals who are susceptible, have been quarantined, recovered and
isolated or are symptomatic towards SARS. Thus, along with the estimation of disease outcomes
and transmission parameters the model by Gumel et al., (2004) greatly emphasizes transmission
changes within the SARS outbreak as individual demographics transition from those who are
susceptible to those who have been quarantined. This implies the usage of a deterministic model
within the study by Gumel et al., (2004), as stated within the study by the authors, for the
purpose of predicting or determining factors enhancing or containing SARS transmission.
Similarities are also observed across in the model used by Chowel et al., (2003), which states to
answer the primary question regarding whether an outbreak of SARS can be contained taking
into account individual patient parameters such as susceptibility, disease exposure,
infectiousness, diagnosis and recovery along with interventions like patient isolation. Thus, it can
be implied that the infectious disease model adopted by Chowel et al., (2003), not only takes into
consideration the role of individual patient parameters in disease transmission but also used the

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same for greater emphasis on development of a predictive model for future prevention of SARS.
While both paper state their usage of a deterministic model, differences can be observed in
Gumel et al., (2004), which specifically addresses the effectiveness of isolation as well as
quarantined for SARS outbreak mitigation. A deterministic model is characterized by the
compartmentalization of populations across different groups, representative of various disease
stages along with their key characteristics expressed as derivatives, mathematically (Blackwood
& Childs, 2018). Both papers by Chowel et al., (2003) and Gumel et al., (2004) seek to define
the effectiveness of SARS control across groups of populations who have been isolated and
quarantined during stages of infection and symptom presentation. To answer this primary
question, a deterministic model is the most appropriate since it allows for the study of disease
outcomes as it progresses through stages represented by groups of populations (Blackwood &
Childs, 2018).
It has been evidenced by de Wit et al., (2016), that the biological host parameters
underlying the widespread transmission of SARS comprise of direct contact practices like
shaking of hands and sharing of personal items as well the airborne mechanisms associated with
direct inhalation of droplets from infected individuals. Thus, as researched by Vijay and Perlman
(2016), preventive interventions are likely to include contact precautions where patients are
isolated or where individual engage in hand hygiene and usage of protective clothing like nose
masks. Upon evaluating the study by Gumel et al., (2004), it can be observed that the chosen
deterministic model predicts associations between disease outcomes and preventive procedures
like effective reduction of rate of contact and stringent adherence to hand hygiene measures
across patients who are isolated rather than emphasis on biological parameters within the host.
Thus, it can be implied that the model evaluated by Gumel et al., (2004), predicts the probable

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outcome of the implementation of preventive disease public health project. In comparison, taking
insights from the study by Chowel et al., (2003), it can be observed that the chosen deterministic
model first emphasizes on the influence of biological parameters like the age, genetics, rate of
contact on the transmission dynamics of SARS outbreaks across individual nations like Hong
Kong, Toronto and Singapore, which is distinctive as considering the absence of the same in the
model by Gumel et al., (2004). However, similar to Gumel et al., (2004), the model developed by
Chowel et al., (2003), ultimately directs these patient parameters to the determination of the
impact of preventive measures like timely diagnosis and isolation of infected patients. Thus,
similar to Gumel et al., (2004), the deterministic model developed by Chowel et al., (2003),
attempts to answer or predict answers to questions associated with the implementation of
preventive measures in a public health disease project. New models have been adopted by the
researchers because of their adherence to compartmentalised, deterministic models in
understanding the disease epidemiology of SARS. Biological parameters are vital for predictive
disease risk but are not appropriate on their own to determine how a disease progresses across
populations and how it may be controlled when specific mitigation strategies are implemented
across these disease progress ‘stages’(or population groups) (Briggs et al., 2016). A deterministic
model, with less emphasis on biological parameters is hence relevant for understanding the
impact of isolation and quarantine in SARS control my Chowel et al., (2003) and Gumel et al.,
(2004).
Current Knowledge:Upon comparing the available scientific evidence reviewed by both
papers, similarities as well as key differences can be observed in both models formulated by
Gumel et al., (2004) and Chowel et al., (2003). A key distinction which initially draws attention
is the prevalence of research on the origins of the SARS virus reviewed by Gumel et al., (2004),

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which is absent however, in the paper by Chowel et al., (2004). Indeed, is discussed by the
Gumel et al., (2004), as well as by Yang et al., (2016), SARS is a zoonotic disease which is
likely to have originated from a coronavirus existing in animals, which is why difficulties are
encountered within the immunological defence mechanisms of humans thus resulting in an
inability to combat or recover a cure for this disease. The role of zoonotic origins of SARS have
also been similarly incorporated in the deterministic model used by Gumel et al., (2004), in the
form of parameter ‘p’, denoting infiltration of infection travellers as well as zoonotic carriers
denoting animal-to-human transmission and thus, increase in the number of infected individuals
within the population. The literature reviewed by the Gumel et al., (2004) and Chowel et al.,
(2003) does demonstrate some similarity in terms of their review on evidence indicating the
mode of transmission characteristic of the SARS virus. Indeed, it has been reviewed by both
papers as well as evidenced by Weber et al., (2016), that the epidemiological transmission of
SARS is strongly associated with droplet and individual-to-individual based contact transmission
comparison of inhalation of ingestion of infected droplets. The resultant respiration of such
infected particles comprises of pneumonic symptoms of coughing, respiratory distress, fever and
even death after an incubation of approximately 3 to 17 days – which has been reviewed by both
studies by Gumel et al., (2004) and Chowel et al., (2003).
Further evaluation also reveals a key difference between the studies by Gumel et al.,
(2004) and Chowel et al., (2003) in terms of patient as well as intervention factors underlying
SARS transmission. As evidenced by the Gumel et al., (2004), as well as by Liu et al., (2016),
the transmission of SARS is largely dependent upon deficiencies in contact precautions across
patients and is hence, is greatly enhanced due to lack of usage of protective masks or apparel,
lack of awareness on preventive measures as well as absence of hygiene practices across

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healthcare workers. The deterministic model by Gumel et al., (2004), incorporates the role of
hygiene within its deterministic model using the parameter eQ > 0, which demotes hygiene
precautions adopted during various stages of disease. There is no inclusion of such a parameter
in the model by Chowel et al., (2003), and instead, rates of contact have only been incorporated
as a ‘crude’ measurement by the authors. In comparison however, while the paper by Chowel et
al., (2003) largely misses out on such critical epidemiological information, the paper does
demonstrate essential information on the role of personal factors like old age and the prevalence
of history of cardiovascular and hepatic conditions in the rapid transmission of SARS across
populations. The model by Gumel et al., (2004) does not include these factors except for the
measurement of ‘age days’ from exposure to quarantine and symptom to isolation. While
Chowel et al., (2003), does not consider old age in its model, it is done so as a crude
measurement and hence, is indicative of incomplete information. Thus, taking insights from the
above comparison on review of literature, it can be estimated that both the studies by Gumel et
al., (2004) and Chowel et al., (2003) provide comprehensive information on the various
causative and epidemiological causative factors underlying the transmission of SARS such as
symptoms, transmission and incubation periods. However, several missing components of
essential epidemiological information are observed across both the papers - which can be
considered a key limitation in terms of lack of comprehensive information and hindrances in
understanding for readers who may otherwise be new to the disease of concern. Another key
limitation observed across both papers is lack of comprehensive information on SARS using
detailed stochastic models. However, both studies have been published at time when SATS
outbreak was relatively new as compared to the extensive information available at present, and

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thus, the reasons for absence of inclusion of updated, comprehensive information in the form of
novel models is understandable.
Another key information which is missing and is of concern across the models adopted
by both the papers is the prevalence of incomplete information on the diagnostic components of
SARS. Both the studies by Gumel et al., (2004) and Chowel et al., (2003) shed light on the
importance of timely and prompt diagnosis in the management and control of transmission of
SARS. However, none of the papers provide any specification as to what type of diagnosis of the
type of diagnostic procedures may be helpful in the timely and accurate identification of SARS –
thus demonstrating a major limitation in terms of missing information. While such information
may not be of relevance as per the authors’ stated research question, the field of disease
epidemiology aims to cover complete, detailed information on a disease and its characteristics
and thus could have been added briefly in the review for comprehensiveness (Liu et al., 2016).
Indeed, it has been postulated by the World Health Organization (WHO, 2019), that an
individual must present multiple symptomatic and clinical evidence cues in order to be
diagnosed with SARS. These include: a prolonged state of fever or elevated body temperature of
38C, prevalence of respiratory illness associated symptoms such as chest tightness, coughing,
breathing difficulties, a radiography based report postulating a presence of pneumonia and the
lack of any alternative forms of illness which may be useful for complete understanding or
diagnosis of the pneumonia-like illness present in the patient (WHO, 2019).
Model Design
Type of Model:Upon extensive reading, it can be observed that both papers have adopted
infectious disease models of the compartmental and deterministic type. A compartmental model
of infectious disease epidemiology is a simplified and segmented version of a mathematic

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predictive model and is characterized by segregating a population of group of individuals into
various groups, for better understanding the transmission of a disease (Roosa &Chowell, 2019).
A prevalent compartmental model is the SIR model where the transmission of a disease is
predicted based on individuals who susceptible, infectious or have been immunized or recovered
(Blackwood & Childs, 2018). Indeed, a variation of this compartmental model is observed to be
adopted in the SEIJR model by Chowel et al., (2003), where the transmission dynamics of SARS
have been predicted based on populations who have been susceptible, exposed, infective,
diagnosed and patients who have been recovered. Similar usage of compartmental models has
been demonstrated in the model by Gumel et al., (2004), where the transmission of disease has
been predicted and determined by compartmentalizing the population into susceptible,
asymptomatic, quarantined, symptomatic, isolated and recovered. Thus, in this case, considering
that compartmental epidemiological models assistsin predicting the parameters underlying the
transmission of a disease, selecting such a model by both Gumel et al., (2004) and Chowel et al.,
(2003) is a highly appropriate choice for understanding and determining the dynamics of
transmission and future prevention of SARS outbreaks. Further, it must be remembered that
compartmental models are beneficial in predicting characteristics of disease progression, its
duration and prevalence and how various control parameters may impact these disease
characteristics (Roosa & Chowell, 2019). Considering the same, usage of a deterministic model
is highly appropriate since the models by Gumel et al., (2004) and Chowel et al., (2003) aim at
determining the impact of isolation and quarantine population compartments on the progression
of SARS outbreak.
Similarly, both models used by Gumel et al., (2004) and Chowel et al., (2003)
demonstrated the usage of deterministic models of infectious disease epidemiology. A

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deterministic disease model is characterized by segregating the population into numerous groups
representative of epidemic stages, for the purpose of studying or ‘determining’ variations in the
rates of transmission of disease as it transitions from one stage to another (Rachaniotis,
Dasaklis&Pappis, 2017). In the case of both the models by Gumel et al., (2004) and Chowel et
al., (2003), it is clearly evident that both papers have divided their chosen populations into
groups to determine factors influencing the impact of SARS transmission and casualties. A
stochastic model comprises of identifying probable outcomes of a disease based on differential
patient variables (Cai, Kang & Wang, 2017). While a stochastic model may seem to have been
appropriate for usage considering the various patient characteristics studied – a deterministic
model chosen by Gumel et al., (2004) and Chowel et al., (2003) is the most appropriate
considering its relevance in answering research questions on determining the impact of patient
isolation and diagnosis on disease transmission. Deterministic models are useful for studying
stages of disease epidemiology across a large population by compartmentalising in groups
(Rachaniotis, Dasaklis & Pappis, 2017). The models used by Gumel et al., (2004) and Chowel et
al., (2003) were fitted as per data obtained from three global SARS outbreaks impacting large
populations, which is why adoption of deterministic models were most appropriate.
Population heterogeneity: It is a worthwhile to note that the transmission of a disease is
not just limited to the biological factors within a pathogen but also within demographic
characteristics of a patient like age, gender and history of illness (Miao et al., 2017). Thus,
consideration of patient heterogeneity is of utmost importance during infectious disease
modeling since it paves the way for a holistic and comprehensive public health intervention plan
for disease prevention (Cai et al., 2018). Thus, in case of population heterogeneity, a major
limitation can be observed in both the deterministic models adopted by Gumel et al., (2004) and

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Chowel et al., (2003). The deterministic model adopted by Gumel et al., (2004) clearly
demonstrates a lack of consideration of age structure as well as spatial distribution in
determining the impact of diagnosis and isolation in SARS prevention. In comparison, while the
paper by Chowel et al., (2003) attempts to incorporate patient age in the crude manner during
segregating patients into highly susceptible and less susceptible groups, still does not
comprehensively address patient heterogeneity. A key advantage can be observed in the model
by Gumel et al., (2004) in its incorporation of environmental exposure underlying SARS
outbreak by determining the role of rate of infection exposure, which is absent in the model by
Chowel et al., (2003). While the adoption of a deterministic model by both Gumel et al., (2004)
and Chowel et al., (2003) allowed the effective stratification of population into several groups,
perhaps adopting a stochastic, individual disease model would have allowed for inclusion of
population variables and a result, consideration of population heterogeneity in SARS outcomes
(Manogaran& Lopez, 2018). While the both models (Gumel et al., 2004; Chowel et al., 2003)
provided detailed information on the impact of SARS outbreaks, it must be noted that patient
responses to such strategies are largely influenced by personal factors. Elderly individuals
demonstrated delayed responses to disease prevention and management interventions due to the
age associated physiological impacts (Miao et al., 2017). Thus, despite sufficiently answering the
research question, inclusion of such individual patient complexities would have provided a better
understanding on exactly how effective are isolation and quarantine strategies in controlling
SARS across various demographic groups of the population. In addition to age, inclusion of
heterogeneities like adherence to hygiene and protective equipment usage, risk of exposure for
healthcare workers as well as risk of exposure and disease transmission from infected individuals

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to the general community would have proved to be beneficial considering the role of contact in
SARS transmission (Weber et al., 2016).
Model Implementation
Uncertainty:Taking insights from the models adopted by Gumel et al., (2004) and
Chowel et al., (2003), an absence of adequate implementation of efforts in addressing model
uncertainties. In the paper by Gumel et al., (2004), the authors have clearly stated the intentional
usage of a single, simple deterministic model for the purpose of preventing inaccuracies due to a
large sclar of patient uncertainty. Indeed, it has been evidenced that uncertainties in the form of
agents responsible for super-spreading of a disease comprises of a very minor fraction of disease
epidemiology which is why inclusion of multiple variables may result in predictive inaccuracies
(DuintjerTebbens& Thompson, 2018). On the other hand, to address uncertainties, the model by
Chowel et al., (2003) attempts to compare multiple disease outbreak scenarios across Toronto,
Hong Kong and Singapore along with an inclusion of heterogeneous factors like age, albeit in a
crude fashion.
Sensitivity Analysis :Further, taking insights from the analytical approach adopted by
both Gumel et al., (2004) and Chowel et al., (2003) it can be observed that both models either
omitted or discussed components of a sensitivity analysis without specifying the same. While the
model by Chowel et al., (2003) did not incorporate a sensitivity analysis, it does assess
sensitivity of outcomes of the model based on changes in isolation effectiveness and rates if
diagnosis. The model by Gumel et al., (2004) does assess a two way sensitivity in terms of
impact on reduction of contact rate of isolated individuals rate on disease control - the authors
do not specifically name this as a sensitivity analysis. Incorporation of uncertainty variables in a
disease model is helpful for the purpose of development of a comprehensive public health