read a scientific paper on a topic of your choice from the mathematical biology literature. Computationally implement the model in the paper and extend the paper’s results. Your extension may be mathematical or computational. Prepare a presentation of the paper and your extensionProposals. Due on Thursday, Mar. 27, or sooner: • What are you planning to do? Specifically, what paper are you planning to read, and how are you planning to extend the model? What question(s) do you plan to investigate? (1 – 3 sentences is fine.)Progress Report. Due Thursday, April 2, or sooner: • Report progress on model development and simulation, data/model parameter estimation, analysis, and model interpretation/conclusions • What have you completed? What is your next step? • What is your role (if part of a group project)?Final paper due April 51. Kajita E, Okano JT, Bodine EN, Layne SP, Blower S. Modelling an outbreak of an emerging pathogen. Nat Rev Microbiol. 2007 Sep;5(9):700-9I prefer the paper in the top but there are more then 40 different papers you can choose any of them and I can send you the paper if you give me the number of itI’ll attach the first paper for nowalso, I have attached the guidelines for the paper please check
a_guide_to_research_papers.pdf
final_project_guidelines_part_1.pdf
kajita__3_.pdf
final_project_guidelines_part_2_1_.pdf
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A Guide to Research Papers
Questions
1. What is the hypothesis of the paper?
2. How do the authors evaluate their hypothesis? (Methods)
3. What are the findings of the paper? (Results)
4. What are the implications of their findings? What does this paper contribute that hasn’t been
known before? (Discussion)
Sections of a research paper
Abstract
• Not necessarily a summary of paper
• The main point from each of the following sections is abstracted here
• This section is supposed to contain answers to the questions above but often it is too
dense to be understood. This is because publishers impose word limits on abstracts
and/or the paper is too complex to be summarized so briefly.
• Skimming the abstract can provide a rough guide to the idea of the paper
Introduction
• Provides brief background of paper
• Introduces hypothesis
• Provides the context for the questions addressed
• Provides the motivation for the paper
• Often contains a summary of the approach used by the authors to reach solution and/or
an outline of the solution
Methods
• Describes approach taken in the paper to address the hypothesis
• Contains the necessary details (sometimes cryptic) required to understand the
methodology
• Sometimes mathematical models are located in an Appendix
Results
• States outcomes of paper
• Provides text for the results that are shown graphically in the figures of the paper
Discussion
• Conclusions of paper
• Recap
• Summarizes contributions of the paper to the field
• Discusses implications of the work
• Includes relevant related work in the field and the future work to be done in the area
References
• Never omit this section
Tips for Biological Research Papers
Experimental biologists construct their papers by asking themselves “What figures will best show
my results?” Therefore a good way to get an idea of the accomplishments of an experimental
paper is to first skim the figures and read the figure legends. Each figure may not be clear
without completely reading the rest of the paper, but this will give an idea of what the authors
are trying to communicate to you. This is not always true for a modeling paper, however, since
the results of modeling papers often come from mathematical analysis and are not best shown
graphically.
Math 340/Biol 340
Spring 2019
Final Project – Part 1
For your final class project, read a scientific paper on a topic of your choice from the
mathematical biology literature. Computationally implement the model in the paper
and extend the paper’s results. Your extension may be mathematical or computational.
Prepare a presentation of the paper and your extension.
You may work individually or in groups up to 3 people. Check your idea with me
before beginning. You may prepare a written report instead of an oral presentation if
you prefer (~ 6 pages including figures, single spaced; longer if there is more than one
person in your group).
A list of papers (journal articles) will be provided soon. You may also choose your own
article in an area of mathematical biology. Please do not choose the following:
•
papers involving only statistical analyses of data (these can be interesting, but the
aim of this project is to focus on modeling)
•
review papers (these present a review of a field or subarea rather than a unique
contribution to the field)
Possible project extensions include
•
•
•
•
•
exploring an aspect neglected by the paper
gathering data
improving the analysis in a creative way
completing stability analysis if applicable
changing terms in the model to see how they affect results and/or running the
model with different parameter values and/or initial conditions than those
investigated by the paper
Be sure to summarize your results and draw conclusions to answer the specific
questions you are asking.
Section III (chap. 9-10) of the de Vries et al. text contains sample projects and ideas.
Computational programs you may want to use include Excel, Maple, Matlab,
Mathematica, or Berkeley Madonna.
Analysis
Modelling an outbreak of an
emerging pathogen
Emily Kajita*‡, Justin T. Okano*, Erin N. Bodine*, Scott P. Layne‡ and Sally Blower*
Abstract | To illustrate the usefulness of mathematical models to the microbiology and
medical communities, we explain how to construct and apply a simple transmission model
of an emerging pathogen. We chose to model, as a case study, a large (>8,000 reported
cases) on-going outbreak of community-acquired meticillin-resistant Staphylococcus aureus
(CA-MRSA) in the Los Angeles County Jail. A major risk factor for CA‑MRSA infection is
incarceration. Here, we show how to design a within-jail transmission model of CA‑MRSA,
parameterize the model and reconstruct the outbreak. The model is then used to assess the
severity of the outbreak, predict the epidemiological consequences of a catastrophic
outbreak and design effective interventions for outbreak control.
Catastrophic outbreak
An extremely large outbreak in
a confined population that may
be caused by the synergistic
interaction of two processes: a
high level of transmission and a
large inflow of infectious
individuals into the
transmission site.
Prevalence
The number of infected
individuals at a specific time.
*Semel Institute of
Neuroscience & Human
Behavior & Department
of Psychiatry, UCLA AIDS
Institute, David Geffen School
of Medicine at UCLA,
1100 Glendon Avenue PH2,
Los Angeles, California 90024,
USA.
‡
Department of Epidemiology,
School of Public Health, UCLA,
Los Angeles, California 90024,
USA.
Correspondence to S.B.
e-mail:
[email protected]
doi:10.1038/nrmicro1660
Mathematical models of infectious disease dynamics
— transmission models — have become valuable tools for
understanding the dynamics of outbreaks and epidemics,
designing effective interventions and making informed
health policy decisions1. The first mathematical model
was published in 1766 by Daniel Bernoulli2. The main
purpose of Bernoulli’s mathematical analysis was to influence public health policy by quantifying the populationlevel benefits of universal inoculation against smallpox2,3.
Since then, the analysis of simple transmission models has
often been shown to provide important and non-intuitive
insights into the dynamics of infectious diseases. Simple
models have been used as ‘building blocks’ to develop
more elaborate complex models that have been analysed
using sophisticated mathematical and computational
techniques. In this Review, we show how to construct
and analyse a simple transmission model of the outbreak
dynamics of an emerging pathogen. We use, as an illustrative example, an outbreak of community-acquired meticillin-resistant Staphylococcus aureus (CA-MRSA). Strains of
CA‑MRSA have recently emerged, and one of the major
risk factors for CA‑MRSA that has been identified is incarceration4. Here, we demonstrate how to use modelling to
understand a large (8,448 cases were reported between
2002 and 2005 (Ref. 5)) on-going outbreak of CA‑MRSA
in the Los Angeles County Jail (LACJ). We show how to
design a within-jail transmission model, parameterize
the model and use it to reconstruct the outbreak. We also
show how to use the model to: first, assess the severity
of the outbreak; second, predict the epidemiological
consequences of a catastrophic outbreak; and, third, design
effective interventions for outbreak control.
700 | September 2007 | volume 5
The epidemiology of CA‑MRSA
CA-MRSA is an emerging pathogen that is currently a
great public health concern, as the prevalence of CA‑MRSA
infection is increasing in many communities6. Until the
mid‑1990s, MRSA was primarily linked to hospitals and
nursing homes and was termed hospital-acquired MRSA
(HA-MRSA)6–7. However, over the past decade new
strains of MRSA have evolved in the community; these
CA‑MRSA strains have substantial genetic, microbiological and clinical differences compared with the HA‑MRSA
strains8–18. Whereas HA‑MRSA strains cause morbidity
and mortality primarily in hospitalized patients, infection
with CA‑MRSA strains has caused the deaths of otherwise healthy individuals16,19,20. Outbreaks of CA‑MRSA
have occurred in communities of men who have sex
with men, homeless populations, inmates in correctional
facilities, military recruits, competitive sports teams and
children in day-care centres4,11. Outbreaks of CA‑MRSA
have also recently been reported in hospitals4,11.
Over the past decade, many mathematical models of
the transmission of HA‑MRSA in hospitals have been
developed21–34, beginning with the first model by Sebille
and colleagues31,32. Strains of HA‑MRSA are transmitted between patients, between healthcare personnel and
between healthcare personnel and patients. Therefore,
some of the HA‑MRSA models that have been developed
are complex, as they model specific mixing interactions
between patients and healthcare personnel. In general,
these transmission models have been formulated and analysed in order to understand the transmission dynamics
of HA‑MRSA within a hospital or within an intensive care
unit (ICU); these models have generally been theoretical
www.nature.com/reviews/micro
© 2007 Nature Publishing Group
A n a ly s i s
Reducing the contact of nurses
with a large group of patients
by assigning specific groups of
nurses to the care of only a
subset of patients. This
intervention reduces the
interaction of nurses with
patients and is therefore
expected to reduce nurse–
patient transmission.
Title 15
Title 15 deals with
“Miscellaneous Crimes” and is
part of the California Penal
Code.
Incidence
The number of newly infected
individuals per unit of time.
and not based on data. The results of these studies have
been used to suggest theoretical intervention strategies
for reducing HA‑MRSA in hospitals or ICUs21,22,24,25,27,28,31.
Suggested intervention strategies have been in the form of
recommendations for healthcare personnel and have
mainly focused on suggesting increases in the levels of
both nurse cohorting and hand washing27,28. Transmission
models have also been linked with economic analyses to
determine the cost-effectiveness of specific interventions
in hospitals33.
Hospitals and long-term-care facilities are obviously the foci for the transmission of HA‑MRSA but
not for CA‑MRSA; it is currently unknown which
locations are high-transmission sites for CA‑MRSA.
Recently it has been proposed that correctional facilities might be important sites for the transmission of
CA‑MRSA4,35–39 as inmates have poor access to medical care, crowded living conditions and suboptimal
hygiene40–42. Furthermore, it has been suggested that
these facilities could be accelerating the progression
rate of CA‑MRSA by limiting access to soap, showers and clean clothes7. According to Title 15 requirements in California, it is only required that inmates
be offered showers three times a week and be given
two pairs of underwear and one jumpsuit per week.
Approximately two million adults in the United States
are currently confined in correctional facilities. Large
outbreaks of CA‑MRSA have been reported in prisons and jails in California, Texas, Missouri, Georgia
and Mississippi8,35,40,41,43. The 3,365 jails in the United
States house fewer inmates than do prisons, but jails
have a higher turnover rate and receive the majority
of the admissions to correctional facilities (approximately ten million adults per year). Thus, it has been
suggested that jails could be an extremely important
contributing factor to the rising number of CA‑MRSA
infections in certain communities4,35. The transmission of CA‑MRSA between jails might also be occurring38. It is also possible that, in certain locations, the
rising epidemic of CA‑MRSA in the community is an
important contributor to jail outbreaks.
Modelling an outbreak of CA‑MRSA
Transmission models can be used to analyse an outbreak
in a specific location to: identify whether the outbreak site
is a transmission ‘hot spot’; to predict if the outbreak is
likely to develop into an epidemic; and to design effective
outbreak-control strategies. To illustrate and apply these
modelling concepts, we will show how to use a model to
analyse an ongoing outbreak of CA‑MRSA in the LACJ,
which is the largest jail in the world. The LACJ houses
~165,000 inmates per year and contains ~20,000 inmates
at any given time. This jail is currently experiencing one
of the largest outbreaks of CA‑MRSA seen so far in any
correctional facility37. The outbreak began in 2001 when
inmates began to complain of skin lesions caused by ‘spider bites’; starting in September 2001, all reported bites
were cultured. In subsequent months the jail screened the
facilities, ensured that pest-control measures were in place,
fumigated many facilities and tested spiders. The spiders
were found to be harmless, yet the number of infections
nature reviews | microbiology
continued to increase and the jail subsequently reported
the outbreak to the Los Angeles County Department
of Health Services (LACDHS)37. In August 2002, the
LACDHS recommended standardizing surveillance, treatment and infection-control protocols. At the beginning of
October in the same year physicians at the LACJ began to
take cultures from all inmates with skin lesions.
The outbreak in the LACJ grew exponentially during
the initial stage of the outbreak, from January 2002 to
September 2002; over this time period 628 clinical infections from skin lesions and the bloodstream were found
(565 in male inmates (FIG. 1) and 63 in female inmates).
During this period of exponential growth the incidence
in the women’s facility increased almost twice as fast
— with a doubling time of 6.5 months (95% confidence
interval (CI): 5.1–7.9 months) — as the incidence in the
men’s facility. In the men’s facility there was a doubling
time of 11.6 months (95% CI: 8.0–15.2 months)36. The
outbreak continues and, to date, more than 8,000 infections have been reported.
Constructing a transmission model of a CA‑MRSA
outbreak. Transmission models can be constructed
to be either deterministic or stochastic. Deterministic
models adequately predict epidemic dynamics in large
populations, where the effect of chance events is small.
Stochastic models, however, can be used to predict the
dynamics of outbreaks in small populations, where
chance events can have major effects. Both deterministic and stochastic models are reasonably straightforward
to analyse numerically. However, simple deterministic
models are much easier to analyse mathematically than
their stochastic counterparts. Therefore, we will first
construct a deterministic transmission model, and then
use a stochastic version of the same model to reconstruct
the temporal dynamics of the outbreak in the LACJ.
To construct a simple deterministic model that
describes the dynamics of an infectious disease it is
necessary to first understand the dynamics of the host
population, the important transmission processes that are
driving the outbreak and the biology of the pathogen. This
information can be determined by studying the demography of the system (for example, the correctional facility
600
500
Cumulative incidence
Nurse cohorting
400
300
200
100
0
Jan
Feb
Mar
Apr
May
June
July
Aug
Sep
Month
Figure 1 | Cumulative incidence of communityacquired meticillin-resistantNature
Staphylococcus
aureus in
Reviews | Microbiology
males in the Los Angeles County Jail from January
2002 to September 2002.
volume 5 | September 2007 | 701
© 2007 Nature Publishing Group
A n a ly s i s
a
Community
Inflow of
susceptibles
Inflow of
colonized
π(1 – γC – γI )
Colonization owing
to transmission
Susceptible
(S)
Inflow of
infected
πγC
πγI
Progression
to infection
Colonized
(C)
cβC S C + cβ I S I
N
N
Infected
(I)
pφC
Decolonization
αC
Outflow of
susceptibles
δS
δC
Outflow of
colonized
Outflow of
infected
δI
Community
b
dS
dt
= π (1 – γC – γΙ )
+
Inflow of
susceptibles
dC
dt
=
πγC
dt
=
πγI
Inflow of
infected
–
+
cβC CS
N
+
Colonized by
a colonized
individual
+
pφC
Progession to
infected from
colonized
cβC CS
N
–
cβI IS
N
Colonized by
an infected
individual
–
cβI IS
N
–
Colonized by
an infected
individual
Colonized by
a colonized
individual
Decolonization
Inflow of
colonized
dI
αC
–
αC
Decolonization
δS
Exiting the jail
–
pφC
Progression to
infected from
colonized
–
δC
Exiting the jail
δI
Exiting the jail
Figure 2 | Graphical depiction, and equations for, the within-jail community-acquired meticillin-resistant
Naturefrom
Reviews
Microbiology
Staphylococcus aureus transmission model. Panel a shows the inflow into the jail and the outflow
the|jail
of
susceptible non-carrier (S), asymptomatically colonized (C) and infected (I) individuals. The arrow pointing from the S to
the C state shows that non-carrier individuals can become colonized (that is, individuals can move from the S to the
C state). The arrow pointing from the C to the S state shows that colonized individuals can become decolonized (that is,
individuals can move from the C to the S state). The arrow pointing from the C to the I state shows that colonized
individuals can become infected (that is, individuals can move from the C to the I state). The three equations that
correspond to this diagram and that specify this simple transmission model are shown in panel b. Parameter definitions
(and values) are shown in Table 1. This model is deterministic but can be simply transformed into a stochastic model by the
addition of probabilities.
or hospital) that is being studied and by working with
infectious disease experts during the model construction
phase to ensure that the model is simple but realistic.
To model the transmission of HA‑MRSA in hospitals it
is sometimes necessary to model transmission among
patients and medical workers, because medical workers
can act as vectors to transmit HA‑MRSA from patient to
702 | September 2007 | volume 5
patient45. In correctional facilities there is almost no direct
contact between staff and inmates, so, it is only necessary
to model transmission among inmates.
To define a model that can be applied to the transmission of CA‑MRSA in a small population that has both
immigration and emigration of the host (such as the
LACJ), we begin by specifying that inmates are always in
www.nature.com/reviews/micro
© 2007 Nature Publishing Group
A n a ly s i s
one of three mutually exclusive states: susceptible (noncarrier) (S); asymptomatically colonized with CA‑MRSA
and infectious (C); or infected with CA‑MRSA and
infectious (I). Therefore, the model is constructed as
a three-state model that is mathematically specified in
terms of three equations. A graphic representation of
the model, including parameters, is shown in FIG. 2a.
The equations that specify the model are shown in
FIG. 2b and the parameters are defined in TABLE 1. The
model tracks the flow, over time, of inmates into and out
of the three states, and also the flow of inmates into and
out of the jail. It includes the three important processes
that drive the jail outbreak: within-jail transmission; the
inflow of infected cases; and the inflow of asymptomatic
colonized individuals that progress to infection while
they are incarcerated. The model that we constructed is
designed to track the dynamics of CA‑MRSA over the
first 9 months of the outbreak, from the beginning of
the outbreak in January 2002 to September 2002, and
therefore it does not include the potential effects of
any interventions, such as treatment. To construct the
model, we make eight assumptions.
Assumption 1. Inmates enter the jail at rate π, and the
average incarceration time (1/δ ) during the initial stage
of the outbreak is constant. Thus, during the outbreak,
the number of …
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