LIFE721 Assignment

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LIFE721 Assignment:
The ecology of infectious diseases
In this assignment you will use your knowledge of the principles of disease
ecology to explore the spread and management of a novel infectious disease.
Feel free to discuss together, but WRITE & SUBMIT A SEPARATE DOCUMENT
EACH. Complete your assignment by putting your responses to the following
questions into the accompanying ‘Report Sheet’.
General overview
You are a government advisor, with expertise on the management of infectious
diseases. A new viral pathogen has emerged, which is rapidly spreading through
the UK wild giraffe population, and your job is to (i) assess alternative control
approaches and (ii) provide clear, evidence-based guidelines on how best to
manage it.
You have available to you:
– Initial data on the number of infected individuals over the first 3 weeks of
the pathogen’s spread through the population (see below for details).
– A mathematical model of host-microparasite dynamics (see below).
– Your knowledge, and some relevant literature (e.g., your class notes, and
assigned readings), on the concepts of infectious disease spread, and the
application of those concepts to the management of other, similar
infectious diseases.
Your report will be structured around the questions in the ‘Report sheet’ below –
these will guide your work in the following areas:
1. Estimate the basic reproductive number (R0) for the pathogen from the
initial data available.
2. Use this value to parameterise your mathematical model, and explore
alternative control/management strategies.
3. Comment on the confidence you have in your recommendations, the
underlying assumptions, and priority areas for future work.
Remember, this report is intended for government employees who are nonexperts in the field. So at each stage please describe clearly any assumptions you
have made, and provide relevant background information to support your work.
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Data and Model information
Data
The available data (‘Assignment 2 data+model.xlsx’, Sheet: Data) comprise
information on the number of infected individuals recorded at regular intervals
over the first 3 weeks of the epidemic.
The ‘Data’ sheet also gives current best-estimates of several key parameters
(highlighted in orange) relating to the disease:
Natural giraffe mortality rate (m = 0.1 week-1),
Pathogen virulence (v = 0.5 week-1),
Mean recovery rate (g = 0.4 week-1),
Mean duration of infection (L = 1/(m+v+g)),
Initial population size of susceptible giraffes (S = 100,000 animals, plus 1
initially infected at the beginning of the epidemic).
At the end of this document you will find guidance notes that provide
information on carrying out various data manipulation tasks in Excel.
Model
The spreadsheet (‘Assignment 2 data+model.xlsx’, Sheet: Model) contains a
standard SIR model (see lecture notes). The yellow-highlighted cells give the
initial numbers of Susceptible, Infected and Recovered animals, and the total
population size (there is no need to change these values for the assignment, but
by all means feel free to explore what happens if you do).
The orange-highlighted cells give the main parameters that control the epidemic.
These are the ones you should focus on for your assignment. They should be
self-explanatory, but note that it is assumed that the birth rate is the same as the
natural death rate, which means the total population size would remain constant
in the absence of the disease.
The blue-highlighted cells give ‘derived’ values that are calculated automatically
from the parameters above – these are just for your information, and there is no
need to change these values.
When you change any parameter values, the spreadsheet and graphs will
automatically update to reflect those changes. Currently there are 3 graphs
plotted:
i) The number of Susceptible individuals (using the scale on the left-hand
axis) and the number of Infected individuals (using the scale on the right-hand
axis) over time.
ii) The cumulative number of Infected individuals and the cumulative
number of infected individuals dying due to infection and any culling
implemented, over time. The final values of these, i.e. at the last time point, will
give the total number infected or killed by the infection throughout the epidemic.
iii) The effective reproduction number Re, over time.
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Potential control alternatives
The model enables you to explore various alternative control methods by
changing the relevant parameters in the green-highlighted cells on the ‘Model’
sheet. Your job is to run the model under various control scenarios, and choose
the best one(s) to recommend, with justification for that decision. In particular,
you can vary the proportion of the population that you target, from 0 (no animals
targeted) up to 1 (all animals targeted), with each of the following control
alternatives:
a) Vaccination. The parameter p determines the proportion of the susceptible
population vaccinated at birth (and therefore protected from future infection;
it is assumed protection is lifelong).
b) Quarantine. The parameter Q represents the proportion of the infected
population that is isolated from contacting susceptible animals, thereby
reducing transmission.
c) Medication. The parameter T represents the proportion of the infected
population treated with a medication that soothes the symptoms of infection,
but does not directly affect the infection. As such infected individuals will
remain infectious, but will not suffer from being infected.
d) Culling. The parameter C represents the proportion of infected animals
culled (removed from the population). Note the model is not set up to explore
pre-emptive culling of uninfected animals.
Note, we assume all strategies have equivalent costs to implement, so don’t
worry about factoring the financial implications of each strategy – focus on the
biological outcomes of them.
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Instructions for completing Report Sheet

– but remember to give full citations, and a reference list at the end, for
any material taken from websites or the literature.

number of decimal places!), or round up/down as deemed
appropriate. It’s up to you how you handle these, but be consistent.
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Guidance notes for Excel
Here are some basic tips for manipulating data and calculating formulae in Excel,
which may be useful for answering some of the questions.
Adding a trendline to a figure
If you want to add a trendline to an existing figure, right click on one of the
datapoints in the figure, and click on ‘Add Trendline…’. Choose which type of
trendline you would like (e.g., Exponential). To see the equation of the best-fit
trendline, click ‘Display Equation on chart’.
Basic formulae
To enter a formula in a cell, start it with an equals ‘=’ sign. You can then either
directly type the formula in (e.g. ‘=5+3’), or refer to values in other cells (e.g.,
‘=A1+B1’).
Remember to use brackets to group terms together – for example if you wanted
to calculate 3/(5 +2) you would have to remember those brackets: ‘=3/(5+2)’.
Also remember that multiplication in Excel uses the ‘*’ symbol, so 3/(5×2) would
be written as ‘=3/(5*2)’.
Reading scientific numbers
Sometimes you may see a value written in Excel like: 1.0E-05. This is Excel’s way
of showing either very big or very small numbers; the ‘E’ means ‘x10 to the
power of…’. So, 1.0E-05 means 1.0×10-5, or 0.00001. Similarly, 1.0xE05 means
1.0×105, or 100000.