However, we should always be wary about visualisations such as these. Perhaps we should be plotting cases per capita instead of absolute numbers of cases. Or should we divide by the area of the country? Some countries, such as China and Canada, are divided into states or regions in the original data set – but others, such as the US, are not. You should always check exactly what is being plotted!
Unfortunately, published visualisations often hide some of this information. This emphasises the need to be able to get our hands on the data, create our own visualisations and draw our own conclusions.
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Here we have used an anonymous function with the syntax x -> ⋯. This is a function which takes the argument x and returns whatever is on the right of the arrow (->).
A visual check for this is to plot the data with a logarithmic scale on the $y$ axis (but a standard scale on the $x$ axis).
The reason for this is that if we observe a straight line on such a semi-logarithmic plot, we have
$$\log(y) \sim ax + b,$$
where we are using $\sim$ to denote approximate equality.
Hence, taking exponentials of both sides, we have
$$y \sim \exp(ax + b) = c \, e^{ax},$$
for some constant $c$.
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DataFrameRow (1147 columns)
1047 columns omitted
Row
province
country
latitude
longitude
1/22/20
1/23/20
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1/25/20
1/26/20
1/27/20
1/28/20
1/29/20
1/30/20
1/31/20
2/1/20
2/2/20
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2/8/20
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2/10/20
2/11/20
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2/14/20
2/15/20
2/16/20
2/17/20
2/18/20
2/19/20
2/20/20
2/21/20
2/22/20
2/23/20
2/24/20
2/25/20
2/26/20
2/27/20
2/28/20
2/29/20
3/1/20
3/2/20
3/3/20
3/4/20
3/5/20
3/6/20
3/7/20
3/8/20
3/9/20
3/10/20
3/11/20
3/12/20
3/13/20
3/14/20
3/15/20
3/16/20
3/17/20
3/18/20
3/19/20
3/20/20
3/21/20
3/22/20
3/23/20
3/24/20
3/25/20
3/26/20
3/27/20
3/28/20
3/29/20
3/30/20
3/31/20
4/1/20
4/2/20
4/3/20
4/4/20
4/5/20
4/6/20
4/7/20
4/8/20
4/9/20
4/10/20
4/11/20
4/12/20
4/13/20
4/14/20
4/15/20
4/16/20
4/17/20
4/18/20
4/19/20
4/20/20
4/21/20
4/22/20
4/23/20
4/24/20
4/25/20
4/26/20
⋯
String?
String
Float64?
Float64?
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
Int64
⋯
261
missing
US
40.0
-100.0
1
1
2
2
5
5
5
6
6
8
8
8
11
11
11
12
12
12
12
12
13
13
14
14
14
14
14
14
14
14
16
16
16
16
16
16
17
17
25
32
55
74
107
184
237
403
519
594
782
1147
1586
2219
2978
3212
4679
6512
9169
13663
20030
26025
34944
46096
56714
68841
86662
105253
127417
143544
165698
192079
227903
260183
292630
324340
353117
385110
415256
446500
482526
516707
545693
571551
598794
627306
653669
683351
716508
743857
768888
799531
825478
855445
887523
919014
949640
975537
⋯
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Now we would like to combine the geographical and temporal (time) aspects. One way to do so is to animate time:
Let's zoom on the part where the growth seems linear on this semi-log plot:
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We see that the correct spelling is "US". (And note how the different provinces of the UK are separated.)
Now we need to parse the date strings, i.e. convert from a string representation into an actual Julia type provided by the Dates.jl standard library package:
Note that we are only passing a single vector to the scatter function, so the $x$ coordinates are taken as the natural numbers $1$, $2$, etc.
Also note that the $y$-axis in this plot gives the cumulative case numbers, i.e. the total number of confirmed cases since the start of the epidemic up to the given date.
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We are starting a new module on modelling epidemic propagation.
Let's start off by analysing some of the data that is now available on the current COVID-19 pandemic.
How can we extract the data for a particular country? First we need to know the exact name of the country. E.g. is the US written as "USA", or "United States"?
We could scroll through to find out, or filter the data to only look at a sample of it, for example those countries that begin with the letter "U".
One way to do this is with an array comprehension:
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If the province is missing we should use the country name instead:
We see that there is a period lasting from around day 38 to around day 60 when the curve looks straight on the semi-log plot. This corresponds to the following date range:
Our data set contains more information: the geographical locations (latitude and longitude) of each country (or, rather, of a particular point that was chosen as being representative of that country).
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i.e. the first 3 weeks of March. Fortunately the imposition of lockdown during the last 10 days of March (on different days in different US states) significantly reduced transmission.
We would like to use actual dates instead of just the number of days since the start of the recorded data. The dates are given in the column names of the DataFrame:
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[Here we used string interpolation with $ to put the text into a Markdown string.]
This is an example of a time series, i.e. a single quantity that changes over time.
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"Australian Capital Territory"text/plain"Australia"text/plain-35.4735text/plain149.012text/plain0text/plain0text/plain0text/plain0text/plainmoremoremissingtext/plain"Azerbaijan"text/plain40.1431text/plain47.5769text/plain0text/plain0text/plain0text/plain0text/plainmoreobjectid8cf06766e559b15eschemanamesprovincecountrylatitudelongitude1/22/201/23/201/24/201/25/20moretypesString?StringFloat64?Float64?Int64Int64Int64Int64moremime"application/vnd.pluto.table+objectrootassigneelast_run_timestampA`persist_js_state·has_pluto_hook_features§cell_id$c5ad4d40-fc57-11ea-23cb-e55487bc6f7adepends_on_disabled_cells§runtime Ypublished_object_keysdepends_on_skipped_cells§errored$b0eb3918-fc1f-11ea-238b-7f5d23e424bbqueued¤logsrunning¦outputbody
How can we extract the list of all the countries? The country names are in the second column.
For some purposes we can think of a DataFrame.as a matrix and use similar syntax. For example, we can extract the second column:
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We will need a couple of new packages. The data is in CSV format, i.e. Comma-Separated Values. This is a common data format in which observations, i.e. data points, are separated on different lines. Within each line the different data for that observation are separated by commas or other punctuation (possibly spaces and tabs).
It turns out that some countries are divided into provinces, so there are repetitions in the country column that we can eliminate with the unique function:
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- Run `import Pkg; Pkg.add("Plots")` to install the Plots package.
stacktracecall_short"require(into::Module, mod::Symbol)inlined£urlehttps://github.com/JuliaLang/julia/tree/742b9abb4dd4621b667ec5bb3434b8b3602f96fd/base/loading.jl#L959path./loading.jlsource_packagecall"require(into::Module, mod::Symbol)linfo_typeCore.MethodInstancelineǤfileloading.jlfuncrequireparent_modulefrom_ccall_shorttop-level scopeinlined£urlpathf/home/runner/work/disorganised-mess/disorganised-mess/covid.jl#==#a26b8742-6a16-445a-ae77-25a4189c0f14source_packagecalltop-level scopelinfo_typeCore.CodeInfolinefile0covid.jl#==#a26b8742-6a16-445a-ae77-25a4189c0f14functop-level scopeparent_modulefrom_c¤mime'application/vnd.pluto.stacktrace+objectrootassigneelast_run_timestampAlpersist_js_state·has_pluto_hook_features§cell_id$a26b8742-6a16-445a-ae77-25a4189c0f14depends_on_disabled_cells§runtimepublished_object_keysdepends_on_skipped_cells§errored$ed383524-e0c0-4da2-9a98-ca75aadd2c9equeued¤logsrunning¦outputbody8
We would also like to see the outlines of each country. For this we can use, for example, the data from Natural Earth, which comes in the form of shape files, giving the outlines in terms of latitude and longitude coordinates.
These may be read in using the Shapefile.jl package.
To extract a single row we need the index of the row (i.e. which number row it is in the DataFrame). The findfirst function finds the first row that satisfies the given predicate:
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Note that this returns an array of booleans of the same length as the vector all_countries. We can now use this to index into the DataFrame:
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Working with cumulative data is often less intuitive. Let's look at the actual number of daily cases. Julia has a diff function to calculate the difference between successive entries of a vector:
Since we need to manipulate the columns, let's rename them to something shorter. We can do this either in place, i.e. modifying the original DataFrame, or out of place, creating a new DataFrame. The convention in Julia is that functions that modify their argument have a name ending with ! (often pronounced "bang").
We can use the head function to see only the first few lines of the data.
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Note that discrete data should always be plotted with points. The lines are just to guide the eye.
Cumulating data corresponds to taking the integral of a function and is a smoothing operation. Note that the cumulative data is indeed visually smoother than the daily data.
The oscillations in the daily data seem to be due to a lower incidence of reporting at weekends. We could try to smooth this out by taking a moving average, say over the past week:
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Now we would like to extract the data for the US alone. How can we access the correct row of the table? We can again filter on the country name. A nicer way to do this is to use the filter function.
This is a higher-order function: its first argument is itself a function, which must return true or false. filter will return all the rows of the DataFrame that satisfy that predicate:
In this notebook we will explore and analyse data on the COVID-19 pandemic. The aim is to use Julia's tools to analyse and visualise the data in different ways.
Here is an example of the kind of visualisation we will be able to produce:
A DataFrame is a standard way of storing heterogeneous data in Julia, i.e. a table consisting of columns with different types. As you can see from the display of the DataFrame object above, each column has an associated type, but different columns have different types, reflecting the type of the data in that column.
In our case, country names are stored as Strings, their latitude and longitude as Float64s and the (cumulative) case counts for each day as Int64s. .
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j$251c06e4-fc77-11ea-1a0f-73139ba11e83cell_id$251c06e4-fc77-11ea-1a0f-73139ba11e83codeamd"However, we should always be wary about visualisations such as these. Perhaps we should be plotting cases per capita instead of absolute numbers of cases. Or should we divide by the area of the country? Some countries, such as China and Canada, are divided into states or regions in the original data set -- but others, such as the US, are not. You should always check exactly what is being plotted!
Unfortunately, published visualisations often hide some of this information. This emphasises the need to be able to get our hands on the data, create our own visualisations and draw our own conclusions."metadatashow_logsèdisabled®skip_as_script«code_folded$68f76d3b-b398-459d-bf39-20bf300dcaa2cell_id$68f76d3b-b398-459d-bf39-20bf300dcaa2code"all_countries = data[:, "country"]metadatashow_logsèdisabled®skip_as_script«code_folded$8990f13a-fc35-11ea-338f-0955eeb23c3ccell_id$8990f13a-fc35-11ea-338f-0955eeb23c3ccodeٵmd"Here we have used an **anonymous function** with the syntax `x -> ⋯`. This is a function which takes the argument `x` and returns whatever is on the right of the arrow (`->`)."metadatashow_logsèdisabled®skip_as_script«code_folded$b3880f40-fc36-11ea-074a-edc51adeb6f0cell_id$b3880f40-fc36-11ea-074a-edc51adeb6f0codemd"## Using dates"metadatashow_logsèdisabled®skip_as_script«code_folded$25c79620-14f4-45a7-b120-05ec72cb77e9cell_id$25c79620-14f4-45a7-b120-05ec72cb77e9code'date_format = Dates.DateFormat("m/d/Y")metadatashow_logsèdisabled®skip_as_script«code_folded$0f87cec6-fc31-11ea-23d2-395e61f38b6fcell_id$0f87cec6-fc31-11ea-23d2-395e61f38b6fcode$md"# Module 2: Epidemic propagation"metadatashow_logsèdisabled®skip_as_script«code_folded$893a417c-fcea-11ea-38f4-1df639c54cbccell_id$893a417c-fcea-11ea-38f4-1df639c54cbccodeset_points(data, daily[:, day])metadatashow_logsèdisabled®skip_as_script«code_folded$252eff18-fc3d-11ea-0c18-7b130ada882ecell_id$252eff18-fc3d-11ea-0c18-7b130ada882ecodemd"A visual check for this is to plot the data with a **logarithmic scale** on the $y$ axis (but a standard scale on the $x$ axis).
The reason for this is that if we observe a straight line on such a semi-logarithmic plot, we have
$$\log(y) \sim ax + b,$$
where we are using $\sim$ to denote approximate equality.
Hence, taking exponentials of both sides, we have
$$y \sim \exp(ax + b) = c \, e^{ax},$$
for some constant $c$.
"metadatashow_logsèdisabled®skip_as_script«code_folded$c939a87a-fcdc-11ea-29dd-c1f6dd3de88fcell_id$c939a87a-fcdc-11ea-29dd-c1f6dd3de88fcodefunction set_points(data, fotoday)
jsondata = sprint(io->JSON.print(io, make_features(data, fotoday)));
HTML("""
""")
endmetadatashow_logsèdisabled®skip_as_script«code_folded$a41db8ea-f0e0-461f-a298-bdcea42a67f3cell_id$a41db8ea-f0e0-461f-a298-bdcea42a67f3codedata[US_row, :]metadatashow_logsèdisabled®skip_as_script«code_folded$a29c8ad0-fc4a-11ea-14c7-71435769b73ecell_id$a29c8ad0-fc4a-11ea-14c7-71435769b73ecodeWbegin
indices = ismissing.(province)
province[indices] .= all_countries[indices]
end;metadatashow_logsèdisabled®skip_as_script«code_folded$4e4cca22-fc4c-11ea-12ae-2b51545799eccell_id$4e4cca22-fc4c-11ea-12ae-2b51545799eccodebegin
scatter(data.longitude, data.latitude, leg=false, alpha=0.5, ms=2)
for i in 1:length(province)
annotate!(data.longitude[i], data.latitude[i], text(province[i], :center, 5, color=RGBA{Float64}(0.0,0.0,0.0,0.3)))
end
plot!(axis=false)
endmetadatashow_logsèdisabled®skip_as_script«code_folded$f8e754ee-fc73-11ea-0c7f-cdc760ab3e94cell_id$f8e754ee-fc73-11ea-0c7f-cdc760ab3e94codesmd"Now we would like to combine the geographical and temporal (time) aspects. One way to do so is to animate time:"metadatashow_logsèdisabled®skip_as_script«code_folded$c2da1f88-fcdb-11ea-0b18-bf801c373a73cell_id$c2da1f88-fcdb-11ea-0b18-bf801c373a73codeEResource("https://api.mapbox.com/mapbox-gl-js/v1.12.0/mapbox-gl.css")metadatashow_logsèdisabled®skip_as_script«code_folded$687409a2-fc43-11ea-03e0-d9a7a48165a8cell_id$687409a2-fc43-11ea-03e0-d9a7a48165a8codeOmd"Let's zoom on the part where the growth seems linear on this semi-log plot:"metadatashow_logsèdisabled®skip_as_script«code_folded$b4264196-fcdc-11ea-2197-512f8363a4d3cell_id$b4264196-fcdc-11ea-2197-512f8363a4d3codeCfunction make_features(data, fotoday)
point(long, lat, n) =
Dict("type"=>"Feature",
"properties"=>Dict("size" => 2 * log10(n)),
"geometry"=>Dict(
"type" => "Point",
"coordinates" => [long, lat]))
Dict("type" => "FeatureCollection",
"features" => map(point, data.longitude, data.latitude, fotoday))
endmetadatashow_logsèdisabled®skip_as_script«code_folded$a8b2db96-fc30-11ea-2eea-b938a3a430fbcell_id$a8b2db96-fc30-11ea-2eea-b938a3a430fbcodesmd"""We see that the correct spelling is `"US"`. (And note how the different provinces of the UK are separated.)"""metadatashow_logsèdisabled®skip_as_script«code_folded$67eebb7e-fc36-11ea-03ef-bd6966487bb5cell_id$67eebb7e-fc36-11ea-03ef-bd6966487bb5code?md"Now we can extract the data into a standard Julia `Vector`:"metadatashow_logsèdisabled®skip_as_script«code_folded$511eb51e-fc38-11ea-0492-19532da809decell_id$511eb51e-fc38-11ea-0492-19532da809decode md"## Exploratory data analysis"metadatashow_logsèdisabled®skip_as_script«code_folded$9ee79840-30ff-4c92-97f4-e178caceceafcell_id$9ee79840-30ff-4c92-97f4-e178caceceafcodeEU_countries = [startswith(country, "U") for country in all_countries]metadatashow_logsèdisabled®skip_as_script«code_folded$5c1ec9ae-fc2e-11ea-397d-937c7ab1edb2cell_id$5c1ec9ae-fc2e-11ea-397d-937c7ab1edb2code4@bind i Slider(1:length(countries), show_value=true)metadatashow_logsèdisabled®skip_as_script«code_folded$80138b30-fc4a-11ea-0e15-b54cf6b402dfcell_id$80138b30-fc4a-11ea-0e15-b54cf6b402dfcodeprovince = data.province;metadatashow_logsèdisabled®skip_as_script«code_folded$546a40eb-7897-485d-a1b5-c4dfae0a4861cell_id$546a40eb-7897-485d-a1b5-c4dfae0a4861code٭md"""
Now we need to **parse** the date strings, i.e. convert from a string representation into an actual Julia type provided by the `Dates.jl` standard library package:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$7b5db0f4-fc36-11ea-09a5-49def64f4c79cell_id$7b5db0f4-fc36-11ea-09a5-49def64f4c79code%US_data = Vector(data[US_row, 5:end])metadatashow_logsèdisabled®skip_as_script«code_folded$7e7d14a2-fc37-11ea-3f1a-870ca98c4b75cell_id$7e7d14a2-fc37-11ea-3f1a-870ca98c4b75codeEmd"Note that we are only passing a single vector to the `scatter` function, so the $x$ coordinates are taken as the natural numbers $1$, $2$, etc.
Also note that the $y$-axis in this plot gives the *cumulative* case numbers, i.e. the *total* number of confirmed cases since the start of the epidemic up to the given date.
"metadatashow_logsèdisabled®skip_as_script«code_folded$79ba0433-2a31-475a-87c9-14103ebbff16cell_id$79ba0433-2a31-475a-87c9-14103ebbff16code!countries = unique(all_countries)metadatashow_logsèdisabled®skip_as_script«code_folded$dc2cfa82-fc86-11ea-1311-bb6e69350d43cell_id$dc2cfa82-fc86-11ea-1311-bb6e69350d43codecdownload("https://www.naturalearthdata.com/downloads/110m-cultural-vectors/110m-admin-0-countries")metadatashow_logsèdisabled®skip_as_script«code_folded$39982810-fc76-11ea-01c3-3987cfc2fd3ccell_id$39982810-fc76-11ea-01c3-3987cfc2fd3ccode5daily = max.(1, diff(Array(data[:, 5:end]), dims=2));metadatashow_logsèdisabled®skip_as_script«code_folded$19f4da16-fc31-11ea-0de9-1dbe668b862dcell_id$19f4da16-fc31-11ea-0de9-1dbe668b862dcode٫md"We are starting a new module on modelling epidemic propagation.
Let's start off by analysing some of the data that is now available on the current COVID-19 pandemic.
"metadatashow_logsèdisabled®skip_as_script«code_folded$1f30a1ac-fc74-11ea-2abf-abf437006babcell_id$1f30a1ac-fc74-11ea-2abf-abf437006babcodedates[day]metadatashow_logsèdisabled®skip_as_script«code_folded$1633abe8-fc2f-11ea-2c7e-21b3348a3569cell_id$1633abe8-fc2f-11ea-2c7e-21b3348a3569codetmd"""How can we extract the data for a particular country? First we need to know the exact name of the country. E.g. is the US written as "USA", or "United States"?
We could scroll through to find out, or **filter** the data to only look at a sample of it, for example those countries that begin with the letter "U".
One way to do this is with an array comprehension:"""metadatashow_logsèdisabled®skip_as_script«code_folded$a054e048-4fea-487c-9d06-463723c7151ccell_id$a054e048-4fea-487c-9d06-463723c7151ccodeubegin
data_2 = rename(data, 1 => "province", 2 => "country", 3 => "latitude", 4 => "longitude")
head(data_2)
endmetadatashow_logsèdisabled®skip_as_script«code_folded$dbaacbb6-fc3b-11ea-0a42-a9792e8a6c4ccell_id$dbaacbb6-fc3b-11ea-0a42-a9792e8a6c4ccode٦begin
daily_cases = diff(US_data)
plot(dates[2:end], daily_cases, m=:o, leg=false, xlabel="days", ylabel="daily US cases", alpha=0.5) # use "o"-shaped markers
endmetadatashow_logsèdisabled®skip_as_script«code_folded$8709f208-fc4a-11ea-0203-e13eae5f0d93cell_id$8709f208-fc4a-11ea-0203-e13eae5f0d93codeHmd"If the `province` is missing we should use the country name instead:"metadatashow_logsèdisabled®skip_as_script«code_folded$07282688-fc3e-11ea-2f9e-5b0581061e65cell_id$07282688-fc3e-11ea-2f9e-5b0581061e65codemd"We see that there is a period lasting from around day $(first(exp_period)) to around day $(last(exp_period)) when the curve looks straight on the semi-log plot.
This corresponds to the following date range:"metadatashow_logsèdisabled®skip_as_script«code_folded$3edd2a22-fc4a-11ea-07e5-55ca6d7639e8cell_id$3edd2a22-fc4a-11ea-07e5-55ca6d7639e8codemd"Our data set contains more information: the geographical locations (latitude and longitude) of each country (or, rather, of a particular point that was chosen as being representative of that country)."metadatashow_logsèdisabled®skip_as_script«code_folded$0f329ece-fc74-11ea-1e02-bdbddf551ef3cell_id$0f329ece-fc74-11ea-1e02-bdbddf551ef3code@bind day_ticks Clock(0.5)metadatashow_logsèdisabled®skip_as_script«code_folded$2f254a9e-fc3e-11ea-2c02-75ed59f41903cell_id$2f254a9e-fc3e-11ea-2c02-75ed59f41903codeٻmd"i.e. the first 3 weeks of March. Fortunately the imposition of lockdown during the last 10 days of March (on different days in different US states) significantly reduced transmission."metadatashow_logsèdisabled®skip_as_script«code_folded$31dc4e46-4839-4f01-b383-1a1189aeb0e6cell_id$31dc4e46-4839-4f01-b383-1a1189aeb0e6code)parse(Date, date_strings[1], date_format)metadatashow_logsèdisabled®skip_as_script«code_folded$f5c29f0d-937f-4731-8f87-0405ebc966f5cell_id$f5c29f0d-937f-4731-8f87-0405ebc966f5code=dates = parse.(Date, date_strings, date_format) .+ Year(2000)metadatashow_logsèdisabled®skip_as_script«code_folded$4f423a75-43da-486f-ac2a-7220032dac9fcell_id$4f423a75-43da-486f-ac2a-7220032dac9fcodedata[U_countries, :]metadatashow_logsèdisabled®skip_as_script«code_folded$6de0800c-fc37-11ea-0d94-2b6f8f66964dcell_id$6de0800c-fc37-11ea-0d94-2b6f8f66964dcode٫md"We would like to use actual dates instead of just the number of days since the start of the recorded data. The dates are given in the column names of the `DataFrame`:
"metadatashow_logsèdisabled®skip_as_script«code_folded$24934438-fc74-11ea-12e4-7f7e50f54029cell_id$24934438-fc74-11ea-12e4-7f7e50f54029code#=
begin
plot(shp_countries, alpha=0.2)
scatter!(data.longitude, data.latitude, leg=false, ms=2*log10.(daily[:, day]), alpha=0.7)
xlabel!("latitude")
ylabel!("longitude")
title!("daily cases per country")
end
=#metadatashow_logsèdisabled®skip_as_script«code_folded$4358c348-91aa-4c76-a443-0a9cefce0e83cell_id$4358c348-91aa-4c76-a443-0a9cefce0e83codeٰbegin
plot(replace(daily_cases, 0 => NaN),
yscale=:log10,
leg=false, m=:o)
xlabel!("day")
ylabel!("confirmed cases in US")
title!("US confirmed COVID-19 cases")
endmetadatashow_logsèdisabled®skip_as_script«code_folded$9484ea9e-fc2e-11ea-137c-6da8212da5bdcell_id$9484ea9e-fc2e-11ea-137c-6da8212da5bdcode\md"[Here we used **string interpolation** with `$` to put the text into a Markdown string.]"metadatashow_logsèdisabled®skip_as_script«code_folded$4ccb2718-fce2-11ea-18c4-89640faec38dcell_id$4ccb2718-fce2-11ea-18c4-89640faec38dcode$day = min(day_ticks, size(daily, 2))metadatashow_logsèdisabled®skip_as_script«code_folded$75d2dc66-fc47-11ea-0e35-05f9cf38e901cell_id$75d2dc66-fc47-11ea-0e35-05f9cf38e901code[md"This is an example of a **time series**, i.e. a single quantity that changes over time."metadatashow_logsèdisabled®skip_as_script«code_folded$b406eec8-fc77-11ea-1a98-d36d6d3e2393cell_id$b406eec8-fc77-11ea-1a98-d36d6d3e2393codelog10(maximum(daily[:, day]))metadatashow_logsèdisabled®skip_as_script«code_folded$861a2c3a-fc88-11ea-2d95-fb076e751203cell_id$861a2c3a-fc88-11ea-2d95-fb076e751203codehtml"""
"""metadatashow_logsèdisabled®skip_as_script«code_folded$c5ad4d40-fc57-11ea-23cb-e55487bc6f7acell_id$c5ad4d40-fc57-11ea-23cb-e55487bc6f7acode-filter(x -> startswith(x.country, "A"), data)metadatashow_logsèdisabled®skip_as_script«code_folded$b0eb3918-fc1f-11ea-238b-7f5d23e424bbcell_id$b0eb3918-fc1f-11ea-238b-7f5d23e424bbcodemd"How can we extract the list of all the countries? The country names are in the second column.
For some purposes we can think of a `DataFrame`.as a matrix and use similar syntax. For example, we can extract the second column:
"metadatashow_logsèdisabled®skip_as_script«code_folded$36c37b4d-eb23-4deb-a593-e511eccd9204cell_id$36c37b4d-eb23-4deb-a593-e511eccd9204codebegin
plot(dates, US_data, xrotation=45, leg=:topleft,
label="US data", m=:o, ms=3, alpha=0.5)
xlabel!("date")
ylabel!("cumulative US cases")
title!("US cumulative confirmed COVID-19 cases")
endmetadatashow_logsèdisabled®skip_as_script«code_folded$a7369222-fc20-11ea-314d-4d6b0f0f72ebcell_id$a7369222-fc20-11ea-314d-4d6b0f0f72ebcodeRmd"We will need a couple of new packages. The data is in CSV format, i.e. *C*omma-*S*eparated *V*alues. This is a common data format in which observations, i.e. data points, are separated on different lines. Within each line the different data for that observation are separated by commas or other punctuation (possibly spaces and tabs)."metadatashow_logsèdisabled®skip_as_script«code_folded$fab64d86-fc28-11ea-0ae1-3ba1b9a14759cell_id$fab64d86-fc28-11ea-0ae1-3ba1b9a14759codemd"## Using the data"metadatashow_logsèdisabled®skip_as_script«code_folded$9e23b0e2-ac13-4d19-a3f9-4a655a1e9f14cell_id$9e23b0e2-ac13-4d19-a3f9-4a655a1e9f14codedate_strings[1]metadatashow_logsèdisabled®skip_as_script«code_folded$1620aa9d-7dcd-4686-b7e4-a72cebe315edcell_id$1620aa9d-7dcd-4686-b7e4-a72cebe315edcodeلmd"""
We can load the data from a CSV using the `File` function from the `CSV.jl` package, and then convert it to a `DataFrame`:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$ada3ceb4-fc2e-11ea-2cbf-399430fa18b5cell_id$ada3ceb4-fc2e-11ea-2cbf-399430fa18b5code@bind country Select(countries)metadatashow_logsèdisabled®skip_as_script«code_folded$34440afc-fc2e-11ea-0484-5b47af235badcell_id$34440afc-fc2e-11ea-0484-5b47af235badcode٣md"It turns out that some countries are divided into provinces, so there are repetitions in the `country` column that we can eliminate with the `unique` function:"metadatashow_logsèdisabled®skip_as_script«code_folded$a26b8742-6a16-445a-ae77-25a4189c0f14cell_id$a26b8742-6a16-445a-ae77-25a4189c0f14codeusing Plotsmetadatashow_logsèdisabled®skip_as_script«code_folded$ed383524-e0c0-4da2-9a98-ca75aadd2c9ecell_id$ed383524-e0c0-4da2-9a98-ca75aadd2c9ecodemd"""
Array comprehension:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$b93b88b0-fc4d-11ea-0c45-8f64983f8b5ccell_id$b93b88b0-fc4d-11ea-0c45-8f64983f8b5ccodemd"We would also like to see the outlines of each country. For this we can use, for example, the data from [Natural Earth](https://www.naturalearthdata.com/downloads/110m-cultural-vectors/110m-admin-0-countries), which comes in the form of **shape files**, giving the outlines in terms of latitude and longitude coordinates.
These may be read in using the `Shapefile.jl` package.
"metadatashow_logsèdisabled®skip_as_script«code_folded$c460b0c3-6d3b-439b-8cc7-1c58d6547f51cell_id$c460b0c3-6d3b-439b-8cc7-1c58d6547f51codedownload(url, "covid_data.csv")metadatashow_logsèdisabled®skip_as_script«code_folded$1a59b12e-fceb-11ea-0634-1b4daee1bc62cell_id$1a59b12e-fceb-11ea-0634-1b4daee1bc62codelog10.(daily[:, day])metadatashow_logsèdisabled®skip_as_script«code_folded$91f99062-fc43-11ea-1b0e-afe8aa8a1c3dcell_id$91f99062-fc43-11ea-1b0e-afe8aa8a1c3dcodeexp_period = 38:60metadatashow_logsèdisabled®skip_as_script«code_folded$ae9149f4-fcdc-11ea-30a3-031d38f38b23cell_id$ae9149f4-fcdc-11ea-30a3-031d38f38b23codeDResource("https://api.mapbox.com/mapbox-gl-js/v1.12.0/mapbox-gl.js")metadatashow_logsèdisabled®skip_as_script«code_folded$a772eadc-fc35-11ea-3d38-4b121f88f1d7cell_id$a772eadc-fc35-11ea-3d38-4b121f88f1d7codeٿmd"To extract a single row we need the **index** of the row (i.e. which number row it is in the `DataFrame`). The `findfirst` function finds the first row that satisfies the given predicate:"metadatashow_logsèdisabled®skip_as_script«code_folded$4f23c8fc-fc43-11ea-0e73-e5f89d14155ccell_id$4f23c8fc-fc43-11ea-0e73-e5f89d14155ccodebegin
plot(replace(daily_cases, 0 => NaN),
yscale=:log10,
leg=false, m=:o,
xlims=(1, 100))
xlabel!("day")
ylabel!("confirmed cases in US")
title!("US confirmed COVID-19 cases")
endmetadatashow_logsèdisabled®skip_as_script«code_folded$a39589ee-20e3-4f22-bf81-167fd815f6f9cell_id$a39589ee-20e3-4f22-bf81-167fd815f6f9codemd"$(Text(countries[i]))"metadatashow_logsèdisabled®skip_as_script«code_folded$cbd9c1aa-fc37-11ea-29d9-e3361406796fcell_id$cbd9c1aa-fc37-11ea-29d9-e3361406796fcodeusing Datesmetadatashow_logsèdisabled®skip_as_script«code_folded$450b4902-fc30-11ea-321d-29faf6188ff5cell_id$450b4902-fc30-11ea-321d-29faf6188ff5codeٔmd"Note that this returns an array of booleans of the same length as the vector `all_countries`. We can now use this to index into the `DataFrame`:"metadatashow_logsèdisabled®skip_as_script«code_folded$38344160-fc27-11ea-220e-95aa00e4b083cell_id$38344160-fc27-11ea-220e-95aa00e4b083codeـbegin
csv_data = CSV.File("covid_data.csv");
data = DataFrame(csv_data) # it is common to use `df` as a variable name
endmetadatashow_logsèdisabled®skip_as_script«code_folded$287f0fa8-fc44-11ea-2788-9f3ac4ee6d2bcell_id$287f0fa8-fc44-11ea-2788-9f3ac4ee6d2bcodemd"## Geographical data"metadatashow_logsèdisabled®skip_as_script«code_folded$d228e232-fc39-11ea-1569-a31b817118c4cell_id$d228e232-fc39-11ea-1569-a31b817118c4codemd"
Working with *cumulative* data is often less intuitive. Let's look at the actual number of daily cases. Julia has a `diff` function to calculate the difference between successive entries of a vector:
"metadatashow_logsèdisabled®skip_as_script«code_folded$9626d74a-fc3d-11ea-2ab3-978dc46c0f1fcell_id$9626d74a-fc3d-11ea-2ab3-978dc46c0f1fcodeٜmd"""Since the data contains some zeros, we need to replace those with `NaN`s ("Not a Number"), which `Plots.jl` interprets as a signal to break the line"""metadatashow_logsèdisabled®skip_as_script«code_folded$3519cf96-fc26-11ea-3386-d97c61ea1b85cell_id$3519cf96-fc26-11ea-3386-d97c61ea1b85codemd"""Since we need to manipulate the columns, let's rename them to something shorter. We can do this either **in place**, i.e. modifying the original `DataFrame`, or **out of place**, creating a new `DataFrame`. The convention in Julia is that functions that modify their argument have a name ending with `!` (often pronounced "bang").
We can use the `head` function to see only the first few lines of the data.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$16a79308-fc36-11ea-16e5-e1087d7ebbdacell_id$16a79308-fc36-11ea-16e5-e1087d7ebbdacode+US_row = findfirst(==("US"), all_countries)metadatashow_logsèdisabled®skip_as_script«code_folded$ada44a56-fc56-11ea-2ab7-fb649be7e066cell_id$ada44a56-fc56-11ea-2ab7-fb649be7e066codeUshp_countries = Shapefile.shapes(Shapefile.Table("./ne_110m_admin_0_countries.shp"));metadatashow_logsèdisabled®skip_as_script«code_folded$64d9bcea-7c85-421d-8f1e-17ea8ee694dacell_id$64d9bcea-7c85-421d-8f1e-17ea8ee694dacodeٞurl = "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv"metadatashow_logsèdisabled®skip_as_script«code_folded$210cee94-fc3e-11ea-1a6e-7f88270354e1cell_id$210cee94-fc3e-11ea-1a6e-7f88270354e1codedates[exp_period]metadatashow_logsèdisabled®skip_as_script«code_folded$539c951c-fc48-11ea-2293-457b7717ea4dcell_id$539c951c-fc48-11ea-2293-457b7717ea4dcodeWmd"We can fit a straight line using **linear regression** to this portion of the data."metadatashow_logsèdisabled®skip_as_script«code_folded$aaa7c012-fc1f-11ea-3c6c-89630affb1dbcell_id$aaa7c012-fc1f-11ea-3c6c-89630affb1dbcode$md"## Extracting useful information"metadatashow_logsèdisabled®skip_as_script«code_folded$e9ad97b6-fdef-4f48-bd32-634cfd2ce0e6cell_id$e9ad97b6-fdef-4f48-bd32-634cfd2ce0e6codeibegin
rename!(data, 1 => "province", 2 => "country", 3 => "latitude", 4 => "longitude")
head(data)
endmetadatashow_logsèdisabled®skip_as_script«code_folded$d3398953-afee-4989-932c-995c3ffc0c40cell_id$d3398953-afee-4989-932c-995c3ffc0c40code$md"""
## Exploring COVID-19 data
"""metadatashow_logsèdisabled®skip_as_script«code_folded$0b01120c-fc3d-11ea-1381-8bab939e6214cell_id$0b01120c-fc3d-11ea-1381-8bab939e6214codeَmd"## Exponential growth
Simple models of epidemic spread often predict a period with **exponential growth**. Do the data corroborate this?
"metadatashow_logsèdisabled®skip_as_script«code_folded$db4c1f10-7c37-4513-887a-2467ce673458cell_id$db4c1f10-7c37-4513-887a-2467ce673458codeټbegin
using Pkg
Pkg.add.(["CSV", "DataFrames", "PlutoUI", "Shapefile", "ZipFile", "JSON"])
using CSV
using DataFrames
using PlutoUI
using Shapefile
using ZipFile
using JSON
endmetadatashow_logsèdisabled®skip_as_script«code_folded$be868a52-fc3b-11ea-0b60-7fea05ffe8e9cell_id$be868a52-fc3b-11ea-0b60-7fea05ffe8e9codembegin
plot(daily_cases, label="raw daily cases")
plot!(running_mean, m=:o, label="running weakly mean")
endmetadatashow_logsèdisabled®skip_as_script«code_folded$16981da0-fc4d-11ea-37a2-535aa014a298cell_id$16981da0-fc4d-11ea-37a2-535aa014a298codedata.latitudemetadatashow_logsèdisabled®skip_as_script«code_folded$12900562-fc3a-11ea-25e1-f7c91a6940e5cell_id$12900562-fc3a-11ea-25e1-f7c91a6940e5codemd"Note that discrete data should *always* be plotted with points. The lines are just to guide the eye.
Cumulating data corresponds to taking the integral of a function and is a *smoothing* operation. Note that the cumulative data is indeed visually smoother than the daily data.
The oscillations in the daily data seem to be due to a lower incidence of reporting at weekends. We could try to smooth this out by taking a **moving average**, say over the past week:
"metadatashow_logsèdisabled®skip_as_script«code_folded$c400ce4e-fc30-11ea-13b1-b54cf8f5630ecell_id$c400ce4e-fc30-11ea-13b1-b54cf8f5630ecodemd"Now we would like to extract the data for the US alone. How can we access the correct row of the table? We can again filter on the country name. A nicer way to do this is to use the `filter` function.
This is a **higher-order function**: its first argument is itself a function, which must return `true` or `false`. `filter` will return all the rows of the `DataFrame` that satisfy that **predicate**:
"metadatashow_logsèdisabled®skip_as_script«code_folded$bcc95a8a-fc2e-11ea-2ccd-3bece42a08e6cell_id$bcc95a8a-fc2e-11ea-2ccd-3bece42a08e6code8md"You can also use `Select` to get a dropdown instead:"metadatashow_logsèdisabled®skip_as_script«code_folded$19bdf146-fc3c-11ea-3c60-bf7823c43a1dcell_id$19bdf146-fc3c-11ea-3c60-bf7823c43a1dcodeebegin
using Statistics
running_mean = [mean(daily_cases[i-6:i]) for i in 7:length(daily_cases)]
endmetadatashow_logsèdisabled®skip_as_script«code_folded$a9c39dbe-fc4d-11ea-2e86-4992896e2abbcell_id$a9c39dbe-fc4d-11ea-2e86-4992896e2abbcodemd"## Adding maps"metadatashow_logsèdisabled®skip_as_script«code_folded$b3e1ebf8-fc56-11ea-05b8-ed0b9e50503dcell_id$b3e1ebf8-fc56-11ea-05b8-ed0b9e50503dcode!# plot!(shp_countries, alpha=0.2)metadatashow_logsèdisabled®skip_as_script«code_folded$e0493940-8aa7-4733-af72-cd6bc0e37d92cell_id$e0493940-8aa7-4733-af72-cd6bc0e37d92code#md"""
## Download and load data
"""metadatashow_logsèdisabled®skip_as_script«code_folded$99d5a138-fc30-11ea-2977-71732ca3aeadcell_id$99d5a138-fc30-11ea-2977-71732ca3aeadcodelength(U_countries)metadatashow_logsèdisabled®skip_as_script«code_folded$85a145c6-fceb-11ea-0c94-27b3ef8270bccell_id$85a145c6-fceb-11ea-0c94-27b3ef8270bccodemd"""Day $day"""metadatashow_logsèdisabled®skip_as_script«code_folded$0c098923-b016-4c65-9a37-6b7b56b13a0ccell_id$0c098923-b016-4c65-9a37-6b7b56b13a0ccodeSdate_strings = String.(names(data)[5:end]) # apply String function to each elementmetadatashow_logsèdisabled®skip_as_script«code_folded$ee27bd98-fc37-11ea-163c-1365e194fc2ecell_id$ee27bd98-fc37-11ea-163c-1365e194fc2ecodebmd"Since the year was not correctly represented in the original data, we need to manually fix it:"metadatashow_logsèdisabled®skip_as_script«code_folded$f099424c-0e22-42fb-894c-d8c2a65715fbcell_id$f099424c-0e22-42fb-894c-d8c2a65715fbcode[scatter(US_data, m=:o, alpha=0.5, ms=3, xlabel="day", ylabel="cumulative cases", leg=false)metadatashow_logsèdisabled®skip_as_script«code_folded$57a9bb06-fc4a-11ea-2665-7f97026981dccell_id$57a9bb06-fc4a-11ea-2665-7f97026981dccodeqmd"Let's extract and plot the geographical information. To reduce the visual noise a bit we will only use those "metadatashow_logsèdisabled®skip_as_script«code_folded$bb6316b7-23fb-44a3-b64a-dfb71a7df011cell_id$bb6316b7-23fb-44a3-b64a-dfb71a7df011codecolumn_names = names(data)metadatashow_logsèdisabled®skip_as_script«code_folded$d911edb6-fc87-11ea-2258-d34d61c02245cell_id$d911edb6-fc87-11ea-2258-d34d61c02245codemetadatashow_logsèdisabled®skip_as_script«code_folded$7b2496b0-fc35-11ea-0e78-473e5e8eac44cell_id$7b2496b0-fc35-11ea-0e78-473e5e8eac44code0filter(x -> x.country == "United Kingdom", data)metadatashow_logsèdisabled®skip_as_script«code_folded$efa281da-cef9-41bc-923e-625140ce5a07cell_id$efa281da-cef9-41bc-923e-625140ce5a07codemd"""
In this notebook we will explore and analyse data on the COVID-19 pandemic. The aim is to use Julia's tools to analyse and visualise the data in different ways.
Here is an example of the kind of visualisation we will be able to produce:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$ad43cea2-fc28-11ea-2bc3-a9d81e3766f4cell_id$ad43cea2-fc28-11ea-2bc3-a9d81e3766f4codemd"A `DataFrame` is a standard way of storing **heterogeneous data** in Julia, i.e. a table consisting of columns with different types. As you can see from the display of the `DataFrame` object above, each column has an associated type, but different columns have different types, reflecting the type of the data in that column.
In our case, country names are stored as `String`s, their latitude and longitude as `Float64`s and the (cumulative) case counts for each day as `Int64`s.
."metadatashow_logsèdisabled®skip_as_script«code_folded$7ec28cd0-fc87-11ea-2de5-1959ea5dc37ccell_id$7ec28cd0-fc87-11ea-2de5-1959ea5dc37ccode6begin
zipfile = download("https://www.naturalearthdata.com/http//www.naturalearthdata.com/download/110m/cultural/ne_110m_admin_0_countries.zip")
r = ZipFile.Reader(zipfile);
for f in r.files
println("Filename: \$(f.name)")
open(f.name, "w") do io
write(io, read(f))
end
end
close(r)
endmetadatashow_logsèdisabled®skip_as_script«code_folded«notebook_id$8cae8068-4aa9-11f0-31ab-a194d2ebba27in_temp_dir¨metadata