# My crude attempt at the SIR model
**URL:** https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919
**Category:** Offtopic
**Created:** [January 29, 2020, 8:29am UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919 "2020-01-29T08:29:06Z")
**Posts on this page:** 10
**Page:** 2
### Author:  [@StevenSiew](https://discourse.julialang.org/u/StevenSiew)
#### Post date: [February 22, 2020, 3:29am UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919/21 "2020-02-22T03:29:12Z")
One word: **PANDEMIC**
Number of cases outside China
Date Predictions Actual Comments
2020-02-21 1260 1378 under\_predicted
2020-02-22 1386
2020-02-23 1524
2020-02-24 1675
2020-02-25 1840
2020-02-26 2022
2020-02-27 2220
2020-02-28 2438
2020-02-29 2676
2020-03-01 2937
2020-03-02 3223
2020-03-03 3536
2020-03-04 3879
2020-03-05 4255
y = 37.68\*exp(x \* 0.09116) + (-58.54)
where x is number of days since 13th Jan 2020
x == 0 at 13th Jan 2020
[https://www.worldometers.info/coronavirus/coronavirus-cases/#active-cases](https://www.worldometers.info/coronavirus/coronavirus-cases/#active-cases)
look for “Total Cases excluding mainland China”
it has both Linear and Logarithmic graphs
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [February 22, 2020, 6:12am UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919/22 "2020-02-22T06:12:29Z")
> [@StevenSiew](#):
>
> y = 37.68\*exp(x \* 0.09116) + (-58.54)
> where x is number of days since 13th Jan 2020
> x == 0 at 13th Jan 2020
```julia
julia> g(x) = 37.68*exp(x * 0.09116) + (-58.54)
g (generic function with 1 method)
julia> g(365)
1.063077455599333e16
```
😉
---
### Author:  [@StevenSiew](https://discourse.julialang.org/u/StevenSiew)
#### Post date: [February 22, 2020, 10:26am UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919/23 "2020-02-22T10:26:04Z")
> [@Tamas\_Papp](#):
>
> julia\> g(x) = 37.68\*exp(x \* 0.09116) + (-58.54)
> g (generic function with 1 method)
>
> julia\> g(365)
> 1.063077455599333e16
**Oh come on!** Tamas Papp, you are an educated man and not a dum dum like me.
You know that early in a pandemic, the growth is exponential but late in a pandemic the growth becomes a logistic function.
---
### Author:  [@mschauer](https://discourse.julialang.org/u/mschauer)
#### Post date: [February 22, 2020, 11:26am UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919/24 "2020-02-22T11:26:35Z")
It is okay to discuss how to use Julia to let the data speak, but let’s not use this thread to try convince each other about how to assess a global health thread.
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [February 22, 2020, 12:44pm UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919/25 "2020-02-22T12:44:35Z")
Sorry if I was coming across as sarcastic. I was just trying to highlight the fact that it is very difficult add value to this question without
1. a more detailed model (preferably grounded in science, even in a stylized form, driven by some model of transmissions, incubation periods, etc)
2. quantification of estimation uncertainty (this is key, and often neglected in news reports),
3. somewhat more micro-level data,
4. model checking (preferably, posterior predictive checks).
In particular, just doing a simple log-linear transformation and estimating the 2–3 parameters is going to give a very poor predictive model.
I don’t know how much detailed data is accessible about this subject, but for the rest, Julia has great tools for answering these questions. For example, for using a simple model based on ODEs,
> **[GitHub - SciML/DiffEqBayes.jl: Extension functionality which uses Stan.jl,...](https://github.com/SciML/DiffEqBayes.jl)**
>
> Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learning - GitHub...
would be a starting point.
---
### Author:  [@mschauer](https://discourse.julialang.org/u/mschauer)
#### Post date: [February 22, 2020, 12:58pm UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919/26 "2020-02-22T12:58:41Z")
More starting points with BridgeSDEInference.jl addressing point 2: [BridgeSDEInference.jl/sir.jl at sir · mmider/BridgeSDEInference.jl · GitHub](https://github.com/mmider/BridgeSDEInference.jl/blob/sir/scripts/inference/sir.jl)
---
### Author:  [@StevenSiew](https://discourse.julialang.org/u/StevenSiew)
#### Post date: [February 24, 2020, 1:02am UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919/27 "2020-02-24T01:02:38Z")
People should be preparing for PANDEMIC
Coronavirus is going global and containment is no longer an option
The coronavirus containment has broken, with cases exploding across the
world. Now experts have revealed what to do to prepare.
Jamie Seidel
news.com.auFebruary 24, 202011:10am
Coronavirus: Australia’s $2.3 billion epidemic
Billions of dollars are at stake for the Australian economy. Which
industry will be most affected by coronavirus?
Coronavirus has broken containment. It’s exploding across the world,
from Italy to Singapore, South Korea and Japan.
Now Australian medicos are sounding the alarm: we must prepare for this
pandemic to strike home, Soon.
There’s been a profound shift in the Covid-19 epidemic.
Health officials are being taken by surprise. New cases of the virus
are appearing seemingly everywhere. And not all of them can be traced
back to travellers.
That means it’s already loose. Deep inside communities, such as Italy
and Japan.
That means it’s entering a new phase.
Last week, the World Health Organisation (WHO) warned that the “window
of opportunity” to contain the disease was narrowing.
But many epidemiologists fear that may have already passed.
It’s in hospitals. It’s in prisons. It’s on cruise ships.
It seems to be spread by carriers long before they show symptoms
themselves.
And that makes the virus almost impossible to contain.
So how bad is it?
University of Queensland associate professor in virology Ian Mackay
yesterday queried a disease risk-assessment think-tank. He wanted to
know the most responsible way to discuss the worsening Covid-19
outbreak.
So, he asked risk communicators Lanard & Sandman about whether it was
time to start using the `P word’.
“Yes,” came the blunt reply.
“It is past time to say `pandemic’.”
The virus is likely to soon be loose in our own country, cities and
towns.
ACTION STATIONS
The Centres for Disease Control (CDC) announced on Saturday it was
initiating preparations for a “likely” spread of Covid-19 in the United
States.
“We are reviewing all of our pandemic preparedness materials and
adapting them to Covid-19,” an official told media.
On Sunday, Victoria’s Chief Health Officer Brett Sutton responded in
kind.
“It’s clear that with local transmission in several countries that a
pandemic is very likely, if not inevitable,” his official Twitter
account reads. “We are working rapidly on planning and surge with our
health sector.”
```
Our latest analysis support that of @mlipsitch and colleagues: At
least 2/3 of cases in travellers from China to other countries have
likely been missed. Surveillance is never perfect.
https://t.co/NXUHzdJkRz
-- neil_ferguson (@neil_ferguson) February 21, 2020
```
A new assessment by the Imperial College London warns the outbreak is
likely dramatically worse than believed:
“We estimated that about two-thirds of Covid-19 cases exported from
mainland China have remained undetected worldwide, potentially
resulting in multiple chains of as yet undetected human-to-human
transmission outside mainland China.”
This is sending shockwaves through international health circles.
```
In sum, many countries likely be dealing w COVID epidemic soon. They
should be quickly preparing to deal, to do best they can w pt
medical
care, work to blunt overall impact, protect HCWs and keep health
care system functioning safely, communicate clearly to public et al.
16/x
-- Tom Inglesby (@T_Inglesby) February 23, 2020
```
“In sum, many countries likely be dealing with a Covid epidemic soon,”
responded the director of the Johns Hopkins Centre for Health Security
in Baltimore, Tom Inglesby. “They should be quickly preparing to deal,
to do best they can with medical care, work to blunt (its) overall
impact, protect health care workers, keep health care system
functioning safely and communicate clearly to the public.”
Risk group Lanard and Sandman say it’s important to point out that,
while it looks like Covid-19 will go global, we don’t yet know how
severe the disease is.
But, they add, the most “crucial (and overdue) risk communication task
for the next few days” is to prepare the public for when the `keeping
it out’ - containment - approach fails.
In other words, get ready for quarantine lockdowns.
`TAKE THE RISK OF SCARING PEOPLE’
“In most countries - including our United States and your Australia -
ordinary citizens have not been asked to prepare,” Lanard and Sandman
write. “Instead, they have been led to expect that their governments
will keep the virus from their doors.”
But such expectations are set to backfire.
And the risk assessors warn concerned academics and medicos to stand
resolute in the face of accusations of `fear-mongering’.
“Take the risk of scaring people … It is better to get through this
OMG moment now rather than later,” they write.
"Respond that hiding your strong professional opinion about this
pandemic-to-be would be immoral, or not in keeping with your commitment
to transparency, or unforgivably unprofessional, or derelict in your
duty to warn, or whatever feels truest in your heart.
“You’re only darned if you warn about something that turns out minor,”
Lanard and Sandman write. “But you’re damned, and rightly so, if you
fail to warn about something that turns out serious.”
Australian National University infectious disease specialist Dr Sanjaya
Senanayake agrees it is time to get prepared. But not to panic.
“Even though we don’t know at this point whether or not a pandemic will
occur, governments should be prepared for one and send out reassuring
messages to the public,” he told News Corp last night.
He says indications are it will be a disruptive disease. But not
devastating.
“While a lot isn’t known about this virus, at this stage it appears to
cause mild illness in the majority of people with a low case fatality
rate. So while it will cause disruption for a time to health services
and economies, they will eventually recover as more and more people
become immune.”
CHANGING TACTICS
The director of the Center for Communicable Disease Dynamics at Harvard
University, Marc Lipsitch, says containment no longer appears to be an
option.
Instead, countermeasures must be identified and implemented.
“Most things we can do to slow the virus’s spread - isolation,
quarantine, social distancing, cancelling public gatherings, treating
cases with antivirals - are temporary,” he wrote. “Once let up,
transmission can resurge.”
When a disease is established in a community, international travel bans
become pointless. Instead of slowing its spread, it makes it harder to
bring in urgently needed supplies and support.
So, Lanard and Sandman write, public health messages must switch from
`stopping them from infecting us' to `keeping us from infecting each
other’.
That means cancelling mass events, considering school closures - and
preparing for community lockdowns.
“We are near-certain that the desperate-sounding last-ditch containment
messaging of recent days is contributing to a massive global
misperception about the near-term future,” they write.
To counter this, public health officials should be talking about
slowing the spread of the virus. Not stopping it.
“One horrible effect of this continued `stop the pandemic' daydream masquerading as a policy goal (is that) it is driving counter-productive and outrage-inducing measures by many countries against travellers," they write. "But possibly more horrible: The messaging is driving resources toward `stopping,’ and away from the
main potential benefit of containment - slowing the spread of the
pandemic and thereby buying a little more time to prepare for what’s
coming.”
BUYING TIME
Lipsitch says slowing Covid-19’s spread will be difficult. Strict
quarantine measures worked well for SARS in 2003 because isolating sick
individuals prevented the disease from spreading.
Not so now.
“For Covid-19 it seems clear from individual well-documented cases that
people can transmit before symptoms (become distinctive),” he wrote.
“The key question - for which we (desperately) need good data - is
whether this is common or rare. Some circumstantial evidence suggests
it could be common.”
This limits the effectiveness of regular medical interventions. So
practices such as social distancing (self-isolation), as well as
“quarantine or lockdown” must be considered.
Slowing the spread of a virus through the community causes an epidemic
to last longer - but with less `peak strain’ on health facilities.
"That is beneficial because: 1) fewer individuals get infected in
total; 2) the burden on the health system is spread out, with lower
peak demand for scarce resources; 3) we will know more as time goes on
about how to care for patients, so it is better to get it late than
early; 4) if we can spread it out enough there may be new drugs,
vaccines, or other countermeasures to aid in preventing and treating
infection.
“Summary: Delay is good.”
Another essential piece of unknown information is how the virus affects
children.
So far, they seem strangely immune to Covid-19’s symptoms.
But are they innocent carriers?
“If kids are important for transmission, school closures may help; if
not, less so,” Lipsitch writes.
And the delaying tactics are already producing results.
“Although a vaccine program is many months away, there are promising
therapeutic options for treating people with the virus,” Dr Senanayake
says.
BE PREPARED
In China, Covid-19 came from nowhere on January 1 to put the entire
province of Wuhan in lockdown by February. Its rapid rate of spread can
be seen again in Italy and Japan.
Can we cope?
“We’ve provided guidance to practitioners and many communications
materials but are now focused on the models of care that will need to
be in place - clinics, phone triage, home care, right through to ICU
and aged care,” Sutton says.
```
Without rapid diagnostics ready to go, healthcare infrastructure may
become rapidly inundated, even if cases turn out all negative - an
abundance of caution will require quarantines until test rules out a
case. Any backlog can quickly hamper hospitals. 4/7...
-- Michael Mina (@michaelmina_lab) February 23, 2020
```
“Victoria and Australia nonetheless remain completely in containment
mode - identifying any possible case; isolating those who are
infectious; and quarantining contacts. Regardless of developments
internationally, this gives all of us time and space to plan and
prepare.”
But the response must be at all levels, Inglesby warns.
“Given the developments and trends of last few days, it’s clear
governments need to be working intently with hospitals and health care
systems to prepare to take care of Covid patients, possibly in high
numbers,” he says.
Key among concerning Covid-19 developments is the number of cases
appearing in countries outside China. And many of these aren’t linked
to travellers … indicating the virus is established in their general
populations.
Inglesby says that, based on China’s experience, preparations should
include:
o Preparing for a substantial increase in the numbers of patients who
need oxygen and mechanical ventilation;
o Getting people with symptoms of Covid-19 diagnosed rapidly and
correctly;
establishing the highest possible infection control procedures;
ensuring health care workers have high-quality personal protection
equipment to keep them from being infected
o Preparing to give those with Covid-19 who are not sick enough to be
in the hospital, instructions for home isolation and self-care, so they
do not pose risks to hospitalised
o Evaluating whether there are public health interventions at community
levels that might slow Covid-19 spread to create fewer numbers of very
sick people all being in hospital at the same time
WHAT TO DO
Lanard and Sandman say preparedness advice must be spread: “Hardly any
officials are telling civil society and the general public how to get
ready for this pandemic.”
To allay panic, they say, health officials should be providing
preparedness guidelines. This way worried people won’t be left feeling
helpless. And the more people getting prepared, the more people will
feel their community is ready.
“We are all stakeholders, and we don’t just want to hear what officials
are doing. We want to hear what we can do, too,” they write.
"We want - and need - to hear advice like this:
o Try to get a few extra months’ worth of prescription meds, if
possible.
o Don’t panic buy. But slowly build up your long-life grocery stocks to
enough for a few weeks.
o Think through now how we will take care of sick family members while
trying not to get infected.
o Cross-train key staff at work, so one person’s absence won’t derail
our organisation’s ability to function.
o Practice touching our faces less. So how about a face-counter app
like the step-counters so many of us use?
o Replace handshakes with elbow-bumps (the “ebola handshake”).
o Start practicing harm-reduction habits like pushing elevator buttons
with a knuckle instead of a fingertip.
But the impact of a pandemic could also reach deep into businesses,
supply chains and essential services.
“We have seen almost nothing in mainstream media citing this guidance,
or recommending business continuity strategies like urgent
cross-training so that core functions won’t be derailed because certain
key employees are out sick, for instance.”
```
I'm speaking to my CHO counterparts daily and briefing the sector -
and indeed all sectors - through our emergency management
arrangements, under @CommissionerEMV. This is critical - pandemics
challenge all sectors with effects on supply, workforce and business
continuity. (4/6)
-- Chief Health Officer, Victoria (@VictorianCHO) February 23, 2020
```
That message is now starting to get out.
At least at a state level.
“Australia absolutely has world-class healthcare, but even the best
healthcare in the world is challenged during pandemics,” Sutton says.
“We’ve got some of the brightest minds in the world in our health
services, laboratories, research sector and emergency management
sector. I’m confident we’re well placed to meet the challenges ahead,
whatever they might be. Hoping for the best and planning for the
worst.”
Dr Senanayake agrees: “Again, it is important to communicate the
message to the public that a pandemic doesn’t always mean a
catastrophic outcome, especially since the majority of cases with this
virus seem to be mild. It will certainly be an imposition, but likely a
temporary one.”
---
### Author:  [@Albert\_Zevelev](https://discourse.julialang.org/u/Albert_Zevelev)
#### Post date: [February 24, 2020, 2:12am UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919/28 "2020-02-24T02:12:49Z")
My understanding is that the mortality rate ~2.3%.
Higher for elderly & those w chronic illness
[https://www.google.com/amp/s/www.forbes.com/sites/ninashapiro/2020/02/22/sex-does-matter-when-it-comes-to-coronavirus/amp/](https://www.google.com/amp/s/www.forbes.com/sites/ninashapiro/2020/02/22/sex-does-matter-when-it-comes-to-coronavirus/amp/)
---
### Author:  [@StevenSiew](https://discourse.julialang.org/u/StevenSiew)
#### Post date: [February 24, 2020, 2:27pm UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919/29 "2020-02-24T14:27:14Z")
**THERE WILL NEVER BE A PANDEMIC - WHO**
[Link to Reuters article](https://www.reuters.com/article/us-china-health-who/who-says-no-longer-uses-pandemic-category-but-virus-still-emergency-idUSKCN20I0N8)
# WHO find a loop hole that enables them not to declare a pandemic. The classic goal posts moved approached. Brilliant.
NEW: WHO says it no longer has a process to declare a pandemic, says old system with 6 phases is no longer being used - Reuters
11:31 PM · Feb 24, 2020
THIS IS A HORROR MOVIE. THIS CANNOT BE REAL. I MUST BE DREAMING. YOU CANT MAKE THIS SHIT UP IN A FICTIONAL NOVEL. NO ONE WILL BELIEVE YOU!
Postscript: Next week, WHO will change the definition of DEATH
---
### Author:  [@klaff](https://discourse.julialang.org/u/klaff)
#### Post date: [March 12, 2020, 3:01am UTC](https://discourse.julialang.org/t/my-crude-attempt-at-the-sir-model/33919/30 "2020-03-12T03:01:38Z")
[https://www.ijidonline.com/article/S1201-9712(20)30117-X/fulltext](https://www.ijidonline.com/article/S1201-9712(20)30117-X/fulltext)
And a start at their model:
```julia
using DifferentialEquations, Plots
function corona!(du,u,p,t)
S,E,I,R,N,D,C = u
F, β0,α,κ,μ,σ,γ,d,λ = p
du[1] = -β0*S*F/N - β(t,β0,D,N,κ,α)*S*I/N -μ*S # susceptible
du[2] = β0*S*F/N + β(t,β0,D,N,κ,α)*S*I/N -(σ+μ)*E # exposed
du[3] = σ*E - (γ+μ)*I # infected
du[4] = γ*I - μ*R # removed (recovered + dead)
du[5] = -μ*N # total population
du[6] = d*γ*I - λ*D # severe, critical cases, and deaths
du[7] = σ*E # +cumulative cases
end
β(t,β0,D,N,κ,α) = β0*(1-α)*(1-D/N)^κ
S0 = 14e6
u0 = [0.9*S0, 0.0, 0.0, 0.0, S0, 0.0, 0.0]
p = [10.0, 0.5944, 0.4239, 1117.3, 0.02, 1/3, 1/5,0.2, 1/11.2]
R0 = p[2]/p[7]*p[6]/(p[6]+p[5])
tspan = [0.0, 365.0]
prob = ODEProblem(corona!, u0, tspan, p)
@time sol = solve(prob, Tsit5())
plot(sol, vars=[2,3,4])
```
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