SIR | Insight Maker

Spring, 2020: in the midst of on-line courses, due to the pandemic of Covid-19.

With the onset of the Covid-19 coronavirus crisis, we focus on SIRD models, which might realistically model the course of the disease.

We start with an SIR model, such as that featured in the MAA model featured in

https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Without mortality, with time measured in days, with infection rate 1/2, recovery rate 1/3, and initial infectious population I_0=1.27x10-4, we reproduce their figure

With a death rate of .005 (one two-hundredth of the infected per day), an infectivity rate of 0.5, and a recovery rate of .145 or so (takes about a week to recover), we get some pretty significant losses -- about 3.2% of the total population.

Resources:

http://www.nku.edu/~longa/classes/2020spring/mat375/mathematica/SIRModel-MAA.nb
https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) with death

Andrew E Long

62

SIR Model

Luis Gustavo Nardin

8

Thanks to
https://insightmaker.com/insight/25229/SIR-model-with-stochastic-events
for this example of adding stochasticity to the SIR model. "A simple extension of the tutorial SIR example, adding in Poisson events for infection and recovery. There is one macro, RandPoissonStep(rate)... to simulate Poisson processes."

I've tried to add in the infection step, as well as turn numbers into integers (without much luck). But it certainly has some interesting dynamics! I've also added in a phase plane graphic.

SIR model with stochastic events

Andrew E Long

6

Aeromonas ABM - Farm

Bradley Richardson

A spatially aware, agent based model of disease spread. There are three classes of people: susceptible (healthy), infected (sick and infectious), and recovered (healthy and temporarily immune).

@LinkedIn, Twitter, YouTube

Spatially Aware SIR Disease Model

Gene Bellinger

56

SIR Model

Sarah Huang

Clone of SIR Model

Robert J. Scott

An SIR model for Covid-19

This is a simple example of an SIR model for my Mathematics for Liberal Arts classes at Northern Kentucky University, Spring of 2022.

Let's think about things on the scale of a week. What happens over a week?

With an Ro of 2 (2 people infected for each infected individual, over the course of a week); recovery rate of 1 (every infected person loses their infectiousness after a week), and resusceptible rate of .05 (meaning .05, or a twentieth of the recovered lose their immunity each week), the disease peaks -- does the wave, then waves again before the year is out, then ultimately becomes

"endemic" (that is, it's never going away, which is clear after two years -- that is, a time of 104 weeks). This is like our seasonal flu (only the disease in this simulation doesn't illustrate seasonality -- that requires a more complicated model).

With an Ro of .9, recovery rate of 1, and resusceptible rate of .05, the disease is eliminated.

Masking, social distancing (including quarantining following contact), and quarantines all serve to reduce infectivity. And if we can drive infectivity down far enough, the disease can be eliminated. Other things that help is slowing down the resusceptibility, by vaccinating. Vaccines (in general) impart an immune response that reduces -- or even eliminates -- your susceptibility. We are still learning the extent to which these vaccines impart long-term immunity.

Other tools at our disposal include Covid-19 treatments, which increase the recovery rate, and vaccinations, which reduce the resusceptible rate. These can also serve to help us eradicate a disease, so that it doesn't become endemic (and so plague us forever).

Andy Long

Mathematics and Statistics

Some resources:

Wear a good mask: https://www.cdc.gov/coronavirus/2019-ncov/your-health/effective-masks.html
Gotta catch those sneezes: https://www.dailymail.co.uk/sciencetech/article-8221773/Video-shows-26-foot-trajectory-coronavirus-infected-sneeze.html

MAT115 Covid Simulation

Andrew E Long

==edited by Prasiantoro Tusono and Rio Swarawan Putra==

Spring, 2020: in the midst of on-line courses, due to the pandemic of Covid-19.

With the onset of the Covid-19 coronavirus crisis, we focus on SIRD models, which might realistically model the course of the disease.

We start with an SIR model, such as that featured in the MAA model featured in

https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Without mortality, with time measured in days, with infection rate 1/2, recovery rate 1/3, and initial infectious population I_0=1.27x10-4, we reproduce their figure

With a death rate of .005 (one two-hundredth of the infected per day), an infectivity rate of 0.5, and a recovery rate of .145 or so (takes about a week to recover), we get some pretty significant losses -- about 3.2% of the total population.

Resources:

http://www.nku.edu/~longa/classes/2020spring/mat375/mathematica/SIRModel-MAA.nb
https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) with death - based on Andrew E Long

prazi.antoro

Spring, 2020: in the midst of on-line courses, due to the pandemic of Covid-19.

With the onset of the Covid-19 coronavirus crisis, we focus on SIRD models, which might realistically model the course of the disease.

We start with an SIR model, such as that featured in the MAA model featured in

https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Without mortality, with time measured in days, with infection rate 1/2, recovery rate 1/3, and initial infectious population I_0=1.27x10-4, we reproduce their figure

With a death rate of .005 (one two-hundredth of the infected per day), an infectivity rate of 0.5, and a recovery rate of .145 or so (takes about a week to recover), we get some pretty significant losses -- about 3.2% of the total population.

Resources:

http://www.nku.edu/~longa/classes/2020spring/mat375/mathematica/SIRModel-MAA.nb
https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Clone of Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) with death

Adheke Silas

This is the first in a series of models that explore the dynamics of and policy impacts on infectious diseases. This basic model divides the population into three categories -- Susceptible (S), Infectious (I) and Recovered (R).

Press the simulate button to run the model and see what happens at different values of the Reproduction Number (R0).

The second model that includes a simple test and isolate policy can be found here.

Future Learn Basic SIR Model

Bob Hawkins

12

Spring, 2020: in the midst of on-line courses, due to the pandemic of Covid-19.

With the onset of the Covid-19 coronavirus crisis, we focus on SIRD models, which might realistically model the course of the disease.

We start with an SIR model, such as that featured in the MAA model featured in

https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Without mortality, with time measured in days, with infection rate 1/2, recovery rate 1/3, and initial infectious population I_0=1.27x10-4, we reproduce their figure

With a death rate of .005 (one two-hundredth of the infected per day), an infectivity rate of 0.5, and a recovery rate of .145 or so (takes about a week to recover), we get some pretty significant losses -- about 3.2% of the total population.

Resources:

http://www.nku.edu/~longa/classes/2020spring/mat375/mathematica/SIRModel-MAA.nb
https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Clone of Clone of Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) with death

Valeria Eunice Salas Flores

This is the third in a series of models that explore the dynamics of infectious diseases. This model looks at the impact of two types of suppression policies.

Press the simulate button to run the model with no policy. Then explore what happens when you set up a lockdown and quarantining policy by changing the settings below. First explore changing the start date with a policy duration of 60 days.

Clone of SIRD Epidemic Model with Suppression Policies

shaun savage

Modelo Baseado em Agente para a dispersão espacial de doenças, considerando o modelo SIR e a dependência comportamental proveniente da interação entre suscetíveis.

Modelo SIR espacial comportamental

NOEMI ZERAICK MONTEIRO

This model is for BME 1300, where we have to model an infectious disease, in this case, a zombie virus: Rage.

RAGE SIR Model

Kendra Simpson

3

Spring, 2020: in the midst of on-line courses, due to the pandemic of Covid-19.

With the onset of the Covid-19 coronavirus crisis, we focus on SIRD models, which might realistically model the course of the disease.

We start with an SIR model, such as that featured in the MAA model featured in

https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Without mortality, with time measured in days, with infection rate 1/2, recovery rate 1/3, and initial infectious population I_0=1.27x10-4, we reproduce their figure

With a death rate of .005 (one two-hundredth of the infected per day), an infectivity rate of 0.5, and a recovery rate of .145 or so (takes about a week to recover), we get some pretty significant losses -- about 3.2% of the total population.

Resources:

http://www.nku.edu/~longa/classes/2020spring/mat375/mathematica/SIRModel-MAA.nb
https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Clone of Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) with death

Jake Moore

This is a first example of a simple SIR (Susceptible, Infected, Recovered) model.

There are three pools of individuals: those who are infected (without them, no disease!), the pool of those who are at risk (susceptible), and the recovered -- who may lose their immunity and become susceptible again.

A comparable model in Mathematica is available at
http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/SIRModel.nb

A Simple SIR (Susceptible, Infected, Recovered) Example

Andrew E Long

154

This is an example of an SIR (Susceptible, Infected, Recovered) model that has been re-parameterized down to the bare minimum, to illustrated the dynamics possible with the fewest number of parameters.

We're rescaled this SIR model, so that time is given in infection rate-appropriate time units, "rates" are now ratios of rates (with infectivity rate in the denominator), and populations are considered proportions (unfortunately InsightMaker doesn't function properly if I give them all values from 0 to 1, which sum to 1 -- so, at the moment, I give them values that sum to 100, and consider the results percentages).

The new display includes the asymptotics: the three sub-populations will tend to fixed values as time goes to infinity; the infected population goes to zero if the recovery rate is greater than the infectivity rate -- i.e., the disease dies out.

Note the use of a "ghost" stock (for Total Population), which I think is a pretty cool idea. It cuts down on the number of arcs in the model graph.

A comparable model in Mathematica is available at
http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/SIRModel-rescaled.nb

Clone of A Sleek, non-dimensionalized SIR (Susceptible, Infected, Recovered) model

Maria E Ruwe

This is an example of an SIR (Susceptible, Infected, Recovered) model that has been re-parameterized down to the bare minimum, to illustrated the dynamics possible with the fewest number of parameters.

We're rescaled this SIR model, so that time is given in infection rate-appropriate time units, "rates" are now ratios of rates (with infectivity rate in the denominator), and populations are considered proportions (unfortunately InsightMaker doesn't function properly if I give them all values from 0 to 1, which sum to 1 -- so, at the moment, I give them values that sum to 100, and consider the results percentages).

The new display includes the asymptotics: the three sub-populations will tend to fixed values as time goes to infinity; the infected population goes to zero if the recovery rate is greater than the infectivity rate -- i.e., the disease dies out.

Note the use of a "ghost" stock (for Total Population), which I think is a pretty cool idea. It cuts down on the number of arcs in the model graph.

A comparable model in Mathematica is available at
http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/SIRModel-rescaled.nb

A Sleek, non-dimensionalized SIR (Susceptible, Infected, Recovered) model

Andrew E Long

31

Model introduction

This is an SIR model that simulates the potential COVID outbreak that can happen in Burnie, Tasmania after the positive case reported on October 2nd 2021, which incorporates three parts: Susceptible – Infectious – Recovered Looping model, government’s health policy that will affect each phase of the SIR process, and the potential economy that will affect people’s behaviours and thus influence the effectiveness of government’s public policy.

For instance, the values of variables deciding the inflection rate are influenced by actions taken to control the situation, such as through the quarantine of those infected, social distancing, travel bans, and personal isolation and protection strategies. Conversely, the magnitude of the problem at various points in time will also influence the magnitude of the response to control the situation.

Assumptions

1. The population is assumed to be homogeneous and well-mixed. And there is no significant change on the total population due to births and deaths.

2. Once lockdown is lifted, no further imported cases are assumed to occur.

3. Super spreader events are not explicitly considered.

4. The interaction among states is assumed to be implicit.

5. All confirmed cases would go to quarantine, and 90% of their contacts can be traced.

6. Contact tracing and testing capacity is sufficient.

Insights

Ideally, both one-way scenario analysis and two-way scenario analysis (amount change in one/two variables each time) will be conducted to find out the variable that has the greatest impact on getting new cases. Insights below can be gained:

1.What happens if people are more/less likely to pass on infection, through washing their hands and sneeze into their elbows (infection rate affected by people’s behaviours that will further induced by government’s policies)

2. How vaccination rate will affect the development of positive cases

3. What if the structure of the contact network changes (extent to which school, workplace and restaurants is shut down)

4. How growth rate is sensitive to the duration of illness and probability of infection

Clone of SIR - Government - Economy model of COVID19 outbreak in Burnie, Tasmania AU

TrungD

This is an example of an SIR (Susceptible, Infected, Recovered) model that has been re-parameterized down to the bare minimum, to illustrated the dynamics possible with the fewest number of parameters.

We're rescaled this SIR model, so that time is given in infection rate-appropriate time units, "rates" are now ratios of rates (with infectivity rate in the denominator), and populations are considered proportions (unfortunately InsightMaker doesn't function properly if I give them all values from 0 to 1, which sum to 1 -- so, at the moment, I give them values that sum to 100, and consider the results percentages).

The new display includes the asymptotics: the three sub-populations will tend to fixed values as time goes to infinity; the infected population goes to zero if the recovery rate is greater than the infectivity rate -- i.e., the disease dies out.

Note the use of a "ghost" stock (for Total Population), which I think is a pretty cool idea. It cuts down on the number of arcs in the model graph.

A comparable model in Mathematica is available at
http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/SIRModel-rescaled.nb

Clone of A Sleek, non-dimensionalized SIR (Susceptible, Infected, Recovered) model

Donna Odhiambo

Spring, 2020: in the midst of on-line courses, due to the pandemic of Covid-19.

With the onset of the Covid-19 coronavirus crisis, we focus on SIRD models, which might realistically model the course of the disease.

We start with an SIR model, such as that featured in the MAA model featured in

https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Without mortality, with time measured in days, with infection rate 1/2, recovery rate 1/3, and initial infectious population I_0=1.27x10-4, we reproduce their figure

With a death rate of .005 (one two-hundredth of the infected per day), an infectivity rate of 0.5, and a recovery rate of .145 or so (takes about a week to recover), we get some pretty significant losses -- about 3.2% of the total population.

Resources:

http://www.nku.edu/~longa/classes/2020spring/mat375/mathematica/SIRModel-MAA.nb
https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Clone of Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) with death

Christian Simon

Динамика описанного заболевания носит сезонный и периодический характер. Предпологается обычный грипп

Циклическая модель динамики заболевания

Канат Байгунусов

Apibendrintas modelis, kuriame modeliuojamas užkrečiamos ligos plitimas, tuo pačiu įvertinant specialių priemonių pritaikymą.

Užkrečiamos ligos epidemiologinis modelis

Julius Neviera

SIR Models