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
Mat375 SIR Math Modeling COVID-19 Coronavirus SIRD
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

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:
Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) with death
Andrew E Long
40
Insight diagram
Disease Agent-Based Model SIR
SIR Model
Luis Gustavo Nardin
7
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
Math Modeling Mat375 SIR
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
116
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
ABM Disease SIR Roam

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
40
Insight diagram
SIR
SIR Model
Sarah Huang
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
SIR Stochastic Math Modelling Math Modeling
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
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
SIR Mat375 COVID-19 Coronavirus SIRD Math Modeling
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

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:
Clone of Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) with death
Jake Moore
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
Coronavirus SIR Math Modeling Mat375 COVID-19 SIRD
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

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:
Clone of Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) with death
Adheke Silas
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,
Math Modeling SIR Mat375
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 Simple, non-dimensionalized SIR (Susceptible, Infected, Recovered) model, with periodic infectivity
Andrew E Long
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,
Non-dimensionalize Math Modeling SIR Mat375
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
29
Modelo Baseado em Agente para a dispersão espacial de doenças, considerando o modelo SIR com perda da imunidade ao vírus, conforme [Bellinger G.]
DOENÇAS SIR ABM

Modelo Baseado em Agente para a dispersão espacial de doenças, considerando o modelo SIR com perda da imunidade ao vírus, conforme [Bellinger G.]

Modelo de dispersão espacial de uma doença baseado em SIR-ABM
Dager Moreira da Silva
3
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,
Mat375 SIR Math Modeling Non-dimensionalize
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
Alyssa Farmer
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,
Math Modeling Non-dimensionalize SIR Mat375
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
Patrick Nielsen
Spring, 2020: 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-mod
Mat375 COVID-19 SIR SIRD Coronavirus Math Modeling
Spring, 2020:

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

Without mortality, with time measured in days, with infection rate 1/2, recovery rate 1/3, and initial infectious population I_0=1.27x10-6, we recover 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:
Key for Lab SIR 2 -- Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) Model for Coronavirus
Andrew E Long
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,
SIR Non-dimensionalize Mat375 Math Modeling
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
Jacob Englert
Insight diagram
Aeromonas Aquaculture SIR Management
Aeromonas Management Model
Bradley Richardson
This model is for BME 1300, where we have to model an infectious disease, in this case, a zombie virus: Rage.
Infectious Disease SIR Zombies
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
A Susceptible-Infected-Recovered (SIR) disease model for Rage
Disease Health Care Health SIR

A Susceptible-Infected-Recovered (SIR) disease model for Rage

SIRKimpossibles
Kimpossibles
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,
Non-dimensionalize SIR Mat375 Math Modeling
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
Connor Edwards
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 infec
Covid-19 SIR
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:
  1. Wear a good mask: https://www.cdc.gov/coronavirus/2019-ncov/your-health/effective-masks.html
  2. 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
Insight diagram
Aquaculture SIR Aeromonas
Aeromonas ABM - Farm
Bradley Richardson
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,
Mat375 Math Modeling SIR Non-dimensionalize
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
Sally Dufek
Modelo epidemiológico simples SIR: Susceptíveis -Infectados - Recuperados Ajuste os PARÂMETROS abaixo. Clique em SIMULATE no menu superior para simular. Dados iniciais de 04 Abr 2020 Fonte:  https://www.worldometers.info/coronavirus/country/brazil/
COVID-19 Coronavirus SIR Epidemiología
Modelo epidemiológico simples
SIR: Susceptíveis -Infectados - Recuperados

Ajuste os PARÂMETROS abaixo.
Clique em SIMULATE no menu superior para simular.
Dados iniciais de 04 Abr 2020
Clone of Modelo SIR simples para Covid-19 - Brasil
Barbara Scoralick Villela
This is a simple example of (part of a) simple SIR (Susceptible, Infected, Recovered) model, suggested by De Vries, et al . in A Course in Mathematical Biology. They wanted to illustrate the comparative behavior of differential equations and discrete difference equations. We know that different
Mat375 SIR Math Modeling
This is a simple example of (part of a) simple SIR (Susceptible, Infected, Recovered) model, suggested by De Vries, et al. in A Course in Mathematical Biology.

They wanted to illustrate the comparative behavior of differential equations and discrete difference equations. We know that differential equations are generally solved numerically by discretizing them, so that the comparison is a little bit rigged....

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

Clone of Clone of A Simple Infection-only SIR (Susceptible, Infected, Recovered) Example
Leah Gillespie