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).

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ABM Disease SIR Roam

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

Zombies Infectious Disease SIR

SIR Agent-Based Model Disease

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.

Epidemic COVID-19 SIR

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.

Epidemic COVID-19 SIR

SIR

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 inhttps://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:

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

SIR Math Modeling Mat375 COVID-19 Coronavirus SIRD

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

SIR Math Modeling Mat375

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

Disease Health Care Health SIR

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

SIR Math Modeling Mat375 Non-dimensionalize

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

SIR Math Modeling 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

SIR Math Modeling Mat375

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

ABM DOENÇAS SIR

This is the second in a series of models that explore the dynamics of and policy impacts on infectious diseases. This basic SIR model explores the impact of a simple test and isolate policy. The first model can be found here.

Epidemic COVID-19 SIR

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.

Math Modeling Math Modelling Stochastic SIR

SIR

Aeromonas SIR Aquaculture Management

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

SIR Math Modeling Mat375

Aeromonas SIR Aquaculture

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 inhttps://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=1.27x10-6, 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:
  * http://www.nku.edu/~longa/classes/2020spring/mat375/mathematica/SIRModel-MAA.nb
  * http://www.nku.edu/~longa/classes/2020spring/mat375/mathematica/SIRModel-MAA-with-Flattening.nb

SIR Math Modeling Mat375 COVID-19 Coronavirus SIRD

SIR Agent-Based Model Disease

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

SIR Math Modeling Mat375 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

SIR Math Modeling Mat375 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

SIR Math Modeling Mat375 Non-dimensionalize