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
A Simple SIR (Susceptible, Infected, Recovered) without infection
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
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
Clone of A Simple SIR (Susceptible, Infected, Recovered) Example
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
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
Clone of Spatially Aware SIR Disease Model
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-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
Clone of Key for Lab SIR 2 -- Coronavirus: A Simple SIR (Susceptible, Infected, Recovered) Model for Coronavirus
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
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
Clone of Spatially Aware SIR Disease Model
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/
Clone of Modelo SIR simples para Covid-19 - Brasil
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
https://www.sciencedirect.com/science/article/pii/S0960077920309851
2 strain SIR model
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
Detta är en enkel SIR-modell (Susceptible, Infected, Recovered).
I den enkla SIR-modellen finns tre kategorier av individer:
1. Grupp av individer som befinner sig i riskzonen för att bli smittade/sjuka - Susceptible (mottagliga).
2. Grupp av individer som är infekterade - Infected.
3. Grupp av individer som är under tillfrisknande men som kan förlora sin immunitet och bli mottagliga igen - Recovered.
Thomas Hedlund Leijon
SIR-model (Susceptible, Infected, Recovered)
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
Clone of Clone of A Simple SIR (Susceptible, Infected, Recovered) Example
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
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
Clone of A Simple SIR (Susceptible, Infected, Recovered) Example
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
Clone of Spatially Aware SIR Disease Model
Modelo epidemiológico simples
SIR: Susceptíveis - Infectados - Recuperados
Dados iniciais do Brasil em 04 Abr 2020
Fonte:
https://www.worldometers.info/coronavirus/country/brazil/
Clone of Clone of Modelo SIR simples - Covid-19
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
Clone of Spatially Aware SIR Disease Model
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
Clone of A Simple SIR (Susceptible, Infected, Recovered) Example
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
Clone of Spatially Aware SIR Disease Model
