Kermack–McKendrick Epidemic SIR Infectious Disease Model - Metrics by Guy Lakeman

This is a simple SIR infectious diseases 3 stock model with Susceptibles, Infectives and Recovereds stocks. In the initial description the R signified Removed and could include Deaths, Recovered with immunity to infection (Resistant) or those who had fled the epidemic. Note the need to initiate the epidemic by adding a pulse of a single infected person at time 0.

This insight is about infection propagation and  population migration influence on this propagation. For this, we defined a world population size and a percentage of it who’s infected. Then, we created an agent where we simulated possible states of an individual. So, he can be healthy, infected (with an infection rate) or immunized ( with a certain rate of immunization). If the individual is infected, he can be alive or dead. Then, we simulated different continents (North-America, Asia and Europe) with a migration between these with a certain rate of migration (we tried to approach reality). Then, thanks to our move action which represents a circular permutation between the different continents with a random probability, the agent will be applied to every individual of the world population.

 How does the program work ?

In order to use this insight, we need to define a size of world population and a probability of every individual to reproduce himself. Every individual of this population can have three different state (healthy, infected or immunized) and infected people can be alive or dead. We need to define a percentage of infection for healthy people and a percentage of death for infected people and also a percentage of immunization.
Finally, there is Migration Part of the program, in this one, we need to define three different continents, states or whatever you want. We also need to define a migration probability between each continent to move these person. With this moving people, we can study the influence of migration on the propagation of a disease.

Vincent Cochet, Julien Platel, Jordan Béguet

SARS-CoV-19 spread in different countries

This model shows the relationship between placement to Bourke Hospital and Infection Rate, Recovery rate and release from Bourke Hospital.  

Here we have a basic SEIR model and we will investigate what changes would be appropriate for modelling the 2019 Coronavirus.

The initial parametrization is based on the suggested current data. The initial population is set for Catalonia.

Here we have a basic SEIR model and we will investigate what changes would be appropriate for modelling the 2019 Coronavirus 

Here we have a basic SEIR model and we will investigate what changes would be appropriate for modelling the 2019 Coronavirus 

SARS-CoV-19 spread in different countries

Ausbreitung von SARS-CoV-19 in verschiedenen Ländern
- bitte passen Sie die Variablen über die Schieberegler weiter unten entsprechend an

Italien

    ältere Bevölkerung (>65): 0,228
    Faktor der geschätzten unentdeckten Fälle: 4-11
    Ausgangsgröße der Bevölkerung: 60 000 000
    hoher Blutdruck: 0,32 (gbe-bund)
    Herzkrankheit: 0,04 (statista)
    kostenlose Intensivstationen: 3 100


Deutschland

    ältere Bevölkerung (>65): 0,195 (bpb)
    geschätzte unentdeckte Fälle Faktor: 2-3 (deutschlandfunk)
    Ausgangsgröße der Bevölkerung: 83 000 000
    hoher Blutdruck: 0,26 (gbe-bund)
    Herzkrankheit: 0,2-0,28 (Herzstiftung)
    kostenlose Intensivstationen: 5 880


Frankreich

    ältere Bevölkerung (>65): 0,183 (statista)
    Faktor der geschätzten unentdeckten Fälle: 3-5
    Ausgangsgröße der Bevölkerung: 67 000 000
    Bluthochdruck: 0,3 (fondation-recherche-cardio-vasculaire)
    Herzkrankheit: 0,1-0,2 (oecd)
    kostenlose Intensivstationen: 3 000


Je nach Bedarf:

    Anzahl der Begegnungen/Tag: 1 = Quarantäne, 2-3 = soziale Distanzierung , 4-6 = erschwertes soziales Leben, 7-9 = überhaupt keine Einschränkungen // Vorgabe 2
    Praktizierte Präventivmassnahmen (d.h. sich regelmässig die Hände waschen, das Gesicht nicht berühren usw.): 0.1 (niemand tut etwas) - 1 (sehr gründlich) // Vorgabe 0.8
    Aufklärung durch die Regierung: 0,1 (sehr schlecht) - 1 (sehr transparent und aufklärend) // Vorgabe 0,9
    Immunitätsrate (aufgrund fehlender Daten): 0 (man kann nicht immun werden) - 1 (wenn man es einmal hatte, wird man es nie wieder bekommen) // Vorgabe 0,4


Schlüssel

    Anfällige: Menschen sind nicht mit SARS-CoV-19 infiziert, könnten aber infiziert werden
    Infizierte: Menschen sind infiziert worden und haben die Krankheit COVID-19
    Geheilte: Die Menschen haben sich gerade von COVID-19 erholt und können es in diesem Stadium nicht mehr bekommen
    Tote: Menschen starben wegen COVID-19
    Immunisierte: Menschen wurden immun und können die Krankheit nicht mehr bekommen
    Kritischer Prozentsatz der Wiederherstellung: Überlebenschance ohne spezielle medizinische Behandlung

Here we have a basic SEIR model and we will investigate what changes would be appropriate for modelling the 2019 Coronavirus 

SARS-CoV-19 spread in different countries

This model simulates a waterborne illness spread from a central reservoir. It illustrates the combination of System Dynamics (modeling pathogen levels in the reservoir) and Agent Based Modeling.

Here we have a basic SEIR model and we will investigate what changes would be appropriate for modelling the 2019 Coronavirus.

The initial parametrization is based on the suggested current data. The initial population is set for Catalonia.

SARS-CoV-19 spread in different countries

Here we have a basic SEIR model and we will investigate what changes would be appropriate for modelling the 2019 Coronavirus.

The initial parametrization is based on the suggested current data. The initial population is set for Catalonia.

Here we have a basic SEIR model and we will investigate what changes would be appropriate for modelling the 2019 Coronavirus.

We add simple containment meassures that affect two paramenters, the Susceptible population and the rate to become infected.

The initial parametrization is based on the suggested current data. The initial population is set for Catalonia.

The questions that we want to answer in this kind of models are not the shape of the curves, that are almost known from the beginning, but, when this happens, and the amplitude of the shapes. This is crucial, since in the current circumstance implies the collapse of certain resources, not only healthcare.

The validation process hence becomes critical, and allows to estimate the different parameters of the model from the data we obtain. This simulation approach allows to obtain somethings that is crucial to make decisions, the causality. We can infer this from the assumptions that are implicit on the model, and from it we can make decisions to improve the system behavior.

Yes, simulation works with causality and Flows diagrams is one of the techniques we have to draw it graphically, but is not the only one. On https://sdlps.com/projects/documentation/1009 you can review soon the same model but represented in Specification and Description Language.

Ausbreitung von SARS-CoV-19 in verschiedenen Ländern
- bitte passen Sie die Variablen über die Schieberegler weiter unten entsprechend an

Italien

    ältere Bevölkerung (>65): 0,228
    Faktor der geschätzten unentdeckten Fälle: 0,6
    Ausgangsgröße der Bevölkerung: 60 000 000
    hoher Blutdruck: 0,32 (gbe-bund)
    Herzkrankheit: 0,04 (statista)
    Anzahl der Intensivbetten: 3 100


Deutschland

    ältere Bevölkerung (>65): 0,195 (bpb)
    geschätzte unentdeckte Fälle Faktor: 0,2 (deutschlandfunk)
    Ausgangsgröße der Bevölkerung: 83 000 000
    hoher Blutdruck: 0,26 (gbe-bund)
    Herzkrankheit: 0,2-0,28 (Herzstiftung)
    Anzahl der Intensivbetten: 5 880


Frankreich

    ältere Bevölkerung (>65): 0,183 (statista)
    Faktor der geschätzten unentdeckten Fälle: 0,4
    Ausgangsgröße der Bevölkerung: 67 000 000
    Bluthochdruck: 0,3 (fondation-recherche-cardio-vasculaire)
    Herzkrankheit: 0,1-0,2 (oecd)
    Anzahl der Intensivbetten: 3 000


Je nach Bedarf:

    Anzahl der Begegnungen/Tag: 1 = Quarantäne, 2-3 = soziale Distanzierung , 4-6 = erschwertes soziales Leben, 7-9 = überhaupt keine Einschränkungen // Vorgabe 2
    Praktizierte Präventivmassnahmen (d.h. sich regelmässig die Hände waschen, das Gesicht nicht berühren usw.): 0.1 (niemand tut etwas) - 1 (sehr gründlich) // Vorgabe 0.8
    Aufklärung durch die Regierung: 0,1 (sehr schlecht) - 1 (sehr transparent und aufklärend) // Vorgabe 0,9
    Immunitätsrate (aufgrund fehlender Daten): 0 (man kann nicht immun werden) - 1 (wenn man es einmal hatte, wird man es nie wieder bekommen) // Vorgabe 0,4


Schlüssel

    Anfällige: Menschen sind nicht mit SARS-CoV-19 infiziert, könnten aber infiziert werden
    Infizierte: Menschen sind infiziert worden und haben die Krankheit COVID-19
    Geheilte: Die Menschen haben sich gerade von COVID-19 erholt und können es in diesem Stadium nicht mehr bekommen
    Tote: Menschen starben wegen COVID-19
    Immunisierte: Menschen wurden immun und können die Krankheit nicht mehr bekommen
    Kritischer Prozentsatz der Wiederherstellung: Überlebenschance ohne spezielle medizinische Behandlung

This model simulates a waterborne illness spread from a central reservoir. It illustrates the combination of System Dynamics (modeling pathogen levels in the reservoir) and Agent Based Modeling.

Kermack–McKendrick Epidemic SIR Infectious Disease Model - Metrics by Guy Lakeman

This is a simple SIR infectious diseases 3 stock model with Susceptibles, Infectives and Recovereds stocks. In the initial description the R signified Removed and could include Deaths, Recovered with immunity to infection (Resistant) or those who had fled the epidemic. Note the need to initiate the epidemic by adding a pulse of a single infected person at time 0.

Slimības

Here we have a basic SEIR model and we will investigate what changes would be appropriate for modelling the 2019 Coronavirus.

We add simple containment meassures that affect two paramenters, the Susceptible population and the rate to become infected.

The initial parametrization is based on the suggested current data. The initial population is set for Catalonia.

The questions that we want to answer in this kind of models are not the shape of the curves, that are almost known from the beginning, but, when this happens, and the amplitude of the shapes. This is crucial, since in the current circumstance implies the collapse of certain resources, not only healthcare.

The validation process hence becomes critical, and allows to estimate the different parameters of the model from the data we obtain. This simulation approach allows to obtain somethings that is crucial to make decisions, the causality. We can infer this from the assumptions that are implicit on the model, and from it we can make decisions to improve the system behavior.

Yes, simulation works with causality and Flows diagrams is one of the techniques we have to draw it graphically, but is not the only one. On https://sdlps.com/projects/documentation/1009 you can review soon the same model but represented in Specification and Description Language.

SARS-CoV-19 spread in different countries

SARS-CoV-19 spread in different countries