Diagram and simulation of disease spread

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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:

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

Andrew E Long

Ce modèle simule l'évolution dynamique d'un paysage méditerranéen en utilisant une Chaîne de Markov. Il modélise la transition d'un paysage (composé de 5 états : Chênaie, Vigne, Pelouse, Garrigue, Pinède) à travers le temps, sous l'effet combiné de la succession naturelle et des perturbations (feu, déforestation).

Ce modèle s'inscrit dans la suite de notre cours sur la dynamique des communautés. Après avoir étudié les interactions entre populations (modèles ODE de Lotka-Volterra), ce modèle fait le "grand saut" conceptuel vers la dynamique des paysages entiers. Il abandonne l'approche déterministe et continue (dx/dt) pour une approche stochastique (probabiliste) et à temps discret (π t+1).

Contrairement aux modèles précédents qui cherchaient un équilibre de populations, ce modèle explore comment un système soumis à des probabilités de transition constantes converge vers une distribution stationnaire (un état d'équilibre stable du paysage).

Le paysage est modélisé comme un total de 100 hectares (ou 100%) répartis entre cinq "Stocks" (les 5 états). À chaque pas de temps, des "Flux" déplacent une proportion de la surface d'un stock à l'autre, en fonction des probabilités de la matrice de transition P.

Les Composants du Modèle

Variables d’état (Stocks) :

/!\ Le total doit faire 100 hectares (ha) /!\

Vi : Surface du paysage (en ha) à l'état de Vigne/Verger (culture)
Gr : Surface du paysage (en ha) à l'état de Pelouse (post-abandon/post-feu).
Ga : Surface du paysage (en ha) à l'état de Garrigue (évolution de la pelouse).
Pi : Surface du paysage (en ha) à l'état de Pinède (forêt pionnière).
Oak : Surface du paysage (en ha) à l'état de Chênaie (climax)

Flux (représentant les probabilités de transitions Pij) :

Deforestation (Oak → Vi) : Action humaine de remise en culture.
Abandon (Vi → Gr) : Début de la succession secondaire
GrGa : Succession naturelle (embroussaillement)
GaPi : Succession naturelle (colonisation par les pins)
PiOak : Succession naturelle (maturation vers le climax).
Wildfire (Pi → Gr) : Perturbation par le feu qui réinitialise la succession

Note Importante : La somme de toutes les probabilités sortant d'un même stock doit être inférieure ou égale à 1.0. Le reste (1.0 - somme des sorties) est la probabilité implicite de rester dans le même état.

Indicateurs produits :

Graphique temporel : Montre l'évolution des 5 états (en hectares) au fil du temps (en pas de simulation). Les courbes convergent-elles vers la distribution stationnaire prédite par le cours ?

Votre Mission d'Exploration :

Votre objectif est d'utiliser ce modèle pour recréer les simulations du cours et explorer différents scénarios de gestion de paysage.

Cliquez sur "SIMULATE" et explorez la dynamique stochastique qui régit l'avenir de nos paysages !

Modèle de Succession (Chaîne de Markov)

Florian Orgeret

3 weeks ago

La situación modelada expresa el crecimiento de las ventas impulsadas por la motivación y productividad, pero es frenada por el tamaño del nicho de mercado.

Límite de Crecimiento

Marcelo A. Castro Iglesias

566 7 months ago

Purpose
Enables the different components in the 5 capability model in a visual manner for Enterprise and Business Architecture stakeholders.

Enter volumes based on transactions from all your applications based on the business process layer. Actual transaction volumes recorded for your expense or revenue stream. Example; how many applications are sponsored by engineering that allow CREATE and UPDATE of a supplier or customer. Enter the number of transactions in the engineering variable. The engineering group has no authority to create either a supplier or customer. All organizations are allowed to submit a certain set of inputs for a super user group to review and then those super users create and update the master record.

Food for thought, the difference between the records created by the super user group and the volume of created party management records is the opportunity to scale and protect the reputation of your client.

Now lets do the same for every update to a party management record. All changes to a supplier or customer could effect pricing and tax or duty fees and each must use the formal change management process with many changes needing to have an authorized representative from the supplier or customer. Digital records are in need of key control designs. These are monitored and reported to the SEC.

BUSINESS ARCHITECTURE

5 Capability Model
The 5 capability model has many stock and flow children which each organization will need to model based on their current state.

Aligns to APQC Process Framework
Aligns to Principles in ISO 9001, 26000 and 27001

ENTERPRISE ARCHITECTURE
Aligns Zachman Framework Enterprise and Business Architecture with Executive and Leaders from a business management level across any organization.

A method in which to align and benchmark any organization or agency, with the system(s) logic required from Architects in Row 3, to enable Row 4 engineers who need to supply physics.

Semantic
Getting terms to align to the generic objects can be a trying task, unless you simply list the stakeholders "semantic" term below the stakeholder in the presentation layer by order shown in the business process management section above the capability management group.

As Is and To Be Business and Technology Architecture

Lisa Marie “Werby-Martinez”

Clusters of interacting methods for improving health services network design and delivery. Includes Forrester quotes on statistical vs SD methods and the Modeller's dilemma. Simplified version of IM-14982 combined with IM-17598 and IM-9773

Complex Decision Technologies