| // SIR.java |
| package org.eclipse.stem.diseasemodels.standard; |
| |
| /******************************************************************************* |
| * Copyright (c) 2006 IBM Corporation and others. |
| * All rights reserved. This program and the accompanying materials |
| * are made available under the terms of the Eclipse Public License v1.0 |
| * which accompanies this distribution, and is available at |
| * http://www.eclipse.org/legal/epl-v10.html |
| * |
| * Contributors: |
| * IBM Corporation - initial API and implementation |
| *******************************************************************************/ |
| |
| import org.eclipse.emf.common.util.URI; |
| import org.eclipse.stem.core.STEMURI; |
| |
| /** |
| * A {@link DiseaseModel} with three states <em>Susceptible</em>, |
| * <em>Infectious</em> and <em>Recovered</em>(SIR). |
| * |
| * <p> |
| * The basic <em>SIR</em> (Susceptible, Infectious, Recovered) disease model |
| * assumes a uniform population at a single location and that the population |
| * members are well "mixed", meaning that they are equally likely to meet and |
| * infect each other. This model, for a normalized population, is defined by the |
| * three equations below: |
| * <ul> |
| * <li><em>Δs = μ − βs i + γr − μs</em> |
| * </li> |
| * <li><em>Δi = βs i − σi − μi</em> </li> |
| * <li><em>Δr = σi − γr − μr</em> </li> |
| * </ul> |
| * |
| * |
| * <p> |
| * Where: |
| * <ul> |
| * <li><em>s</em> is the normalized <em>Susceptible</em> population </li> |
| * <li> <em>i</em> is the normalized <em>Infectious</em> population</li> |
| * <li>μ is the background mortality rate, and, because it is assumed that |
| * the population was not growing or shrinking significantly before the onset of |
| * the disease, μ is also assumed to be the birth rate. </li> |
| * <li> <em>β</em> is the disease transmission (infection) rate. This |
| * coefficient determines the number of population members that become |
| * infected/exposed per population member in the <em>Infectious</em> state, |
| * assuming the entire population is in the <em>Susceptible</em> state. </li> |
| * <li> σ is the <em>Infectious</em> recovery rate. This coefficient |
| * determines the rate at which <em>Infectious</em> population members |
| * <em>Recover</em>.</li> |
| * <li><em>γ</em> is the immunity loss rate. This coefficient |
| * determines the rate at which <em>Recovered</em> population members lose |
| * their immunity to the disease and become <em>Susceptible</em> again.</li> |
| * </ul> |
| * </p> |
| * Following basically the same derivation as outlined in {@link SI} for the SI |
| * model, these become: |
| * |
| * <p> |
| * Let |
| * <ul> |
| * <li><em>x</em> be the <em>Infectious Mortality</em> which is the |
| * proportion of the population members who become <em>Infectious</em> that |
| * will eventually die.</li> |
| * <li><em>μ<sub>i</sub></em> be the <em>Infectious Mortality Rate</em>. |
| * This is the rate at which fatally infected population members die |
| * specifically due to the disease. </li> |
| * </ul> |
| * Thus, we now have two types of <em>Infectious</em> population members, |
| * those that will eventually recover at rate <em>σ</em>, and those that |
| * will eventually die at rate <em>μ<sub>i</sub></em> (of course, members |
| * in all three states still die at the background rate <em>μ</em>). |
| * </p> |
| * <p> |
| * Let |
| * <ul> |
| * <li><em> i <sup>R</sup></em> be the normalized infectious population that |
| * will recover.</li> |
| * <li><em> i <sup>F</sup></em> be the normalized infectious population that |
| * will die from the disease.</li> |
| * <li><em> i = i <sup>R</sup> + i <sup>F</sup></em> be the total normalized |
| * infectious population (as before).</li> |
| * </ul> |
| * </p> |
| * |
| * <p> |
| * We modify our model to include these additional states and rates. |
| * <ul> |
| * <li><em>Δs = μ − βs i + γr − μ s</em> |
| * </li> |
| * <li><em>Δi <sup>R</sup> = (1-x)βs i − σi <sup>R</sup> − μi <sup>R</sup></em> |
| * </li> |
| * <li><em>Δi <sup>F</sup> = x βs i − (μ + μ<sub>i</sub>) i <sup>F</sup></em> |
| * </li> |
| * <li><em>Δr = σi<sup>R</sup> − γr − μr</em> |
| * </li> |
| * |
| * </ul> |
| * </p> |
| * <h3>Spatial Adaptation</h3> |
| * <p> |
| * <ul> |
| * <li><em>Δs P<sub>l</sub>= μP<sub>l</sub> − β<sub>l</sub> s i P<sub>l</sub> + γ r P<sub>l</sub> − μ s P<sub>l</sub></em> |
| * </li> |
| * <li><em>Δi <sup>R</sup> P<sub>l</sub> = (1-x)β<sub>l</sub> s i P<sub>l</sub> − σ i <sup>R</sup> P<sub>l</sub> − μi <sup>R</sup> P<sub>l</sub></em> |
| * </li> |
| * <li><em>Δi <sup>F</sup> P<sub>l</sub> = x β<sub>l</sub>s i P<sub>l</sub> − (μ + μ<sub>i</sub>) i <sup>F</sup> P<sub>l</sub></em> |
| * </li> |
| * <li><em>Δr P<sub>l</sub>= σi<sup>R</sup>P<sub>l</sub> − γr P<sub>l</sub>− μr P<sub>l</sub></em> |
| * </li> |
| * </ul> |
| * |
| * <p> |
| * Let <em>S<sub>l</sub> = s P<sub>l</sub></em> be the number of |
| * <em>Susceptible</em> population members at location <em>l</em>. |
| * Similarly, let <em>I<sub>l</sub> = i P<sub>l</sub></em> be the number |
| * of population members at location <em>l</em> that are <em>Infectious</em> |
| * (both states combined), and let |
| * <em>r P<sub>l</sub> be the <em>Recovered</em> population. |
| * For readability, we drop the <em>l</em> subscript and substitute. |
| * </p> |
| * Substituting |
| * |
| * </p> |
| * <ul> |
| * <li><em>ΔS = μP<sub>l</sub> − β<sub>l</sub> S i + γR − μ S</em> |
| * </li> |
| * <li><em>ΔI <sup>R</sup> = (1-x)β<sub>l</sub> S i − σI <sup>R</sup> − μI <sup>R</sup> </em> |
| * </li> |
| * <li><em>ΔI <sup>F</sup> = x β<sub>l</sub>S i − (μ + μ<sub>i</sub>) I <sup>F</sup> </em> |
| * </li> |
| * <li><em>ΔR= σI<sup>R</sup> − γR − μR</em> </li> |
| * </ul> |
| * |
| * Continuing with <em> i = I/P<sub>l</sub></em>, we have: |
| * <ul> |
| * <li><em>ΔS = μP<sub>l</sub> − (β<sub>l</sub>/P<sub>l</sub>) S I + γR − μ S</em> |
| * </li> |
| * <li><em>ΔI <sup>R</sup> = (1-x)(β<sub>l</sub>/P<sub>l</sub>) S I − σI <sup>R</sup> − μI <sup>R</sup> </em> |
| * </li> |
| * <li><em>ΔI <sup>F</sup> = x (β<sub>l</sub>/P<sub>l</sub>) S I − (μ + μ<sub>i</sub>) I <sup>F</sup> </em> |
| * </li> |
| * <li><em>ΔR= σI<sup>R</sup> − γR − μR</em> </li> |
| * </ul> |
| * |
| * Letting |
| * <em>β<sup>*</sup> = β<sub>l</sub>/P<sub>l</sub> = β (d<sub>l</sub>/(APD * P<sub>l</sub>)) |
| * </em> |
| * gives: |
| * |
| * <ul> |
| * <li><em>ΔS = μP<sub>l</sub> − β<sup>*</sup> S I + γR − μ S</em> |
| * </li> |
| * <li><em>ΔI <sup>R</sup> = (1-x)β<sup>*</sup> S I − σI <sup>R</sup> − μI <sup>R</sup> </em> |
| * </li> |
| * <li><em>ΔI <sup>F</sup> = x β<sup>*</sup> S I − (μ + μ<sub>i</sub>) I <sup>F</sup> </em> |
| * </li> |
| * <li><em>ΔR= σI<sup>R</sup> − γR − μR</em> </li> |
| * </ul> |
| * TSF |
| * <ul> |
| * <li><em>TSF<sub>l</sub> = ((S+I+R)/Area<sub>l</sub>) / (P/Area * (S+I+R))</em></li> |
| * <li><em>TSF<sub>l</sub> = (1/Area<sub>l</sub>) / (P/Area )</em></li> |
| * <li><em>TSF<sub>l</sub> = Area / (P *Area<sub>l</sub> )</em></li> |
| * <li><em>TSF<sub>l</sub> = (1 / P)* (Area/Area<sub>l</sub> )</em></li> |
| * </ul> |
| * <h3>Neighboring Infectious Populations</h3> |
| * </p> |
| * <ul> |
| * <li><em>ΔS = μP<sub>l</sub> − β<sup>*</sup> S (I + I<sub>neighbor</sub>() ) + γR − μ S</em> |
| * </li> |
| * <li><em>ΔI <sup>R</sup> = (1-x)β<sup>*</sup> S (I + I<sub>neighbor</sub>() ) − σI <sup>R</sup> − μI <sup>R</sup> </em> |
| * </li> |
| * <li><em>ΔI <sup>F</sup> = x β<sup>*</sup> S (I + I<sub>neighbor</sub>() ) − (μ + μ<sub>i</sub>) I <sup>F</sup> </em> |
| * </li> |
| * <li><em>ΔR= σI<sup>R</sup> − γR − μR</em> </li> |
| * </ul> |
| * |
| * Specific statistics on the total number of births, deaths and deaths due to |
| * the disease can be computed by adding the appropriate terms of the equations |
| * above. |
| * <ul> |
| * <li><em>B= μ (S + I + R)</em>, is the number of <em>Births</em> </li> |
| * <li><em>D = μ S + (μ + μ<sub>i</sub> )I<sup>F</sup> + μI<sup>R</sup> + μR</em>,is |
| * the total number of <em>Deaths</em></li> |
| * <li><em>DD= μ<sub>i</sub> I<sup>F</sup></em>, is the number of |
| * <em>Disease Deaths</em> </li> |
| * </ul> |
| * @see SI |
| * @see SIRLabel |
| * @see SIRLabelValue |
| * @see SEIR |
| * @see SEIRLabel |
| * @see SEIRLabelValue |
| * |
| * @model abstract="true" |
| */ |
| public interface SIR extends SI { |
| /** |
| * This is the segment of the type URI that prefixes all other segments in a |
| * standard disease model type URI. |
| */ |
| String URI_TYPE_STANDARD_SIR_DISEASE_MODEL_SEGMENT = URI_TYPE_STANDARD_DISEASEMODEL_SEGMENT |
| + "/sir"; |
| |
| /** |
| * The Type URI for the standard SIR disease model |
| */ |
| URI URI_TYPE_STANDARD_SIR_DISEASE_MODEL = STEMURI |
| .createTypeURI(URI_TYPE_STANDARD_SIR_DISEASE_MODEL_SEGMENT); |
| |
| /** |
| * This coefficient determines the number of population members that lose |
| * their immunity to a disease and become Susceptible to the disease per |
| * population member in the <em>Recovered</em> state. A value of zero |
| * (0.0), the default, means the population members never lose their |
| * immunity. This is <em>γ</em>. |
| * |
| * @return the proportion of <em>Recovered</em> population members that |
| * lose their immunity per time period. |
| * @model default="0.0" |
| */ |
| double getImmunityLossRate(); |
| |
| /** |
| * Sets the value of the '{@link org.eclipse.stem.diseasemodels.standard.SIR#getImmunityLossRate <em>Immunity Loss Rate</em>}' attribute. |
| * <!-- begin-user-doc --> <!-- end-user-doc --> |
| * @param value the new value of the '<em>Immunity Loss Rate</em>' attribute. |
| * @see #getImmunityLossRate() |
| * @generated |
| */ |
| void setImmunityLossRate(double value); |
| |
| /** |
| * Compute the immunity rate adjusted for a time delta potentially different |
| * from the time period specified for the rate. |
| * |
| * @param timeDelta |
| * the time period (milliseconds) to which the rate is to be |
| * adjusted. |
| * @return the adjusted rate |
| * |
| * @model volatile="true" transient="true" changeable="false" |
| */ |
| double getAdjustedImmunityLossRate(final long timeDelta); |
| |
| } // SIR |
