org.eclipse.ohf.stem.diseasemodels.standard
Interface SEIR
- All Superinterfaces:
- Decorator, DiseaseModel, org.eclipse.emf.ecore.EObject, Identifiable, NodeDecorator, org.eclipse.emf.common.notify.Notifier, SanityChecker, SI, SIR, StandardDiseaseModel
- All Known Subinterfaces:
- DeterministicSEIRDiseaseModel, StochasticSEIRDiseaseModel
- All Known Implementing Classes:
- DeterministicSEIRDiseaseModelImpl, SEIRImpl, StochasticSEIRDiseaseModelImpl
public interface SEIR
- extends SIR
A DiseaseModel
with four states Susceptible,
Exposed, Infectious and Recovered(SEIR).
The basic SEIR (Susceptible, Exposed, 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:
- Δs = μ − βs i + γr − μs
- Δe = βs i − φe − μe
- Δi = φe − σi − μi
- Δr = σi − γr − μr
Where:
- s is the normalized Susceptible population
- i is the normalized Infectious population
- 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.
- β is the disease transmission (infection) rate.
This coefficient determines the number of population members that become
Exposed per population member in the Infectious state,
assuming the entire population is in the Susceptible state.
- σ is the Infectious recovery rate. This coefficient
determines the rate at which Infectious population members
Recover.
- γ is the immunity loss rate. This
coefficient determines the rate at which Recovered population
members lose their immunity to the disease and become Susceptible
again.
- φ is the incubation rate. This coefficient
determines the rate at which Exposed population members become
Infectious.
Following basically the same derivation as outlined for the SI
and
SIR
models, these become:
Let
- x be the Infectious Mortality which is the
proportion of the population members who become Infectious that
will eventually die.
- μi be the Infectious Mortality Rate.
This is the rate at which fatally infected population members die
specifically due to the disease.
Thus, we now have two types of Infectious population members,
those that will eventally recover at rate σ, and those that
will eventually die at rate μi (of course, members
in all three states still die at the background rate μ).
Let
- i R be the normalized infectious population that
will recover.
- i F be the normalized infectious population that
will die from the disease.
- i = i R + i F be the total normalized
infectious population (as before).
We modify our model to include these additional states and rates.
- Δs = μ − βs i + γr − μ s
- Δe = βs i − φe − μe
- Δi R = (1-x)φe − σi R − μi R
- Δi F = xφe − (μ + μi) i F
- Δr = σiR − γr − μr
Spatial Adaptation
- Δs Pl= μPl − βl s i Pl + γ r Pl − μ s Pl
- Δe Pl= βsiPl − φePl − μePl
- Δi R Pl = (1-x)φe Pl − σ i R Pl − μi R Pl
- Δi F Pl = x φe Pl − (μ + μi) i F Pl
- Δr Pl= σiRPl − γr Pl− μr Pl
Let Sl = s Pl be the number of
Susceptible population members at location l.
Similarly, let Il = i Pl be the number
of population members at location l that are Infectious
(both states combined), and let
r Pl be the Recovered population.
For readability, we drop the l subscript and substitute.
Substituting
- ΔS = μPl − βl S i + γR − μ S
- ΔE = βS i − φE − μE
- ΔI R = (1-x)φE − σI R − μI R
- ΔI F = xφE − (μ + μi) I F
- ΔR= σIR − γR − μR
Continuing with i = I/Pl, we have:
- ΔS = μPl − (βl/Pl)SI + γR − μ S
- ΔE = (βl/Pl)SI − φE − μE
- ΔI R = (1-x)φE − σI R − μI R
- ΔI F = xφE − (μ + μi) I F
- ΔR= σIR − γR − μR
Letting
β* = βl/Pl = β (dl/(APD * Pl))
gives:
- ΔS = μPl − β* S I + γR − μ S
- ΔE = β* S I − φE − μE
- ΔI R = (1-x)φE − σI R − μI R
- ΔI F = xφE − (μ + μi) I F
- ΔR= σIR − γR − μR
TSF
- TSFl = ((S+E+I+R)/Areal) / (P/Area * (S+E+I+R))
- TSFl = (1/Areal) / (P/Area )
- TSFl = Area / (P *Areal )
- TSFl = (1 / P)* (Area/Areal )
Neighboring Infectious Populations
- ΔS = μPl − β* S (I + Ineighbor() ) + γR − μ S
- ΔE = β* S (I + Ineighbor() ) − φE − μE
- ΔI R = (1-x)φE − σI R − μI R
- ΔI F = xφE − (μ + μi) I F
- ΔR= σIR − γR − μR
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.
- B= μ(S + E + I + R), is the number of Births
- D = μS + μE + (μ + μi )IF + μIR + μR,is
the total number of Deaths
- DD= μi IF, is the number of
Disease Deaths
- See Also:
SIR
,
SIRLabel
,
SIRLabelValue
,
SEIRLabel
,
SEIRLabelValue
Methods inherited from interface org.eclipse.ohf.stem.diseasemodels.standard.SI |
getAdjustedInfectiousMortalityRate, getAdjustedRecoveryRate, getAdjustedTransmissionRate, getInfectiousMortality, getInfectiousMortalityRate, getNonLinearityCoefficient, getPhysicallyAdjacentInfectious, getPhysicallyAdjacentInfectiousProportion, getRecoveryRate, getTransmissionRate, setInfectiousMortality, setInfectiousMortalityRate, setNonLinearityCoefficient, setPhysicallyAdjacentInfectiousProportion, setRecoveryRate, setTransmissionRate |
Methods inherited from interface org.eclipse.ohf.stem.diseasemodels.standard.DiseaseModel |
createDiseaseModelLabel, createDiseaseModelLabelValue, createDiseaseModelState, createInfector, getAdjustedBackgroundMortalityRate, getBackgroundMortalityRate, getDiseaseName, getPopulationIdentifier, getTimePeriod, initializeDiseaseState, initializeDiseaseState, setBackgroundMortalityRate, setDiseaseName, setPopulationIdentifier, setTimePeriod |
Methods inherited from interface org.eclipse.emf.ecore.EObject |
eAllContents, eClass, eContainer, eContainingFeature, eContainmentFeature, eContents, eCrossReferences, eGet, eGet, eIsProxy, eIsSet, eResource, eSet, eUnset |
Methods inherited from interface org.eclipse.emf.common.notify.Notifier |
eAdapters, eDeliver, eNotify, eSetDeliver |
URI_TYPE_STANDARD_SEIR_DISEASE_MODEL_SEGMENT
static final java.lang.String URI_TYPE_STANDARD_SEIR_DISEASE_MODEL_SEGMENT
- This is the segment of the type URI that prefixes all other segments in a
standard disease model type URI.
- See Also:
- Constant Field Values
URI_TYPE_STANDARD_SEIR_DISEASE_MODEL
static final org.eclipse.emf.common.util.URI URI_TYPE_STANDARD_SEIR_DISEASE_MODEL
- The Type URI for the standard SEIR disease model
getIncubationRate
double getIncubationRate()
- Returns:
- the number of population members in the Exposed state
that move to the infectious state, per time period.
setIncubationRate
void setIncubationRate(double value)
- Sets the value of the '
Incubation Rate
'
attribute.
- Parameters:
value
- the new value of the 'Incubation Rate' attribute.- See Also:
getIncubationRate()
getAdjustedIncubationRate
double getAdjustedIncubationRate(long timeDelta)
- Compute the incubation rate adjusted for a time delta potentially
different from the time period specified for the rate.
- Parameters:
timeDelta
- the time period (milliseconds) to which the rate is to be
adjusted.
- Returns:
- the adjusted rate