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Mass-action and standard incidence models
At the moment, this is not possible to explicit say in a Kendrick model is written with a mass-action incidence or a standard incidence. In the second kind of model, the value of beta should be normalized by the total population size. What are the consequence on patch models (with different Ni for each patches)?
Mass action and standard incidence differ when N is not constant. We should be aware of this.
When a defined a SIR model like below, we don't know if this is the incidence is mass action or standard.
| model |
model := KEModel new.
model attributes: {(#status -> #(#S #I #R))}.
model atCompartment: {(#status -> #S)} put: 99999.
model atCompartment: {(#status -> #I)} put: 1.
model atCompartment: {(#status -> #R)} put: 0.
model
addParameters:
{(#beta -> 0.0052).
(#gamma -> 52)}.
model
addTransitionFrom: {(#status -> #S)}
to: {(#status -> #I)}
probability:
[ :m | (m atParameter: #beta) * (m atCompartment: {(#status -> #I)}) ].
model
addTransitionFrom: {(#status -> #I)}
to: {(#status -> #R)}
probability: [ :m | m atParameter: #gamma ].
This may be because the terminology is not clear enough. Chapter 2 of the book (Keeling and Rohani) on page 17 gives us more precision in this regard. Knowing that we consider S, I and R to be the number of susceptible, infectious and recovered individuals, respectively. So,
In the case of the incidence of mass action (frequency dependent), the force of infection lambda = beta*I/N.
In the case of standard incidence, the force of infection lambda = beta I. This is the case with the example you presented.
But some formula it differently. For example in this document https://mysite.science.uottawa.ca/rsmith43/MAT3395/AdvancedEpidemic.pdf we specify that the law of mass action depends on density (page 4) and that the standard incidence depends on frequency.
(Keeling and Rohani) on page 17 of chapter 2 also specifies that these notions are subject to many controversies.
merci pour cette remarque Yvan en effet le passage de Keeling est intéressant. Martcheva dit que mass action et standard incidence sont équivalentes quand N est fixe et comme le dit Keeling quand N varie il faut distinguer les deux
Le ven. 5 mars 2021 à 11:45, Yvan Guifo [email protected] a écrit :
This may be because the terminology is not clear enough. Chapter 2 of the book (Keeling and Rohani) on page 17 gives us more precision in this regard. Knowing that we consider S, I and R to be the number of susceptible, infectious and recovered individuals, respectively. So, In the case of the incidence of mass action (frequency dependent), the force of infection lambda = beta*I/N. In the case of standard incidence, the force of infection lambda = beta I. This is the case with the example you presented.
But some formula it differently. For example in this document https://mysite.science.uottawa.ca/rsmith43/MAT3395/AdvancedEpidemic.pdf we specify that the law of mass action depends on density (page 4) and that the standard incidence depends on frequency.
(Keeling and Rohani) on page 17 of chapter 2 also specifies that these notions are subject to many controversies.
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