KendrickOrg/kendrick

Mass-action and standard incidence models

SergeStinckwich opened this issue · 4 comments

SergeStinckwich commented

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)?

mikalziane commented

Mass action and standard incidence differ when N is not constant. We should be aware of this.

  • 👍1
SergeStinckwich commented

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 ].
YvanGuifo commented

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.

mikalziane commented