Example 7: SEIRS Model using dependent concern

Specification of the SEIRS Model

We specify the SEIRS Model by combining the SEIR Concern and the SEIRS Concern that extends SEIR one

KendrickModel SampleModel
	population: 5000.
	
Concern SEIRConcern
	attribute: #(status -> S  E  I  R);
	parameters: #(beta lambda sigma gamma mu);
	lambda: #(beta*I/N);
	transitions: #(
		S -- lambda --> E.
		E -- sigma --> I.
		I -- gamma --> R.
		status -- mu --> Empty.
		Empty -- mu --> S.
	).

Composition SEIRModel
	model: 'SampleModel';
	concern: 'SEIRConcern';
	S: 4999;
	I: 1;
	others: 0;
	mu: 0.0000351;
	sigma: 0.125;
	gamma: 0.143;
	beta: 2.14.
	
Simulation SEIRRK rungeKutta
	for: 'SEIRModel';
	from: 0; 
	to: 365; 
	step: 1.
	
(Visualization SEIRDiagramViz diagram 
	for: 'SEIRRK';
	xLabel: 'Time (days)') open.
	
Concern SEIRSConcern
	extends: 'SEIRConcern';
	parameters: #(v);
	addTransition: #(R -- v --> S).
	
Composition SEIRSModel
	model: 'SEIRModel';
	concern: 'SEIRSConcern';
	S: 4999;
	I: 1;
	others: 0;
	v: 0.00274.
	
Simulation SEIRSRK rungeKutta
	for: 'SEIRSModel';
	from: 0; 
	to: 365; 
	step: 1.
	
(Visualization SEIRSDiagramViz diagram 
	for: 'SEIRSRK';
	xLabel: 'Time (days)') open.
	

Old Script

| model SEIRConcern SEIRSConcern simulator dB|
	model := KEModel new.
	model population: (KEPopulation size: 5000).
	SEIRConcern := KEConcern new.
	SEIRConcern attributes: {#status->#(#S #E #I #R)}.
	SEIRConcern addParameters: { #beta. #gamma. #mu. #sigma }.
	SEIRConcern
		addTransitionFrom: '{#status: #S}'
		to: '{#status: #E}'
		probability: [ :aModel | 
			(aModel atParameter: #beta) * 
			(aModel atCompartment: {#status->#I}) / (aModel atParameter: #N) ].
	SEIRConcern 
		addTransitionFrom: '{#status: #E}' 
		to: '{#status: #I}' 
		probability: [ :aModel | aModel atParameter: #sigma ].
	SEIRConcern 
		addTransitionFrom: '{#status: #I}' 
		to: '{#status: #R}' 
		probability: [ :aModel | aModel atParameter: #gamma ].
	SEIRConcern 
		addTransitionFrom: '{#status: #S}' 
		to: #empty 
		probability: [ :aModel | aModel atParameter: #mu ].
	SEIRConcern 
		addTransitionFrom: '{#status: #I}' 
		to: #empty 
		probability: [ :aModel | aModel atParameter: #mu ].
	SEIRConcern 
		addTransitionFrom: '{#status: #R}' 
		to: #empty 
		probability: [ :aModel | aModel atParameter: #mu ].
	SEIRConcern 
		addTransitionFrom: '{#status: #E}' 
		to: #empty 
		probability: [ :aModel | aModel atParameter: #mu ].
	SEIRConcern 
		addTransitionFrom: #empty 
		to: '{#status: #S}' 
		probability: [ :aModel | aModel atParameter: #mu ].
			
	model integrate: SEIRConcern.
	model atParameter: #beta assignValue: 2.14.
	model atParameter: #gamma assignValue: 0.143.
	model atParameter: #sigma assignValue: 0.125.
	model atParameter: #mu assignValue: 0.0000351.
	model atCompartment: { #status->#S } put: 4999.
	model atCompartment: { #status->#I } put: 1.
	model atCompartment: { #status->#R } put: 0.
	model atCompartment: { #status->#E } put: 0.
	
	simulator := KESimulator new: #RungeKutta from: 0.0 to: 100 step: 1.
	simulator executeOn: model.
	dB := KEDiagramBuilder new.
	dB data: (simulator timeSeriesAt: '{#status: #I}').
	dB xLabel: 'Time (year)'.
	dB open.
	
	SEIRSConcern := KEConcern dependOn: SEIRConcern.
	SEIRSConcern addParameter: #v.
	SEIRSConcern addTransitionFrom: { #status->#R } to: { #status->#S } probability: [ :aModel| aModel atParameter: #v].
	
	model integrate: SEIRSConcern.
	model atParameter: #v assignValue: 0.0.
	model atCompartment: { #status->#S } put: 4999.
	model atCompartment: { #status->#I } put: 1.
	model atCompartment: { #status->#R } put: 0.
	model atCompartment: { #status->#E } put: 0.
	simulator := KESimulator new: #RungeKutta from: 0.0 to: 100 step: 1.
	simulator executeOn: model.
	dB := KEDiagramBuilder new.
	dB data: (simulator timeSeriesAt: '{#status: #I}').
	dB xLabel: 'Time (year)'.
	dB open.