Example 1: Measles Model

The SEIR with demographic model

The most appropriate model representing measles epidemics is the SEIR with demography model in which individuals are categorised in for classes: first, all the newborn individuals are assumed in Susceptible (S), then enter in Exposed (E) class who are infected but not yet infectious, become Infectious (I) and finally change to Recovery R. The system of ODEs represents this model is following:

Kendrick script to specify this model

KModel SIR
	attribute: #(status -> S I R);
	parameters: #(beta lambda gamma mu);
	transitions: #(
		S -- lambda --> I.
		I -- gamma --> R.
		status -- mu --> Empty.
		Empty -- mu --> S.
	).	
    
KModel SEIR
	extends: 'SIR';
	parameters: #(sigma);
	delay: #(sigma , S -- lambda --> I  , E).
    
Composition Measles
    model: 'SEIR'.
    
Scenario MeaslesParameters
	 on: 'Measles';
    beta: 0.0000214; 
    gamma: 0.143; 
    mu: 0.0000351; 
    sigma: 0.125;
	 lambda: #(beta*I).

    
Scenario MeaslesPopulation
    on: 'Measles';
    S: 99999;
    I: 1;
    others: 0.
    
Simulation MeaslesRKSim rungeKutta
	scenarios: #(MeaslesParameters MeaslesPopulation);
	from: 0.0; 
	to: 150; 
	step: 1.
	
Visualization MeaslesDiagramViz diagram 
	for: 'MeaslesRKSim';
	xLabel: 'Time (days)';
	open.