Example 4.5: Model 5 SEIRS Multi species Multi strains Spatial model

From the Model 3, we create the model 5 by defining a multi-strains concern and apply it to the Model 3.

KendrickModel SEIRS
    attribute: #(status -> S E I R);
    parameters: #(beta lambda gamma mu sigma nu);
    lambda: #(beta*I/N);
    transitions: #(
        S -- lambda --> E.
        E -- sigma --> I.
        I -- gamma --> R.
        R -- nu --> S.
        status -- mu --> Empty.
        Empty -- mu --> S.).

KendrickModel TwoStrains
	extends: 'SEIRS';
	splitStatus: #(I strains #(1 2)).

KendrickModel MultiSpecies
	attribute: #(species -> human bird).

Map SoutheastAsia
    countries: #(MyanmarBurma Cambodia Laos Thailand Vietnam);
    routesFrom: #Thailand toAll: #(Cambodia);
    routesFrom: #Cambodia toAll: #(Vietnam);
    routesFrom: #Vietnam toAll: #(Laos);
    routesFrom: #Laos toAll: #(MyanmarBurma);
    routesFrom: #MyanmarBurma toAll: #(Thailand);
    routesToTransitions: 'rho'.

KendrickModel Spatial
    from: SoutheastAsia;
    parameters: #(rho).

Composition Influenza
	model: 'TwoStrains';
	model: 'MultiSpecies';
        model: 'Spatial'.

Scenario Scr1
	on: 'Influenza';
	populationSize: 27500;
        mu_species: #(0.000365 0.00137);
	beta1_species: #(#(0 0.21) #(0 0.42));
        gamma_species_status: #(#(0 0 0 0 0.25 0.0025) #(0 0 0 0 0.233 0.0023));
        sigma_species_status_next: #(#(0 0 0 0 0.5 0.005) #(0 0 0 0 0.67 0.0067));
	nu: 0.00274;
	rho_species: #(0.03 0.1);
        beta2_species: #(#(0 0.021) #(0 0.042));
        lambda: #((beta1*(I1_patch/N))+(beta2*(I2_patch/N)) sum);
	N: #(patch_species);
	S_species_patch: #(#(500 500 500 500 500) #(4990 5000 5000 5000 5000));
	I1_species_patch: #(#(0 0 0 0 0) #(9 0 0 0 0));
	I2_species_patch: #(#(0 0 0 0 0) #(1 0 0 0 0)).

Simulation InfluenzaSim rungeKutta
	scenario: 'Scr1';
	from: 0;
	to: 500;
	step: 1.

Visualization InfluenzaViz diagram
	for: 'InfluenzaSim';
	data: #(I1_species I2_species);
	legendTitle: 'Infectious';
	legends: #('humans strains 1' 'birds strains 1' 'humans strains 2' 'birds strains 2');
	xLabel: 'Time (days)';
        exportToPng.