Basic SIR Model

Overview


The SIR model models two variables:

  • {% S(t) %} - the number of susceptible individuals
  • {% I(t) %} - the number of infected individuals

where the dynamics are specified by
{% S'(t) = -\beta S(t) I(t) %}
{% I'(t) = \beta S(t) I(t) - \alpha I(t) %}

Scripts


The script models the {% S %} and {% I %} as an array, [S,I]. The initial values are set as 


let boundary = [763 - 25, 25];


The derivatives are specified by the derivative function 


let derivative = function(values){
	return [-1*beta*values[0]*values[1], beta * values[0]*values[1] - alpha*values[1]];
}


The evaluation of {% S %} and {% I %} over time is computed by using the euler function of the finite difference library.