Difference between revisions of "SIR model: swine flu"

From JSXGraph Wiki
Jump to navigationJump to search
Line 18: Line 18:
 
   
 
   
 
var s = brd.createElement('slider', [[0,-0.3], [60,-0.3],[0,1E-6,1]], {name:'s'});
 
var s = brd.createElement('slider', [[0,-0.3], [60,-0.3],[0,1E-6,1]], {name:'s'});
brd.createElement('text', [40,-0.3, "initially infected population rate"]);
+
brd.createElement('text', [90,-0.3, "initially infected population rate"]);
 
var beta = brd.createElement('slider', [[0,-0.4], [60,-0.4],[0,0.2857,1]], {name:'β'});
 
var beta = brd.createElement('slider', [[0,-0.4], [60,-0.4],[0,0.2857,1]], {name:'β'});
brd.createElement('text', [40,-0.4, "β: infection rate"]);
+
brd.createElement('text', [90,-0.4, "β: infection rate"]);
 
var gamma = brd.createElement('slider', [[0,-0.5], [60,-0.5],[0,0.1428,1]], {name:'γ'});
 
var gamma = brd.createElement('slider', [[0,-0.5], [60,-0.5],[0,0.1428,1]], {name:'γ'});
brd.createElement('text', [40,-0.5, "γ: recovery rate = 1/(days of infection)"]);
+
brd.createElement('text', [90,-0.5, "γ: recovery rate = 1/(days of infection)"]);
 
   
 
   
 
var t = 0; // global
 
var t = 0; // global

Revision as of 13:32, 10 August 2009

The SIR model tries to model influenza epidemics. Here, we try to medel the spreading of the swine flu.

  • According to the CDC Centers of Disease Control and Prevention: "Adults shed influenza virus from the day before symptoms begin through 5-10 days after illness onset. However, the amount of virus shed, and presumably infectivity, decreases rapidly by 3-5 days after onset in an experimental human infection model." So, here we set [math]\gamma=1/7=0.1428[/math] as the recovery rate. This means, on average an infected person sheds the virus for 7 days.
  • In Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1) the authors estimate the reproduction rate [math]R_0[/math] of the virus to be about [math]2[/math]. For the SIR model this means: the reproduction rate [math]R_0[/math] for influenza is equal to the infection rate of the strain ([math]\beta[/math]) multiplied by the duration of the infectious period ([math]1/\gamma[/math]), i.e.
[math]\beta = R_0\cdot \gamma[/math]. Therefore, we set the :[math]\beta = 2\cdot 1/7 = 0.2857[/math]
  • We run the simulation for a population of 1 million people, where 1 person is infected initially, i.e. [math]s=1E{-6}[/math].

Thus S(0) = 1, I(0) = 1.E-6, R(0) = 0