SIR Economic Model

[Susceptible; Infected; Recovered]
:: Beta Test - Not for Official Use ::
(c) Health Decision Strategies, LLC
:: You can change parameter values in yellow boxes below ::
DATA ENTRY PAGE
                 
 
  Group A Group B   Treat_A Prevention Cost Treat_B Prevention Cost  
 
Total
Population
   
 
QOL loss per Pt Sick Day (or Unit of Time)  
   Maximum WTP Per Effect -->>






Group A




Group B

  Beta Rate per 100   Infection Rate   Rate per 100   Infection Rate
  Gamma Rate per 100   Recovery Rate   Rate per 100   Recovery Rate
  Alpha Rate per 100   Inoculation rate   Rate per 100   Inoculation Rate
  Delta Rate per 100   "Herd protection" factor   Rate per 100   "Herd protection" factor
  Rho Rate per 100   "Hygiene" factor   Rate per 100   "Hygiene" factor
                   


SAMPLE GRAPHICS FROM RESULTS PAGE

SIR Econ Model :: Susceptible, Infected, Recovered

SIR Graph A SIR Graph B
  
Inc. Cost Effectiveness Ratio Inc. Net Beneft vs WTP
(c) HDS


SIR MODEL CONSIDERATIONS
A classic model for exploring the spread of infectious diseases is the SIR model.
It is sometimes considered in the examination of the "diffusion of innovation".
The SIR model evaluates the fractions of the population which are:

(S)usceptible









(I)nfected









(R)ecovered




















The SIR mathematical approach below is based on the Kermack–McKendrick model:
[Formulas require additional beta testing.]
















 dS/dT = S' = - beta * SI   - alpha*SR     beta = "infection" rate.  





 
alpha = "inoculation" rate
 dI/dT = I' = +(1-rho)* beta*SI - gamma*I   - delta*IR   gamma = "recovery" rate.  







delta = "herd" effect
 dR/dT = R' = +rho*beta*SI + gamma*I + alpha*SR + delta*IR   rho = "hygiene" factor












 Note: S + I + R= 1 and S' + I' + R'= 0.







 :: Transitions from S to I occur when these groups of individuals interact. 
 :: Transitions from I to R occur when infected individuals recover (or expire).  


Resources:
(1) Weisstein, Eric W. "Kermack-McKendrick Model."
From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Kermack-McKendrickModel.html
(2) SIR Model -- http://www.docstoc.com/docs/104243450/SIR-Model
(3) SIR Model Seminar -- http://www.bluffton.edu/mat/dept/seminar_docs

(c) Health Decision Strategies, LLC
HDS