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' = 
+(1rho)* 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). 