Editing Compartmental models (epidemiology) (section)

====The force of infection====

Note that in the above model the function:

:<math> F = \beta I,</math>

models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the [[force of infection]]. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population <math>N</math>):

:<math> F = \beta \frac{I}{N} .</math>

Capasso<ref name="Capasso">{{cite book | vauthors = Capasso V |title=Mathematical Structure of Epidemic Systems |location=Berlin |publisher=Springer |year=1993 |isbn=3-540-56526-4 }}</ref> and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process.