Aguiar, Izabel P.

Models state transitions through differential equations over continuous time \(t\). Commonly used to model the spread of diseases.

Possible states that proportions of the population could be in at time \(t\) are: susceptible \(S(t)\), infected \(I(t)\), and recovered \(R(t)\)

The SI Model

Assumes that one can only move from state \(S\) to state \(I\), with probability \(\beta\).

$$ S’(t) = - \beta S(t) I(t);\ \ \ \ I’(t) = \beta S(t) I(t) $$