We will assume that each individual in the population falls into one of the following categories:
\begin{align*}
s(t) & = \text{Susceptible individuals}\\
i(t) & = \text{Infected individuals}\\
r(t) & = \text{Removed individuals}
\end{align*}
Susceptible individuals are those who do not yet have the disease and can catch the disease from infected individuals. Individuals enter the removed population by either recovering from the disease or dying. If an infected individual recovers, then the individual is immune to the disease. Schematically, we can represent the effect of the disease by the diagram
\begin{equation*}
s \longrightarrow i \longrightarrow r.
\end{equation*}
Since the population is closed, we know that
\begin{equation*}
s(t) + i(t) + r(t) = N.
\end{equation*}
This model is called an SIR model.