# Epidemic Equation

Let p the portion of  population infected by the contagious disease
(like SARS) at time t.

The rate of infection is known empirically and historically
proportional to p(t).

$\frac {dp}{dt}=k.p$
where k is constant.

Solving the differential equation by A-level math,
$p=p_0.e^{kt}$
where $p_0$  is p at t=0 (initial infected population).
=> the infection growth rate is exponential, and multiplied by a factor $p_0$.

That is why there is a need to contain $p_0$ at the beginning of the epidemic by:
1. Isolate all $p_0$;
2. Destroy all dead $p_0$ by burning, etc.
3. For flu (H1N1), put on masks by the sick…

Math saves our life !

By taking measure to reduce $p_0$ to very small population, say, $p_0 \to 0$

$p=p_0.e^{kt} \to 0$

The epidemic will die off over time, although there is still no
medical cure for it (eg. SARS).