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,
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).


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