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).
where k is constant.
Solving the differential equation by A-level math,
where is p at t=0 (initial infected population).
=> the infection growth rate is exponential, and multiplied by a factor .
That is why there is a need to contain at the beginning of the epidemic by:
1. Isolate all ;
2. Destroy all dead by burning, etc.
3. For flu (H1N1), put on masks by the sick…
Math saves our life !
By taking measure to reduce to very small population, say,
The epidemic will die off over time, although there is still no
medical cure for it (eg. SARS).