From an epidemiological model with differential equation, we can compute the basic reproductive number R0 (the number of expected secondary case per primary case in a disease free population).
Biologicaly (from this site):
- R0 < 1: Each existing infection is causing less than one new infection. In this case, the disease will decline and eventually die out.
- R0 > 1: Each existing infection is causing more than one new infection. The disease will spread between people and there may be an outbreak or an epidemic.
- R0 = 1: Each existing infection is causing one new infection. The disease will stay alive without epidemic.
There is many mathematical methods to calculate the R0 from ODE models. One is based on the Disease-Free Equilibrium (DFE). From what I understood:
if 0 < R0<1: DFE is stable (LAS), no epidemic
if R0> 1: DFE is unstable (LAS), there is an epidemic: the introduction of an infected may lead to an endemic point (if this point is stable)
But, what happen if R0=1 ?
I read this is a "central variety", and it's impossible to know what happen in term of stability of the DFE.
Is there any paper talking about endemicity from the mathematical and biological point of view ?