Endemic equilibria
An endemic equilibrium is a steady state at which infection remains present in the population.
Definition
For a compartmental model, equilibrium values are found by setting every time derivative equal to zero. An endemic equilibrium additionally requires a positive infected component.
SIS example
For the simple SIS model with \(S+I=N\), a positive equilibrium satisfies
\[I^*=N\left(1-\frac{1}{R_0}\right),\]which is positive when \(R_0>1\).
Interpretation
An endemic equilibrium represents persistence at constant modelled compartment sizes, not absence of individual infection and recovery events.
Key idea. Endemic equilibrium describes long-term persistence of infection in the deterministic model.