The authors study nonlinear
-group epidemic models of SEIR type. Under the assumption that the basic reproduction number
is bigger than one and that the transmission matrix
is irreducible the authors show that there exists a unique endemic equilibrium which is locally stable and globally attractive. For the proof, the authors use a Lyapunov function of the form
, is the state,
is the equilibrium and
are some coefficients. To show that the function
some graph-theoretical arguments like special properties of unicyclic graphs are used.