Multiple Time Scales in the Dynamics of Infectious Diseases

For an age-structured SIR-model with constant host life span, the dominant eigenvalues of the endemic equilibrium are computed using asymptotic expansions of the stability equation. To the first order the eigenvalues are purely imaginary and the real part of the second order term is negative showing that the endemic equilibrium is always stable. In an age-structured epidemic model with two interacting viral strains that confer partial cross-immunity, purely imaginary eigenvalues exists for some parameter values indicating the possibility of a limit cycle appearing through a Hopf bifurcation.