The effect of age-dependent host mortality on the dynamics of an endemic disease

Using asymptotic expansions in the ratio between the duration of infection and host lifetime, equilibrium conditions are analyzed for an SIR-type epidemic model with age-dependent mortality and age-independent disease transmission. Disease incidence at equilibrium depends on the distribution of lifetimes. Incidence is maximal if host life span is fixed and, for vanishing higher moments, it decreases with increasing variance of the distribution. The spectrum of the linearization about the endemic equilibrium has two dominant components, one near 0 and one with a large imaginary part. All roots of the characteristic equation have a negative real part so the model is always stable. The roots with a large imaginary part dominate in most cases, indicating that the approach to equilibrium will be through slowly damped oscillations.