Global analysis of age-structured multi-stage epidemic models for infectious diseases

We formulate a multi-stage SEIR model for infectious diseases with continuous age structure for each successive infectious stage during a long infective period. The model can describe disease progression through multiple infectious stages as in the case of HIV, hepatitis B and hepatitis C. Mathematical analysis shows that the global dynamics are completely determined by the basic reproductive number R0. If R0≤1, the disease-free equilibrium is globally asymptotically stable and the disease dies out. If R0>1, a unique endemic equilibrium is globally asymptotically stable, and the disease persists at the endemic equilibrium. The proof of global stability of endemic equilibria utilizes a Lyapunov functional. Numerical simulations are illustrated and model generalization is also discussed.