Global Dynamics of a General Class of Multistage Models for Infectious Diseases

Abstract

We propose a general class of multistage epidemiological models that allow possible deterioration and amelioration between any two infected stages. The models can describe disease progression through multiple latent or infectious stages as in the case of HIV and tuberculosis. Amelioration is incorporated into the models to account for the effects of antiretroviral or antibiotic treatment. The models also incorporate general nonlinear incidences and general nonlinear forms of population transfer among stages. Under biologically motivated assumptions, we derive the basic reproduction number $R_0$ and show that the global dynamics are completely determined by $R_0$: if $R_0\leq 1$, the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if $R_0>1$, then the disease persists in all stages and a unique endemic equilibrium is globally asymptotically stable.