Global dynamics of a staged progression model for infectious diseases - Hongbin Guo; Michael Yi Li (Mathematical Biosciences and Engineering)
We analyze a mathematical model for infectious diseases thatprogress through distinct stages within infected hosts. An exampleof such a disease is AIDS, which results from HIV infection. For ageneral $n$-stage stage-progression (SP) model with bilinearincidences, we prove that the global dynamics are completelydetermined by the basic reproduction number $R_0.$ If $R_0\le 1,$then the disease-free equilibrium $P_0$ is globally asymptoticallystable and the disease always dies out. If $R_0>1,$ $P_0$ isunstable, and a unique endemic equilibrium $P^*$ is globallyasymptotically stable, and the disease persists at the endemicequilibrium. The basic reproduction numbers for the SP model withdensity dependent incidence forms are also discussed.