Global stability of an epidemic model with carrier state in heterogeneous networks

Abstract

This paper presents a network disease model that incorporates balanced birth and death event and has infectious force in the infected state and carrier state, such as hepatitis B virus (HBV). By investigating the local stability of the disease-free equilibrium, the basic reproduction number R0 is derived and established as a sharp threshold. In particular, by using suitable Lyapunov functions and graph-theoretic results based on Kirchhoff's Matrix Tree Theorem, it is proved that if R0<1, then the disease-free equilibrium is globally asymptotically stable; whereas if R0>1, there exists a unique endemic equilibrium, which is globally asymptotically stable. When birth and death event are ignored, the final size formula is determined. Moreover, the effects of various immunization strategies are investigated and compared by numerical simulations. The results obtained are informative for us to further understand the disease propagation and devise some effective interventions to combat the diseases.