Dynamic stability of an SIVS epidemic model with imperfect vaccination on scale-free networks and its control strategy

Abstract

Vaccination is the most effective and extensive method to prevent and control the spread of infectious diseases. In this paper, we develop an SIVS epidemic model with demographics and variable population size on scale-free networks. Firstly, we derive two threshold parameters R0 and R˜0 with death rate, and present existence conditions of equilibria. Not only the global asymptotical stability of the disease-free equilibrium is obtained for R˜0<1, but also the global attractivity of the unique endemic equilibrium is proved for R0 > 1. Secondly, the effects of various immunization schemes including uniform immunization, targeted immunization and acquaintance immunization are compared, and the optimal vaccination strategy is analyzed by Pontryagin Maximum Principle. Finally, we perform numerical simulations to verify the correctness of the theoretical results.