Analysis of SVEIR worm attack model with saturated incidence and partial immunization

Abstract

Internet worms can propagate across networks at terrifying speeds, reduce network security to a remarkable extent, and cause heavy economic losses. Thus, the rapid elimination of Internet worms using partial immunization becomes a significant matter for sustaining Internet infrastructure. This paper addresses this issue by presenting a novel worm susceptible-vaccinated-exposed-infectious-recovered model, named the SVEIR model. The SVEIR model extends the classical susceptible-exposed-infectious-recovered model (refer to SEIR model) through incorporating a saturated incidence rate and a partial immunization rate. The basic reproduction number in the SVEIR model is obtained. By virtue of the basic reproduction number, we prove the global stabilities of an infection-free equilibrium point and a unique endemic equilibrium point. Numerical methods are used to verify the proposed SVEIR model. Simulation results show that partial immunization is highly effective for eliminating worms, and the SVEIR model is viable for controlling and forecasting Internet worms.