Epidemic dynamics of complex networks under pulse treatment and vaccination

Abstract

The dynamics of a new Susceptible-Vaccinated-Infected-Recovered (SVIR) epidemic model in complex networks under constant and pulse control are investigated. Firstly, the epidemic model in complex networks under constant control is proposed. Utilizing the basic reproduction number, the sufficient conditions for stabilizing the epidemic under constant control are established. Since constant control is not conducive to resource conservation, it has been replaced by pulse control in epidemic model. The paper demonstrates the global attractiveness of the disease-free periodic solution of the model under pulse treatment and pulse vaccination. In addition, a sufficient condition is put forward to make sure that the system persists under pulse control, indicating periodic outbreaks of the epidemic. Furthermore, the epidemic is uniformly persistent when the pulse period is greater than the pulse period threshold or the vaccination rate is less than the vaccination threshold. Finally, several numerical simulations prove the feasibility of the theoretical results. By comparing the pulse period with a critical value, the strategy that most contributes to controlling the epidemic propagation is chosen from constant control and pulse control to achieve maximum utilization of resources. Moreover, it shows that decreasing the fraction of pulse treatment and pulse vaccination or prolonging the pulse period is beneficial to epidemic propagation. The topology of complex networks has a non-negligible influence on the epidemic propagation under pulse control, which is demonstrated both theoretically and numerically.