In order to investigate how different levels of vigilance affect the spread of a virus and changes in public opinion, this article introduces a network-based susceptible-exposed-infectious-vigilant (SEIV)-Opinion model. The model incorporates vigilance influence functions that depend on infection and recovery rates, which are associated with opinion states. A basic reproduction number dependent on both the viral transmission state and public opinion dynamics is constructed to analyze the conditions for virus eradication or pandemic persistence. These findings indicate that during severe epidemics, people are very concerned about the epidemic, leading to an increased vigilance, thereby significantly slowing the spread of the virus. On the other hand, during milder epidemics, people do not respond adequately to the threat of the epidemic, and thus are less vigilant and have less impact on the spread of the virus. These insights correlate closely with real-world trends. This article uses numerical simulations to demonstrate and confirm these patterns under various conditions.

This article investigates the group consensus problem for heterogeneous multiagent systems with time delays via pinning control. Under the designed control protocol, agents in the system could be grouped arbitrarily, and agents in the same subgroup could converge to a constraint position. Meanwhile, the kinetics of agents in the same subgroup could be same or different. Both the fixed and switching topologies are considered. Based on the frequency domain method and stability theory, sufficient conditions for the system achieve group consensus are derived. Finally, several numerical examples are presented to verify the performance of the control protocol.