A class of delay SIQR-V models considering quarantine and vaccination: Validation based on the COVID-19 perspective

To contain the novel SARS-CoV-2 (COVID-19) spreading worldwide, governments generally adopt two measures: quarantining the infected people and vaccinating the susceptible people. To investigate the disease latency's influence on the transmission characteristics of the system, we establish a new SIQR-V (susceptible-infective-quarantined-recovered-vaccinated) dynamic model that focus on the effectiveness of quarantine and vaccination measures in the scale-free network. We use theoretical analysis and numerical simulation to explore the evolution trend of different nodes and factors influencing the system stability. The study shows that both the complexity of the network and latency delay can affect the evolution trend of the infected nodes in the system. Still, only latency delay can destroy the stability of the system. In addition, through the parameter sensitivity analysis of the basic reproduction number, we find that the effect of the vaccination parameter $$ on the basic reproduction number $$ is more significant than that of transmission rate $$ and quarantine parameter $$ . It shows that vaccination is one of the most effective public policies to prevent infectious diseases' spread. Finally, we calculate the basic reproduction numbers that are greater than one for Germany and Pakistan under COVID-19 and validate the model's effectiveness based on the disease data of COVID-19 in Germany. The results show that the changing trend of the infected population in Germany based on the SIQR-V model is roughly the same as that reflected by the actual epidemic data in Germany. Therefore, providing suggestions and guidance for treating infectious diseases based on this model can effectively reduce the harm caused by the outbreak of contagious diseases.