The Stability of the SAIR Infectious Disease Model on Community Networks

The existence of asymptomatic carriers, individuals infected without showing symptoms, exacerbates the spread of infectious diseases, especially when people migrate between communities, leading to large-scale outbreaks. Therefore, we established the SAIR infectious disease model on a network to investigate the impact of individual migration on disease transmission in the presence of asymptomatic carriers. Based on this model, we studied how to control the spread of the epidemic when a community gets infected and migrates between communities. Consequently, we calculated the threshold value R
0
, and found that when R
0
< 1, the disease-free equilibrium point exists and is stable. Furthermore, we proved its global asymptotic stability using the decomposition theorem, and demonstrated the global stability of the local disease equilibrium point by constructing a Lyapunov function.