Epidemic propagation dynamics of an SIS model on networks with population mobility between regions

Abstract The impact of population mobility is non-negligible on the spread of infectious diseases. In this study, we construct a network SIS model that accounts for the impact of population mobility between regions, using a nonlinear infection rate and dividing the infected into symptomatic and asymptomatic groups. First, the study analyses the stability of equilibrium points by constructing the Lyapunov function and validating it using numerical experiments. Secondly, a special form of the basic regeneration number was attained using the next generation matrix method. This result inspires us to pay more attention to asymptomatic infections in the disease control process so that we can stabilize the population to a state where asymptomatic infections are extinct as quickly as possible and facilitate the subsequent epidemic control. Additionally, the results of numerical simulations further demonstrate that for people with different degrees, we can adopt corresponding ideas respectively to determine the optimal movement rate, which will avoid disease infection to a greater extent. Our study will serve as a guide for the development of infectious disease prevention and control policies.