Dimensional reduction of an SIS epidemic network model with saturated treatment and human mobility

Globalization and intensified socioeconomic activities have led to complex interconnected social networks that enhance global interactions while also increasing the risks of transmitting infectious diseases. Presented here is a susceptible–infected–susceptible epidemic model incorporating a saturated treatment function and human mobility within social networks. Using Gao–Barzel–Barabási theory, the original high-dimensional system is reduced to a two-dimensional model, and the dynamics of this two-dimensional system are investigated theoretically. This includes the presence and stability of equilibria and a Hopf bifurcation that may only manifest at a specific equilibrium point. Numerical experiments validate the reduced model and predict network resilience through a bifurcation resilience function. Also examined are the effects of saturated treatment and human mobility on the infected proportion. This work provides a framework for assessing social network resilience and optimizing containment strategies during public health crises.