Simplicial epidemic model with individual resource

The investment and rational use of medical resources are crucial for the prevention and control of epidemics. Here we propose a coupled dynamics model of individual resource and disease transmission on simplicial complexes that considers the dynamic changes of resource quantity during the spreading of the epidemic. Firstly, we derive the solutions (infection density) of the disease transmission dynamics equations under the mean-field approximation, and analyze their stability. We find that the number of stable solutions is related to the infection rates of both interactions and higher-order interactions, and we obtain the transmission threshold under different initial infection densities. Secondly, in the numerical simulation, we discover a double hysteresis loop of infection density as it evolves with the infection rate of interactions. Moreover, we find a critical value for the cost of disease recovery; when the recovery cost is above this critical value, the system state transitions from partial infection to complete infection. Interestingly, we find a maximum value for infection density when the system is in partial infection state. Finally, we verify the existence of the double hysteresis loop on real-world networks.