Pattern formation of network epidemic model and its application in oral medicine

The prevention and control of infectious diseases is one of the major public safety issues in the 21 st century. In this paper, a Susceptible-Infected-Recovered (SIR) epidemic model with disease recurrence behavior is established based on continuous space and network environment. The Turing pattern, optimal control and parameter identification of infectious disease models under different network structures are studied.

We analyze the sufficient conditions for the existence of the disease equilibrium point of the system, and discuss the necessary conditions of Turing instability of the system on homogeneous and heterogeneous networks, respectively. Our work further derives the global optimal solution of the parameters under the target pattern based on optimal control theorem.

The validity of the theoretical analysis is verified by a series of numerical simulations. Meanwhile, we have explored the impact of disease recurrence rate on the spread of infectious diseases on three network structures. It is found that when the recurrence rate α increases, it will result in a decrease in the recovered population R as well as an increase in the infected population I. Furthermore, the public Corona Virus Disease 2019 data are used for fitting verification. The verification results are basically consistent with the development trend of the epidemic, as well as the validity of the model is visually demonstrated.

The complex network model can more accurately simulate the dynamic propagation process of infectious diseases. Combined with optimal control and parameter identification methods, it can provide theoretical support for public health departments to prevent and control infectious diseases. In particular, optimization parameter identification technology can be successfully applied to oral image recognition and adjuvant therapy.