A non-Markovian SIR network model with fixed infectious period and preventive rewiring

In the face of disease occurrence, susceptible individuals tend to protect themselves by rewiring their links, i.e., cutting off connection with infected person and switching to contact with healthy ones. Therefore, the adaptive rewiring mechanism is considered in the network epidemic model. Moreover, the infection periods for different diseases do not always follow exponential distributions in the process of disease transmission, which may be of fixed length. Using the idea of age-structure, we establish the susceptible-infected-recovered epidemic model for each node and each link, resulting in a delayed non-Markovian SIR pairwise model with fixed infectious period and preventive rewiring, then give the pairwise reproduction number R0p and provide the formula for the final epidemic size by rigorous analysis and tedious computation. The simulation results show that adaptive rewiring inhibits the spread of disease and decreases the size of disease outbreak, while the extension of the infectious period promotes disease transmission. In addition, the numerical simulation results are in good agreement with the stochastic simulation. To our best knowledge, the approach in building our model is novel, the results may provide new insights into the study of the network disease transmission.