Dynamical analysis of an enhanced epidemic model in complex network

Population dynamics factors, such as the mobility of individuals, are inherently linked with the evolution of populations. Traditional network-based epidemic models operate under the assumption of a stable population size, often overlooking the impactful role of population mobility. Therefore, in this work, we present an enhanced SIR model, which incorporates population mobility and bidirectional immunization into the standard SIR model. Through theoretical analysis, we calculate the fundamental reproduction numbers and outbreak thresholds for both homogeneous and heterogeneous networks. The influence of two-way immunization and population mobility on the diffusion of infectious diseases is then examined via numerical simulations in both ER and BA networks. The simulation outcomes highlight the effectiveness of the outflow of infected and recovered individuals in curbing the extent of epidemics. Additionally, immunization measures targeting infected individuals not only shrink the transmission range of infectious diseases but also act to postpone the spread of epidemics. Notably, compared with homogeneous networks, infectious diseases have stronger transmission ability in heterogeneous networks, indicating heterogeneity of networks facilitates epidemic spreading.