An Edge-Based Model of SEIR Epidemics on Static Random Networks

Studies have been done using networks to represent the spread of infectious diseases in populations. For diseases with exposed individuals corresponding to a latent period, an SEIR model is formulated using an edge-based approach described by a probability generating function. The basic reproduction number is computed using the next generation matrix method and the final size of the epidemic is derived analytically. The SEIR model in this study is used to investigate the stochasticity of the SEIR dynamics. The stochastic simulations are performed applying continuous-time Gillespie's algorithm given Poisson and power law with exponential cut-off degree distributions. The resulting predictions of the SEIR model given the initial conditions match well with the stochastic simulations, validating the accuracy of the SEIR model. We varied the contribution of the disease parameters and the average degree of the network in order to investigate their effects on the spread of disease. We verified that the infection and the recovery rates show significant effects on the dynamics of the disease transmission. While the exposed rate delays the spread of the disease, increasing it towards infinity would lead to almost the same dynamics as that of an SIR case. A network with high average degree results to an early and higher peak of the epidemic compared to a network with low average degree. The results in this paper can be used as an alternative way of explaining the spread of disease and it provides implications on the control strategies applied to mitigate the disease transmission.