A simple formulation of non-Markovian SEIR

Hern'andez, P.; Pena, C.; Ramos, A.; G'omez-Cadenas, J. J.

We present a formulation of the SEIR concept that represents the evolution of an epidemic under the assumption of homogeneity and uniformity of the microscopic parameters: rate of infection, incubation and recovery/removal times. Non-homogeneities in the basic parameters are easily included by integration for arbitrary distributions of incubation and removal times, recovering the classical SEIR model under the assumption of exponential distributions. We compare the solution to these equations, uSEIR, to two types of agent-based model simulations, a spatially homogeneous one where infection occurs by proximity, and a model on a scale-free network with varying clustering properties, where the infection between any two agents occurs via their link if it exists. We find good agreement in both cases with the uSEIR solution. Furthermore a family of asymptotic solutions of the uSEIR equations is found in terms of a logistic curve, which after a non-universal time shift, fits extremely well all the microdynamical simulations. A link to software packages for the numerical solution of the uSEIR equations is provided.