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The paradigm for compartment models in epidemiology assumes exponentiallydistributed incubation and removal times, which is not realistic in actualpopulations. Commonly used variations with multiple exponentially distributedvariables are more flexible, yet do not allow for arbitrary distributions. Wepresent a new formulation, focussing on the SEIR concept that allows to includegeneral distributions of incubation and removal times. We compare the solutionto two types of agent-based model simulations, a spatially homogeneous onewhere infection occurs by proximity, and a model on a scale-free network withvarying clustering properties, where the infection between any two agentsoccurs via their link if it exists. We find good agreement in both cases.Furthermore a family of asymptotic solutions of the equations is found in termsof a logistic curve, which after a non-universal time shift, fits extremelywell all the microdynamical simulations. The formulation allows for a simplenumerical approach; software in Julia and Python is provided.

A new formulation of compartmental epidemic modelling for arbitrary distributions of incubation and removal times