Delay-differential SEIR modeling for improved modelling of infection dynamics

SEIR (Susceptible–Exposed–Infected–Recovered) approach is a classic modeling method that is frequently used to study infectious diseases. However, in the vast majority of such models transitions from one population group to another are described using the mass-action law. That causes inability to reproduce observable dynamics of an infection such as the incubation period or progression of the disease's symptoms. In this paper, we propose a new approach to simulate the epidemic dynamics based on a system of differential equations with time delays and instant transitions to approximate durations of transition processes more correctly and make model parameters more clear. The suggested approach can be applied not only to Covid-19 but also to the study of other infectious diseases. We utilized it in the development of the delay-based model of the COVID-19 pandemic in Germany and France. The model takes into account testing of different population groups, symptoms progression from mild to critical, vaccination, duration of protective immunity and new virus strains. The stringency index was used as a generalized characteristic of the non-pharmaceutical government interventions in corresponding countries to contain the virus spread. The parameter identifiability analysis demonstrated that the presented modeling approach enables to significantly reduce the number of parameters and make them more identifiable. Both models are publicly available.