A Discrete SEIRS Model for Pandemic Periodic Infectious Diseases

A deterministic SEIRS epidemiological model that captures the essential properties of pandemic recurrent diseases is developed here, in terms of a system of delay-difference equations. A non-linear system of difference equations is proposed, based on the assumptions of exponential incidence and of constant periods of latency, infectiousness and immunity. The model is able to reproduce observed data behaviors such as sustained oscillations and seasonality, typical of many childhood epidemics.We explore the stability of the system in parameter space and show its robustness and versatility to be applied to many infectious diseases. This new model is able to exhibit a wider range of dynamics than previous epidemiological models which make it ideal for a wide use in several infectious diseases. In order to illustrate this, we use this model in combination with a deliberately simplified spatially distributed population, and verify that it captures the essential features of communicable disease spread, such asfade-outs, and a great variability in epidemic sizes.We conclude that realistic models of geographical spread of infections could be improved by describing separately the properties of the diseases, from the social and human mobility aspects of the process. This model helps to fill the theoretical gap that exists between the classical compartmental models and the true stochastic nature of the spread of pandemics.

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