Modelling Cyclic Fluctuations of SEIR Epidemic Diseases

Seasonality of infectious disease is an important factor in disease incidence, outbreaks, control and prevention. Many mathematical models that incorporate seasonality in the transmission were formulated and analyzed. In this essay a qualitative analysis is given in terms of the effective reproduction number R₀, the existence and stability of the disease-free equilibrium and endemic equilibrium of both the SEIR model and seasonal SEIR model. We perform numerical simulations  to validate the model formulation.