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Mathematical Modeling, Simulation, And Time Series Analysis Of Seasonal Epidemics., Eric Shu Numfor

Electronic Theses and Dissertations

Seasonal and non-seasonal Susceptible-Exposed-Infective-Recovered-Susceptible (SEIRS) models are formulated and analyzed. It is proved that the disease-free steady state of the non-seasonal model is locally asymptotically stable if R_v < 1, and disease invades if R_v > 1. For the seasonal SEIRS model, it is shown that the disease-free periodic solution is locally asymptotically stable when R̅_v < 1, and I(t) is persistent with sustained oscillations when R̅_v > 1. Numerical simulations indicate that the orbit representing I(t) decays when R̅_v < 1 < R_v. The seasonal SEIRS model with routine and pulse vaccination is simulated, and results depict an unsustained decrease …