Nonlinear dynamic epidemiological analysis of effects of vaccination and dynamic transmission on COVID-19

This paper is concerned with nonlinear modeling and analysis of the COVID-19 pandemic. We are especially interested in two current topics: effect of vaccination and the universally observed oscillations in infections. We use a nonlinear Susceptible, Infected, & Immune model incorporating a dynamic transmission rate and vaccination policy. The US data provides a starting point for analyzing stability, bifurcations and dynamics in general. Further parametric analysis reveals a saddle-node bifurcation under imperfect vaccination leading to the occurrence of sustained epidemic equilibria. This work points to the tremendous value of systematic nonlinear dynamic analysis in pandemic modeling and demonstrates the dramatic influence of vaccination, and frequency, phase, and amplitude of transmission rate on the persistent dynamic behavior of the disease.

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This paper focuses on the nonlinear modeling and analysis of the COVID-19 pandemic. It explores the impact of vaccination and the observed oscillations in infections. By incorporating a nonlinear Susceptible, Infected, & Immune model with dynamic transmission rate and vaccination policy, the study analyzes stability, bifurcations, and dynamics using US data as a starting point. Further parametric analysis reveals the influence of imperfect vaccination on the occurrence of sustained epidemic equilibria. This work highlights the importance of systematic nonlinear dynamic analysis in pandemic modeling and demonstrates the significant influence of vaccination and transmission rate on the disease's persistent dynamics.