The global analysis of the SEIR epidemic model with vaccination and population births

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Abstract

This paper constructs a Susceptible-Exposed-Infectious-Recovered (SEIR) model that takes into account the dynamic changes in the birth population and includes both vaccinated and unvaccinated populations. The basic reproduction number R₀ is derived, and its global stability is analyzed. It is proven that when R₀ < 1, the disease-free equilibrium point is globally stable. When R₀ > 1, there exist an unstable disease-free equilibrium and a unique endemic equilibrium. Subsequently, we conduct the numerical simulations to validate theoretical results and plot data visualizations for various scenarios. In addition, the parameter sensitivity analysis and the forward bifurcation of the model are performed to examine how each system parameter specifically affects disease transmission. Our results offer practical insights for public health planning, particularly in optimizing vaccination strategies in populations with high birth rates or waning immunity.

Keywords

SEIR model / vaccination / bifurcation / global stability / basic reproduction number

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