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Ehrhardt, M., Gašper, J. and Kilianová, S. (2019) Sir-Based Mathematical Modeling of Infectious Diseases with Vaccination and Waning Immunity. Journal of Computational Science, 37, Article ID: 101027.
https://doi.org/10.1016/j.jocs.2019.101027

has been cited by the following article:

• TITLE: A Reaction-Diffusion SIR Model with Saturated Incidence Rate and Vaccination

  AUTHORS: Shaoyi Geng, Xiaolin Lin, Danfeng Pang, Guoqing Li

  KEYWORDS: Reaction-Diffusion Model, Saturated Incidence Rate, Basic Reproduction Number, Threshold Dynamics, Asymptotic Profile

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.2, February 14, 2025

  ABSTRACT: In this paper, we establish an SIR reaction-diffusion infectious disease model with saturated incidence rate and vaccination. Firstly, we prove the uniform boundedness of the solution of this model. Secondly, we establish the threshold dynamic behavior of the model based on the basic reproduction number R 0 , specifically, we prove the globally asymptotic stability of the disease-free equilibrium and the uniform persistence of the model. Thirdly, we show the existence and stability of the endemic equilibrium of the homogeneous system and obtain different cases of positive solution. Fourthly, we investigate the effects of vaccination rate and saturated incidence rate on the basic reproduction number. The results indicate that increasing vaccination rate and saturation rate can effectively control the transmission of the disease. Finally, we conduct numerical simulations to verify the aforementioned conclusions.