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.