An SIR epidemic model with free boundary

2013/02/02 by Kwang Ik Kim, Kim, Kwang Ik, Zhigui Lin +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #COVID-19 epidemiological studies #Evolution and Genetic Dynamics #Mathematical and Theoretical Epidemiology and Ecology Models #math.AP #msc:35B35 #msc:35K60

paper · pdf · doi:10.48550/arxiv.1302.0326

26 pages

arxiv created 2013/02/02 · arxiv updated 2013/02/05

Abstract

An SIR epidemic model with free boundary is investigated. This model describes the transmission of diseases. The behavior of positive solutions to a reaction-diffusion system in a radially symmetric domain is investigated. The existence and uniqueness of the global solution are given by the contraction mapping theorem. Sufficient conditions for the disease vanishing or spreading are given. Our result shows that the disease will not spread to the whole area if the basic reproduction number R₀<1 or the initial infected radius h₀ is sufficiently small even that R₀>1. Moreover, we prove that the disease will spread to the whole area if R₀>1 and the initial infected radius h₀ is suitably large.

Cited by

• A SIS reaction-diffusion-advection model in a low-risk and high-risk domain

Related

• Diffusion-Reaction Epidemic Model with a Free Boundary
• The spreading fronts of an infective environment in a man-environment-man epidemic model
• A SIS reaction-diffusion-advection model in a low-risk and high-risk domain
• Spatial SIR epidemic model with varying infectivity in an unbounded domain: Law of Large Numbers
• Qualitative properties of solutions to nonlocal infectious SIR epidemic models