Math. Model. Nat. Phenom.
Volume 14, Number 5, 2019
Nonlocal and delay equations
|Number of page(s)||22|
|Published online||05 December 2019|
An infection age-space-structured SIR epidemic model with Dirichlet boundary condition
Laboratoire d’Analyse Nonlinéaire et Mathématiques Appliquées, University of Tlemcen,
2 Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan.
* Corresponding author: email@example.com
Accepted: 28 October 2019
In this paper, we are concerned with the global asymptotic behavior of an SIR epidemic model with infection age-space structure. Under the homogeneous Dirichlet boundary condition, we first reformulate the model into the coupled reaction-diffusion and difference system by using the method of characteristics. We then obtain the spatially heterogeneous disease-free steady state and define the basic reproduction number ℛ0 by the spectral radius of the next generation operator. We then show the existence and uniqueness of the global classical solution by constructing suitable upper and lower solutions. As a threshold result, we establish that the disease-free steady state is globally attractive if ℛ0 < 1, whereas the system is uniformly weakly persistent in norm if ℛ0 > 1. Finally, numerical simulations are exhibited to illustrate our theoretical results together with how to compute ℛ0.
Mathematics Subject Classification: 35K20 / 35Q92 / 92D30
Key words: SIR epidemic mode / infection age / diffusion / Dirichlet boundary condition / basic reproduction number
© EDP Sciences, 2019
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