Affiliation:
1. School of Mathematics and Statistics Lanzhou University Lanzhou Gansu China
2. School of Finance Lanzhou University of Finance and Economics Lanzhou Gansu China
Abstract
AbstractThis work is concerned with the spatiotemporal propagation phenomena for a time‐periodic reaction‐diffusion susceptible‐infectious (SI) epidemic model with treatment in terms of the asymptotic speed of spread and periodic traveling waves. First, the asymptotic speed of spread is characterized and the spreading properties of the model are analyzed by combining the periodic principal eigenvalue problem, comparison method, and the uniform persistence idea for a dynamical system. Second, by constructing suitable super‐ and subsolutions for truncation problems corresponding to the traveling wave system, the existence of periodic traveling waves is established via the fixed point theorem twice. It turned out that the asymptotic speed of spread coincides with the minimum wave speed of periodic traveling waves. Finally, via numerical simulation, the effects of some important parameters (such as diffusion rate, treatment rate, etc.) on the spreading speed are discussed, and the asymptotic properties of the periodic traveling waves are explored.
Funder
National Natural Science Foundation of China
Fundamental Research Funds for the Central Universities
Reference41 articles.
1. Factors in the Emergence of Infectious Diseases
2. Large-Scale Spatial-Transmission Models of Infectious Disease
3. Etude De Lequation De La Diffusion Avec Croissance De La Quantite De Matiere Et Son Application a Un Probleme Biologique;Kolmogorov AN;Bull Univ dEtat a Moscou, Ser Intern A,1937
4. Run for your life. A note on the asymptotic speed of propagation of an epidemic
5. Research Notes in Mathematics, No. 14;Aronson DG,1977