Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 29, Issue 2, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127419500275
Keywords
Disease transmission; nonlocal delay; bifurcation analysis; spatiotemporal patterns; Turing instability
Funding
- National Natural Science Foundation of China [11671241, 11331009]
- 131 Talents of Shanxi University
- Natural Science Foundation of Shanxi Province [201601D021002]
- Program for the (Reserved) Discipline Leaders of Taiyuan Institute of Technology
- Program for the Outstanding Innovative Teams (OIT) of Higher Learning Institutions of Shanxi
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In this paper, we study an SIS epidemic model with nonlocal delay based on reaction-diffusion equation. The spatiotemporal distribution of the model solution is studied in detail, and sufficient conditions for the occurrence of the Turing pattern were obtained using the analysis of Turing instability. It was found that the delay not only prohibited the spread of infectious disease, but also had great effects on the spatial steady-state patterns. More specifically, the spatial average density of the infected populations will decrease, as well the width of the stripe pattern will increase as delay increases. When the delay increases to a certain value, the stripe pattern changes to the mixed pattern. The results in this work provide new theoretical guidance for the prevention and treatment of infectious diseases.
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