Stochastic periodic solution of a susceptible-infective epidemic model in a polluted environment under environmental fluctuation
type: Item
instance of: scholarly article
title: Stochastic periodic solution of a susceptible-infective epidemic model in a polluted environment under environmental fluctuation
zbMATH Open document ID: 1411.92301
DOI: 10.1155/2018/7360685
author: Yu Zhao
author: Jiangping Li
author: Xu Ma
published in: Computational \& Mathematical Methods in Medicine
publication date: 2019-03-27T00:00:00Z
review text: Summary: It is well known that the pollution and environmental fluctuations may seriously affect the outbreak of infectious diseases (e.g., measles). Therefore, understanding the association between the periodic outbreak of an infectious disease and noise and pollution still needs further development. Here we consider a stochastic susceptible-infective (SI) epidemic model in a polluted environment, which incorporates both environmental fluctuations as well as pollution. First, the existence of the global positive solution is discussed. Thereafter, the sufficient conditions for the nontrivial stochastic periodic solution and the boundary periodic solution of disease extinction are derived, respectively. Numerical simulation is also conducted in order to support the theoretical results. Our study shows that (i) large intensity noise may help the control of periodic outbreak of infectious disease; (ii) pollution may significantly affect the peak level of infective population and cause adverse health effects on the exposed population. These results can help increase the understanding of periodic outbreak patterns of infectious diseases.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 7042945
zbMATH Keywords: stochastic periodic solution
zbMATH Keywords: susceptible-infective epidemic model
zbMATH Keywords: polluted environment
Wikidata QID: Q55016537
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/7360685
OpenAlex ID: W2801904685
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description: scientific article; zbMATH DE number 7042945