ANALYSIS OF A STOCHASTIC RECOVERY-RELAPSE EPIDEMIC MODEL WITH PERIODIC PARAMETERS AND MEDIA COVERAGE

Tao Feng; Zhipeng Qiu; Xinzhu Meng

doi:10.11948/2156-907X.20180231

2019 Volume 9 Issue 3

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Article navigation > Journal of Applied Analysis & Computation > 2019 > 9(3): 1007-1021

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Tao Feng, Zhipeng Qiu, Xinzhu Meng. ANALYSIS OF A STOCHASTIC RECOVERY-RELAPSE EPIDEMIC MODEL WITH PERIODIC PARAMETERS AND MEDIA COVERAGE[J]. Journal of Applied Analysis & Computation, 2019, 9(3): 1007-1021. doi: 10.11948/2156-907X.20180231

Citation:

Tao Feng, Zhipeng Qiu, Xinzhu Meng. ANALYSIS OF A STOCHASTIC RECOVERY-RELAPSE EPIDEMIC MODEL WITH PERIODIC PARAMETERS AND MEDIA COVERAGE[J]. Journal of Applied Analysis & Computation, 2019, 9(3): 1007-1021. doi: 10.11948/2156-907X.20180231

ANALYSIS OF A STOCHASTIC RECOVERY-RELAPSE EPIDEMIC MODEL WITH PERIODIC PARAMETERS AND MEDIA COVERAGE

1.
Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China
2.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Corresponding author: Email address:mathfengtao@163.com(Q. Huang)
Fund Project: The authors were supported by the National Natural Science Foundation of China (11671206), the Scholarship Foundation of China Scholarship Council (201806840120), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18 0370), the Fundamental Research Funds for the Central Universities (30918011339), the SDUST Research Fund (2014TDJH102) and the Research Fund for the Taishan Scholar Project of Shandong Province of China

Abstract

Abstract

This paper addresses, motivated by mathematical work on infectious disease models, the impacts of environmental noise and media coverage on the dynamics of recovery-relapse infectious diseases. A susceptibleinfectious-recovered-infectious model is formulated with both vertical transmission and horizontal transmission. The existence and uniqueness of the positive global solution is studied by constructing suitable Lyapunov-type function. Then, the existence of positive periodic solutions is verified by applying Khasminskii's theory. The existence of positive periodic solutions indicates the continued survival of the diseases. Besides, sufficient conditions for the extinction of the diseases are obtained. Numerical simulations then demonstrate the dynamics of the solutions. The paper extends the results of the corresponding deterministic system.
- Stochastic epidemic model /
- media coverage /
- periodic solution /
- vertical transmission /
- recovery-relapse
MSC: 15A18, 15A24

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