Qualitative analysis of a class of SISM epidemic model influenced by media publicity

Dongmei Li; Bing Chai; Weihua Liu; Panpan Wen; Ruixue Zhang; Dongmei Li; Bing Chai; Weihua Liu; Panpan Wen; Ruixue Zhang

doi:10.3934/mbe.2020308

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5727-5751. doi: 10.3934/mbe.2020308

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Research article

Qualitative analysis of a class of SISM epidemic model influenced by media publicity

College of Science, Harbin University of Science and Technology, Harbin 150080, China

Received: 16 April 2020 Accepted: 17 August 2020 Published: 28 August 2020

Considering the influence of media lagging publicity on the awareness rate of epidemic situation, this paper introduces the accumulation of epidemic awareness variables, establishes the SISM infectious disease model influenced by media publicity, and gives the sufficient conditions for the global asymptotic stability of the model disease-free equilibrium, the stability of the endemic disease equilibrium and the existence of the Hopf bifurcation. The variation trend of different effects of delayed media publicity on the outbreak is simulated. Based on the data of A (H1N1), the interference degree of the parameters in the model is analyzed. The results show that shortening the lag time of the media report and increasing the implementation rate and the transfer rate of media propaganda can effectively control the epidemic and gradually end the epidemic.
- SISM model,
- time delay,
- Hopf bifurcation,
- numerical simulation
Citation: Dongmei Li, Bing Chai, Weihua Liu, Panpan Wen, Ruixue Zhang. Qualitative analysis of a class of SISM epidemic model influenced by media publicity[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5727-5751. doi: 10.3934/mbe.2020308

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Abstract

Considering the influence of media lagging publicity on the awareness rate of epidemic situation, this paper introduces the accumulation of epidemic awareness variables, establishes the SISM infectious disease model influenced by media publicity, and gives the sufficient conditions for the global asymptotic stability of the model disease-free equilibrium, the stability of the endemic disease equilibrium and the existence of the Hopf bifurcation. The variation trend of different effects of delayed media publicity on the outbreak is simulated. Based on the data of A (H1N1), the interference degree of the parameters in the model is analyzed. The results show that shortening the lag time of the media report and increasing the implementation rate and the transfer rate of media propaganda can effectively control the epidemic and gradually end the epidemic.

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