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Dynamic behavior of infectious diseases influenced by TV and social media advertisement

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  • Zhou, Yaxin
  • Jiang, Daqing

Abstract

TV and social media advertisements play an significant role in curbing the spread of infectious diseases as most of the populations are depend on what media transmits to them. In this paper, taking into account white noises, we propose a mathematical model to study the influences of TV and media advertisements on the dissemination of diseases. Construction of Lyapunov function is the top priority of this paper, which makes us draw a series of meaningful conclusions. We first discuss the local stability of the endemic equilibrium by Lyapunov function method which avoids the tedious calculation process when studying the local stability of the positive solution of the high-dimensional model. Then we obtain that the stochastic system has a unique global positive solution with any initial value. Next, the persistence of the diseases is proved and it also means that this model has an ergodic stationary distribution. Moreover, constructing a Lyapunov function can be used to derive the sufficient conditions for extinction. Finally, the numerical simulations illustrate our above theoretical results and several parameters that have a significant impact on the model are pointed out.

Suggested Citation

  • Zhou, Yaxin & Jiang, Daqing, 2023. "Dynamic behavior of infectious diseases influenced by TV and social media advertisement," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000280
    DOI: 10.1016/j.chaos.2023.113127
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    References listed on IDEAS

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    1. Li, Dingshi, 2013. "The stationary distribution and ergodicity of a stochastic generalized logistic system," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 580-583.
    2. Wei, Fengying & Xue, Rui, 2020. "Stability and extinction of SEIR epidemic models with generalized nonlinear incidence," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 1-15.
    3. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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