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Misra, A.K., Sharma, A. and Shukla, J.B. (2011) Modeling and Analysis of Effects of Awareness Programs by Media on the Spread of Infectious Diseases. Mathematical and Computer Modelling, 53, 1221-1228.
https://doi.org/10.1016/j.mcm.2010.12.005

has been cited by the following article:

• TITLE: Deterministic and Stochastic Analysis of a New Rumor Propagation Model with Nonlinear Propagation Rate in Social Network

  AUTHORS: Chunxin Liu

  KEYWORDS: Rumor Model, Nonlinear Incidence Rate, Secondary Propagation Rate, Stochastic Fluctuation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.11, November 16, 2023

  ABSTRACT: This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.