Research On Dynamic Properties Of Rumor Propagation Model On Complex Networks

The rise of various online social platforms such as Weibo,We Chat,and Tieba has brought convenience to people’s communication and exchange but also cre-ated conditions for the breeding of rumors.The spread of rumors not only damages a healthy social network environment but also reduces the public’s trust in the govern-ment due to false online public opinion.Therefore,constructing a feasible rumor prop-agation model and analyzing the dynamic properties of the rumor propagation model has important practical significance for controlling the spread of rumors.This arti-cle proposes two types of rumor propagation models considering latent states,online marketing accounts,skeptics,and refutation mechanisms.It analyzes their dynamic properties,such as the existence of equilibrium points,basic regeneration numbers,and stability.The main research content includes:（1）Based on the characteristics of social networks and user nature,SEIDR and SEIMR rumor propagation models were established on a uniform network,taking into account the existence of latent states,network marketing accounts,skeptics,and rumor refutation mechanisms simulate and analyze the parameters and population density of two types of rumor propagation models,and provide complementary strategies for controlling rumors.（2）The existence of equilibrium points and basic regeneration numbers of SEI-DR and SEIMR rumor propagation models were analyzed using differential equation theory and the next-generation matrix method,respectively.The primary regeneration number₀of the SEIDR model is related to parameters such as,,.In contrast,the primary regeneration number₀of the SEIMR model is related to parameters such as,,,.The correctness of the theory has been verified through simulation analysis.（3）The local asymptotic stability and global asymptotic stability of SEIDR and SEIMR rumor propagation models at equilibrium points were analyzed using the Routh Hurwitz criterion and Lyapunov stability theorem;respectively,Research has shown that when R₀<1,the SEIDR model is locally asymptotically stable,when R₀<1and θ（?）/β+μ<1,the SEIMR model is locally asymptotically stable,and the experimental simulation results are consistent with the theoretical results.（4）According to the propagation mechanism of the rumor propagation model,considering the minimum loss caused by rumor propagation,a rumor propagation model with control was established for the SEIDR and SEIMR rumor propagation models,and relevant control functions were introduced to construct a Hamilton func-tion.The Pontryagin minimum principle was used to obtain the optimal control strat-egy.