Research On The Model Of Infectious Disease By The Different Random Noise And The Media Coverage

With the wide development of smartphones and social platforms,the impact of information dissemination on the prevention of infectious diseases is highlighted,and the human infection and the prevalence of infectious diseases will change due to environmental fluctuations.Therefore,based on the previous studies,this paper focuses on the analysis of disease information-aware infectious disease models affected by media reports,adding different random white noise disturbances,and constructing two random types of random infectious disease models.And using the relevant theoretical knowledge of the stochastic differential equation to analyze it.A random infectious disease model with information transmission with constant input was established,and the natural mortality rate accompanied by random disturbance was used to describe the influence of the media on infectious diseases.Using the theory of differential equations,the deterministic disease-free equilibrium is calculated and the existence and uniqueness of the endemic equilibrium is verified.The randomness model is established and the existence and uniqueness of the global positive solution of the system are studied by theIt?o formula.The strong law of large numbers of local sputum analyzes the conditions of disease extinction and persistence;numerical simulation supports theoretical analysis and can control the spread of infectious diseases through random basic regeneration numbersR₀^s andR₀.Secondly,it analyzes the random extinction of infectious disease models affected by media reports.A stochastic model with random disturbances in contact rate and propagation rate is established.The Lyapunov analysis method is used to prove that the stochastic system has a unique global positive solution.Using the non-negative semi-convergence convergence theorem,we obtain the random extinction whenR₀?27?1 andR₀^s?27?1;using numerical simulation to support theoretical analysis.Through simulation,it can be seen that when the noise intensity is large,the solution of the stochastic model will change significantly,and its solution tends to be stable in a shorter time.In short,people can increase their understanding and prevention of infectious diseases through media coverage,take effective measures to reduce the chance of infection,and consider the effects of different random noises in the infectious disease model affected by media coverage,which is more comprehensive and realistic.