Research On Transmission Model Of COVID-19 Under Information Diffusion

With the advent of omnimedia era,information diffusion is playing an increasingly important role in preventing and controlling the spread of infectious diseases,and the role of information diffusion is even more prominent in the outbreak and control of COVID-19.Therefore,this paper introduces information related to the COVID-19 epidemic and the impact of the incubation period into the traditional SIR model for COVID-19 outbreak analysis.Firstly,this paper studies the dynamic behavior of a class of nonlinear COVID-19 models considering incubation period under information diffusion.The next generation matrix method is used to calculate the basic regeneration number of the model and conduct sensitivity analysis.The existence and stability of the disease-free equilibrium point and endemic equilibrium point are discussed.On the one hand,the local asymptotic stability of the disease-free equilibrium and the endemic equilibrium is proved by Routh-Hurwitz criterion when time delay is ignored.On the other hand,when the latency delay is considered,the Lyapunov functional is constructed to prove that the disease-free equilibrium is globally asymptotically stable when R0<1 and Q≤1,and its stability is independent of the delay.When R0>1,the system has a unique endemic equilibrium.The sufficient condition for Hopf bifurcation and the critical value τn0(0)of the corresponding delay are given.In addition,the theoretical results are verified by numerical simulation,and the influence of other factors(such as time delay,information index generation rate,vaccination ratio and information index decay rate)on the dynamic characteristics of COVID-19 model is further analyzed.Secondly,a control simulation model of cellular automata(CA)under the influence of information diffusion is constructed to simulate the transmission process of COVID-19.Taking the data of the infected population during the epidemic in Shijiazhuang as the reference factor,the CA model is established and simulated by MATLAB.The numerical solution of the dynamics model,the actual epidemic data and the CA simulation results are compared.The CA results obtained are feasible,reasonable and effective.At the same time,a GUI interface is designed to reproduce the dynamic situation of the transmission process of COVID-19,so as to realize the visualization of the entire transmission process of COVID-19.The influence of other factors,such as time point of control,population density in the outbreak area,incubation period,treatment period,initial number of latent population,maximum stride length of population and proportion of movement,on the transmission of COVID-19 is further analyzed.Finally,based on the above dynamic model of COVID-19,a class of optimal control problems are established with vaccination and information dissemination as control variables,so as to intervene in the transmission process of COVID-19 and balance the costs of intervention.In this paper,the weighted combination of the number of patients,the number of immunized people and the cost of vaccination and information publicity in a certain period of time is taken as the optimal performance index.The existence of the optimal control pair is proved by the optimal control theory,and the optimal path of the control function is given by using the Pontryagin maximum principle.In addition,the effectiveness and applicability of vaccination and information promotion as the optimal control pair are verified by numerical simulation,and the final simulation results show that the combination of the two interventions is the most cost-effective.