Analysis Of Several Models On The Infectious Diseases With The Effect Of Awareness

Infectious disease is a kind of diseases that can spread widely among people or between peo?ple and animals.In recent years,due to the limitation of medical resources,the lack of effective treatment programs and specific vaccines,many infectious diseases can not be controlled in time,which has brought many disasters to mankind.With the development of science and technology,human communication is more convenient.Once an epidemic occurs in an area,the people would obtain disease information in time through the media reports.and taking corresponding preven-tive measures can reduce disease infection.In order to further understand the effect of disease awareness on the spread of infectious diseases,two kinds of mathematical models are established to study thisIn the first chapter,the basic background knowledge about infectious diseases and disease aware behavior was mainly introduced.Some domestic and foreign status were analyzed.Finally,the main research contents of this paper was elaboratedIn the second chapter,an SIS infectious disease model considering the effect of awareness was established.The effect of awareness is reflected by reducing individual infection rate and improving individual recovery rate nd so on.Four kinds of equilibria were calculated,according to the existence of equilibria,the threshold of awareness R1a was given,and the threshold of disease Rad when awareness do not spread(R1a<1)was also given.Through the next generation matrix method,the disease threshold was calculated as R2d when awareness spread(R1a>1).Through Lyapunov function and Cooperative system theory.It was proved that when R1a<1 and R1d<1,the disease-free unawareness equilibrium E01 was globally asymptotically stable,when R1a>1 and R2d<1,the disease-free awareness equilibrium E02 was globally asymptotically stable,when R1a<1 and R1d>1,the endemic unawareness equilibrium E1 was globally asymptotically stable,when R1a>1 and R2d>1,the endemic awareness equilibrium E2 was globally asymptotically stable.The effect of awareness parameters on the disease threshold was analyzed in detail,and numerical simulation was carried out.Finally,the accuracy of theoretical results was verified by numerical simulationIn the third chapter,an SEIR infectious disease model considering the effect of media reports was established.On the basis of the second chapter,a compartment was introduced to reflect the change process of media information with time,and the natural birth rate and mortality rate were considered.The basic reproduction number R0 was calculated by the next generation matrix method.Two kinds of equilibria were calculated.Through the Lyapunov function,it was proved that when B0<1,the disease-free equilibrium P0 was globally asymptotically stable,when R0>1,the endemic equilibrium P*was globally asymptotically stable.In order to verify the reasonable of the model,the SEIR model was fitted with the actual data of COVID-19,and the fitting effect was good.In addition,the sensitivities of the basic reproduction number R0 and the endemic equilibrium P*were analyzed.The effect of awareness parameters on the peak value of diseases was discussed,and the accuracy of the theoretical results was verified by numerical simulation.In the fourth chapter,the work of this paper is summarized,and corresponding suggestions are put forward in connection with the current situation of the COVID-19.