Improve Epidemic Disease Model And Research On Its Stability And Application Based On Markov Process

Markov chains are important tools for prediction and are widely used in various fields,such as finance and hydrology.This paper focuses on improving the traditional infectious disease model based on the Markov process.The main work is as follows:(1)Establishing a class of high-dimensional infectious disease models that take into account the viral load of infected patients.Based on the SEIR infectious disease model,the paper classifies latent patients,confirmed patients,and cured patients into seven compartments:unisolated latent patients,isolated latent patients,confirmed mild patients,confirmed severe patients,asymptomatic infected patients,cumulative asymptomatic self-cured patients,and cumulative confirmed cured patients.The basic regeneration number of the model is obtained using the method of basic regeneration matrix,and the existence conditions of disease-free equilibrium points are analyzed.Four disease-free equilibrium points of this model are obtained.Secondly,the stability of the four disease-free equilibrium points of the model is discussed using Routh-Hurwitz theory and LaSalle invariant set principle.Theoretical results are verified by numerical simulations.(2)Establishing a class of high-dimensional infectious disease hospital-acquired transmission models with a small base population as a background based on multidimensional continuous-time Markov process.Firstly,a traditional SEIR infectious disease model is developed using a hospital intensive care unit as a context.To address the limitations of the SEIR infectious disease model,the paper models the 2019-nCoV nosocomial transmission using a multidimensional continuous-time Markov process to characterize individual differences and develops an improved model for nosocomial transmission of infectious diseases.Secondly,the stability of the model is analyzed,and stability conditions are given.Due to the complexity of the model,the density matrix of the model is given in the form of a four-level matrix nesting,and the model is solved in the steady state using the density matrix and the transfer probability matrix.The improved model is compared with the traditional SEIR infectious disease model to demonstrate the superiority of the model.Finally,numerical simulations are conducted to study the factors affecting the transmission of nosocomial infection,and reasonable control measures are suggested.Overall,the paper proposes improved high-dimensional infectious disease models that take into account the viral load of infected patients and the hospital-acquired transmission of infectious diseases.The stability of the models is analyzed using various theories,and numerical simulations are conducted to validate the results.The paper provides valuable insights for predicting and controlling the spread of infectious diseases.