Modeling And Analysis Of Tuberculosis With Media Coverage And Inter Patch Influence

Tuberculosis has been theratening human health for thousands of years.According to the data,the number of patients has reached tens of millions of people each year,and the death toll is nearly one million.Therefore,tuberculosis is still a rather thorny public health problem in the world.In the information age,the media,as an important tool for information dissemination,is the main source of public access to information,and has an important impact on the spread of TB prevention.However,with the development of social economy and the progress of science and technology,people travel more conveniently and quickly,and the population flow between different regions is more frequent,which is equivalent to providing favorable conditions for the spread of diseases.Therefore,this paper mainly studies two types of TB models with media coverage and interactions among patches.In the second part,in the early stage of disease outbreak,people pay high attention to the information released by the media and take epidemic prevention measures immediately,resulting in a great impact on the infection rate by the media.After a long time,the attention gradually decreases,so the impact of the media on the infection rate gradually weakens.Considering this factor,we establish a TB model with infectious rate function.Firstly,we calculate the basic re-production number,analyze the conditions for the existence of the equilibria and further study the stability of them.Finally,we obtain the influence of each parameter on the spread and epidemic of the disease by using LHS/PRCC and sensitivity index methods to analyze the sensitivity of the basic reproduction number and the endemic equilibrium respectively.Meanwhile,we simulate the impact of media coverage on tuberculosis.The results show that the media should timely report the disease information after the outbreak of the disease,so that people realize the seriousness of the epidemic and take measures to reduce contact with infectious individuals,as well as preventing the spread of the disease.In addition,it is necessary to improve the level of medical treatment to raise the cure rate.In the third part of the paper,we consider that infectious individuals and exposed individuals are not suitable to travel because of the control measures.Therefore,we establish a TB model that they do not migrate between patches.Firstly,we analyze the existence of equilibrium of patch model by using matrix theory,and then the stability of disease-free equilibrium of two patch model is analyzed.By numerical simulation,we find when the threshold₀₁<1 and₀₂<1,the disease-free equilibrium is stable,which means that the disease disappears;when₀₁>1 and₀₂<1 or₀₁<1 and₀₂>1,the boundary equilibrium of the system is stable,indicating that the disease is prevalent in one of patch;when₀₁>1and₀₂>1,the system has a unique stable positive equilibrium,at this time,the disease continues to prevail.Finally,we simulat the effect of migration rate on TB transmission and find that the increase in migration rate would lead to a significant increase in the risk of disease flow.Therefore,when the disease breaks out,we should take timely measures to reduce unnecessary population mobility in order to control the spread of the disease...