Information-Related Epidemic Model With Age-Dependent Latency And Relapse

Based on the information-related contact rate of infectious diseases,it's worth to establish a mode for information-related infectious disease with latent age and relapse age,and find its mathematical conclusions and biological significanceIn the first chapter,there are two kinds of epidemic models briefly introduced in background and research progress.One type is information-dependent epidemic model and another type is epidemic model with latent and relapse age.For literature research and the reality of contagion,In this paper,we further study the effects of human resistance on the spread of infectious diseases with latent and relapse age after receiving the signal of these diseasesIn the second chapter,it is constructed and studied for the information-dependent epidemic system with latent and relapse age.Contact rate is a subtractive function of information variables,indicating a negative feedback with disease information.Infor-mation variable is the sum of disease cases collected from the past to the present.It is proved that the solution of the system is asymptotically smooth and exists in the positive invariant bounded set.By comparing with a system of Volterra type integro-differential equations,the uniform persistence of the system is obtained.Importantly,it follows from appropriate conditions that the local asymptotic stability and global asymptotic stability of equilibria can be concluded by the methods of corresponding characteristic equations and proper Lyapunov functionals,respectively.Applying numerical simulations illustrate the influence of the information on changing the coordinate of endemic equilibrium by increasing susceptible population and decreasing infectious population.It is remarkable to find that information coverage and the length of disease-relate memory would work effectively on the progression of diseaseIn the third chapter,it is established and studied the epidemic model with latent age,recovery rate,and information-dependent contact rate.Taking a kind of simple information-dependent contact rate into consideration,it decreases with the increase of the number of infected population regarded as a signal of whether the transmission of infectious diseases is serious or not.So the information-dependent contact rate is defined as the reduction function of the infection variable.The information-dependent contact simplifies the structure of the model,using a suitable Lyapunov function and setting rational conditions,the solution of the system is globally stableIn the fourth chapter,there is a briefly reviews of previous main work and conclu-sions.Furthermore,it is significant to discuss the biological and practical value of the epidemic model in this paper,meanwhile,rethink the shortcomings of the work in this paper,as well as the further research problems and work.