Modelling the preventive treatment under media impact on tuberculosis:A comparison in four regions of China

Preventive treatment for people with latent Tuberculosis infection(LTBI)has aroused our great interest.In this paper,we propose and analyze a novel mathematical model of TB considering preventive treatment with media impact.The basic reproduction number R_(0)is defined by the next generation matrix method.In the case without media impact,we prove that the disease-free equilibrium is globally asymptotically stable(unstable)if R_(0)<1(R_(0)>1).Furthermore,we obtain that a unique endemic equilibrium exists when R_(0)>1,which is globally asymptotically stable in the case of permanent immunity and no media impact.We fit the model to the newly reported TB cases data from 2009 to 2019 of four regions in China and estimate the parameters.And we estimatedR_(0)=0.5013<1 in Hubei indicating that TB in Hubei will be eliminated in the future.However,the estimatedR_(0)=1.015>1 in Henan,R_(0)=1.282>1 in Jiangxi andR_(0)=1.930>1 in Xinjiang imply that TB will continue to persist in these three regions without further prevention and control measures.Besides,sensitivity analysis is carried out to illustrate the role of model parameters for TB control.Our finding reveals that appropriately improving the rate of timely treatment for actively infected people and increasing the rate of individuals with LTBI seeking preventive treatment could achieve the goal of TB elimination.In addition,another interesting finding shows that media impact can only reduce the number of active infections to a limited extent,but cannot change the prevalence of TB.

Global stability for an SEI model of infectious diseases with immigration and age structure in susceptibility

In this paper, we propose an SEI age-structured model for infectious diseases where the susceptibility depends on the age and with immigration of new individuals into the susceptible, exposed and infectious classes. The existence of a global attractor and the asymptotic smoothness of the solution semi-flow generated by the model are addressed. Using a Lyapunov functional, we show that the unique endemic equilibrium is globally asymptotically stable.