The Study Of Media Impact On Several Classes Of Epidemic Models

With the globalization trend, changes in the way humanity inhabits the planet have spurred the emergence of epidemics related to emerging and re-emerging infec-tious diseases in historically unprecedented numbers at present, such as HIV/AIDS, SARS, H1N1, H7N9, EVD, MERS, Zika virus. Moreover, the cost of vaccines is high and the protection offered by certain vaccines is temporary, even there are still no effective treatment and vaccines available for some diseases. Undoubtedly, the facts pose a considerable threat to the people’s health as well as bring about crisis to economic and social stability. Fortunately, the new media time arrival provides us an effective measure for disease prevention and control. During the outbreak of the diseases, mass media is extensively utilized by public health departments and organizations to keep the public aware of information associated with the epidemic, bringing in changes in public behavior so that the severity of a disease outbreak would be significantly diminished. In this thesis, our subject is to explore how to re-flect the intrinsic characteristics of media impact in epidemic models, and investigate their dynamics for bettering our understanding of disease prevention and control.Six chapters comprise the body of our thesis. The first chapter introduces the background and the research status of media impact on the epidemic dynamical models, and some preliminaries are presented.Chapter 2 aims at identifying the most effective measure and combinations of several measures to control influenza spread. An SVEIAR influenza model with me-dia coverage, imperfect vaccination and antiviral treatment is formulated, and its threshold dynamics is established. In order to evaluate the effectiveness of influenza control measures, sensitivity analysis of the control reproduction number and the endemic equilibrium is conducted. Furthermore, an optimal control problem incor-porating the three measures is proposed to design optimal control strategies. The cost-effectiveness analysis reveals that combining the three measures is the most cost-effective among the strategies considered. Numerical simulations show that media propaganda can play a dominant role in curbing influenza transmission.Chapter 3 is concerned with an SEIR epidemic model with media impact and latency and relapse delays, where the transmission rate of population is modeled as a decreasing and saturated function depending on the number of infected individuals. The permanence and global stability of the model are carefully resolved by suitable Lyapunov functionals. Numerical results reveal that timely response of media and individuals may play a more key role in disease control.In Chapter 4, one sets up an SVEIR epidemic model with media impact, imper-fect vaccination and a general latent distribution. The stability analysis concludes that the vaccination reproduction number completely determines whether the dis-ease dies out or not. Furthermore, two special probability distribution of remaining in latency are discussed. When the probability is negatively exponentially distribut-ed, we present an efficient approach of proving global stability of the endemic equi-librium of the SVEIR system of ordinary differential equations (ODEs), which may improve some known approaches. When the probability is a step-function, the delay differential equation (DDE) system derived is used to fit the mumps data of China from 2012 to 2015. In this chapter, vaccination effects are also carefully discussed.In Chapter 5, we consider an SIS epidemic model incorporating both the media effect and logistic growth. In general, media alert would not be implemented unless the number of infected cases reaches certain critical number. The media effect and the critical number are incorporated into the disease transmission rate which is a non-smooth but continuous function. Our model analysis shows that early media alert and strong media effects are preferable to decrease the numbers of infected cases at endemic equilibria. Most importantly, it is found that there exists a threshold interval for the critical number. In the threshold interval, the model has up to three endemic equilibria and bi-stability can occur. Otherwise, the model admits a unique globally asymptotically stable endemic equilibrium.Finally, Chapter 6 summarizes the current work and makes a prospect to media impact on epidemic dynamical models.