Dynamics Modeling And Theoretical Study Of Several Infectious Diseases

Emerging Infectious Diseases is a disease which seriously affects social stability, form a major threat to human health, needs urgent treatment, including plague, SARS, Ebola and so on. Therefore, it is particularly important to study propagation characteristics of disease and look for effective control measures, mathematical model a useful tool in studying infectious diseases. In this paper, we study Ebola and MERS:In chapter 1, we give the significance of investigating Ebola and MERS, development of this filed and the main work in this thesis.In chapter 2, we study dissemination of Ebola in Liberia,based on the data released by World Health Organization and the actual transmission situations, we investigate the impact of different transmission routes on the EVD outbreak and estimate the basic reproduction number R0= 2.012 in the absence of effective control measures. Through sensitivity and uncertainty analysis, we reveal that the transmission coefficients of suspected and probable cases have stronger correlations on the basic reproduction number. Furthermore, we study the influence of control measures(isolation and safe burial measures) on EVD outbreak. It is found that if combined control measures are taken, the basic reproduction number will be less than one and thus EVD in Liberia may be well contained.In chapter 3, we mainly study the dissemination of MERS in the Republic of Korea,based on the detailed data of patients released by World Health Organization(WHO) and actual propagation of the epidemic, we construct two dynamical models to simulate the propagation processes from May 20 to June 8 and from June 9 to July 10, 2015, respectively.we find that the basic reproduction number R0 reaches up to 4.422. The numerical analysis shows that the reasons of the outbreak spread quickly are lack of self-protection sense and targeted control measures. Through partial correction analysis, the parameters β1and γ have strong correlations with R0, i.e., the infectivity and proportion of the asymptomatic infected cases have much influence on the spread of disease. By sensitivity analysis, strengthening self-protection ability of susceptible and quickly isolating or monitoring close contacts are effective measures to control the disease.