BackgroundMumps, an infectious viral disease, classically manifested by inflammation of salivary glands and is best known as a common childhood viral disease with no specific treatment. Although it can be protected by vaccine, there are more than 100,000 reported mumps cases according to the Chinese Center for Disease Control and Prevention. However, the factors and mechanisms behind the persistence and prevalence of mumps have not been well understood.MethodsA mumps model with seasonal fluctuation is formulated and investigated. We evaluate the basic reproduction number ℛ0 and analyze the dynamical behavior of the model. We also use the model to simulate the monthly data of mumps cases and carry out some sensitivity analysis of ℛ0 in terms of various model parameters.ResultsIt is shown that there exists only disease-free solution which is globally asymptotically stable if ℛ0 < 1, and there exists a positive periodic solution if ℛ0 > 1. ℛ0 is a threshold parameter, and its magnitude determines the extinction or persistence of the disease.ConclusionOur analysis shows that vaccination rate and invalid vaccination rate play important roles in the spread of mumps. Hence, Our study suggests to increase the vaccine coverage and make two doses of MMR (Measles, mumps and rubella vaccine) vaccine freely available in China.

Background Hepatitis C virus (HCV) is a leading cause of chronic liver disease. As yet there is no approved vaccine protects against contracting hepatitis C. HCV seriously affects many people’s health in the world. Methods In this article, an epidemiological model is proposed and discussed to understand the transmission and prevalence of hepatitis C in mainland China. This research concentrates on hepatitis C data from Chinese Center for Disease Control and Prevention (China’s CDC). The optimal parameters of the model are obtained by calculating the minimum chi-square value. Sensitivity analyses of the basic reproduction number and the endemic equilibrium are conducted to evaluate the effectiveness of control measures. Results Vertical infection is not the most important factor that causes hepatitis C epidemic, but contact transmission is. The proportion of acute patients who are transformed into chronic patients is about 82.62%. The possibility of the hospitalized patients who are restored to health is about 76.24%. There are about 92.32% of acute infected are not treated. The reproduction number of hepatitis C in mainland China is estimated as approximately 1.6592. Conclusion We find that small changes of transmission infection rate of acutely infected population, transmission infection rate of exposed population, transition rate for the acutely infected, and rate of progression to acute stage from the exposed can achieve the purpose of controlling HCV through sensitivity analysis. Finally, based on the results of sensitivity analysis, we find out several preventions and control strategies to control the Hepatitis C.

Natural fish have evolved with an excellent swimming performance after millions of years. Based on the flexible features of the pectoral fin, this paper focuses on the kinematics and hydrodynamics of the fin when fish are swimming stably in still water in labriform mode. The locomotion mechanism based on the morphology of the pectoral fin is applied to establish a kinematic model composed of five rays and membranes, which is adopted to control the pectoral fin to reach deformation in approximately the same way as the labriform mode. A semi-empirical theoretical model based on the kinematics is proposed to calculate the hydrodynamic force. In order to study the flow field, the numerical simulation of fluid-structure interaction is carried out and the results are validated by the present semi-empirical model, which also verifies the feasibility of the semi-empirical theoretical model for describing the dynamics of the pectoral fin under a complex water environment. In addition, the relationship between propulsion performance and locomotion parameters (e.g. frequency of motion, amplitude of flapping and rowing angle, and phase lag between flapping and rowing) of the multi-degree of freedom flexible pectoral fin is also revealed. It is found that the frequency and amplitude of the flapping angle have a significant influence on the hydrodynamic thrust, while the rowing angle and phase lag have little effect. The established models and the results provide effective tools and significant reference for the design of bionic pectoral fins.

The linear Euler-Bernoullibeam model is employed for the studies on the interactions between a flexible plate and incoming flow. The flow field was simulated by the immersed-boundary method. It is shown that the plate was inhibited at a relative low Reynolds number. When the Reynolds increases, the plate begins to flap and its amplitude increases with the increasing of Reynolds number. The amplitude is small with a large stiffness coefficient. When the mass ratio becomes large, the inertial effect enhances, and the amplitude of the plate is large. With the same material parameters, different initial trailing edge inclination lead to different flapping amplitudes.