Modeling the effect of health education and individual participation on the increase of sports population and optimal design.

Health education plays an important role in cultivating people's awareness of participating in physical exercise. In this paper, a new differential equation model is established to dynamically demonstrate the different impact of mass communication and interpersonal communication in health education on people's participation in physical exercise. Theoretical analysis shows that health education does not affect the system threshold, but individual participation does. The combination of the two leads to different equilibria and affects the stability of equilibria. When mass communication, interpersonal communication and individual participation satisfy different conditions, the system will obtain different positive equilibrium with different number of sports population. If the interpersonal transmission rate of information is bigger, there is a positive equilibrium with a large number of sports population in the system. Sensitivity and optimal design analysis show some interesting results. First, increasing interpersonal communication and mass communication can both increase the number of conscious non-sports population and sports population. For increasing the number of conscious non-sports population, the effect of mass communication is better than that of interpersonal communication. For increasing the number of sports population, the effect of interpersonal communication is better than that of mass communication. However, individual participation has the best effect on increasing the sports population. Second, increasing the daily fixed amount of new information will be more helpful for media information dissemination. Finally, the three control measures need to be implemented simultaneously for a period of time at first, and then health education and participation of sports people need to be implemented periodically in order to maximize the sports population.

Dynamic analysis and optimal control of a class of SISP respiratory diseases.

In this paper, the actual background of the susceptible population being directly patients after inhaling a certain amount of PM2.5 is taken into account. The concentration response function of PM2.5 is introduced, and the SISP respiratory disease model is proposed. Qualitative theoretical analysis proves that the existence, local stability and global stability of the equilibria are all related to the daily emission P0 of PM2.5 and PM2.5 pathogenic threshold K. Based on the sensitivity factor analysis and time-varying sensitivity analysis of parameters on the number of patients, it is found that the conversion rate ß and the inhalation rate η has the largest positive correlation. The cure rate γ of infected persons has the greatest negative correlation on the number of patients. The control strategy formulated by the analysis results of optimal control theory is as follows: The first step is to improve the clearance rate of PM2.5 by reducing the PM2.5 emissions and increasing the intensity of dust removal. Moreover, such removal work must be maintained for a long time. The second step is to improve the cure rate of patients by being treated in time. After that, people should be reminded to wear masks and go out less so as to reduce the conversion rate of susceptible people becoming patients.

Modeling the Influence of Nonclinic Visits on the Transmission of Respiratory Diseases.

According to the information reflected by Anhui Center for Disease Control (Anhui CDC) in Hefei, Anhui province of China, some patients infected with respiratory diseases did not seek medical treatment (nonclinic visits) due to their strong resistance, and the influence of them on the spread of respiratory diseases has not been known. A SIS model with considering the nonclinic visits was established; a qualitative theory of the model was analyzed to obtain the basic reproduction number R 0, disease-free equilibrium, endemic equilibrium, and stability of two equilibriums. Then, the model is combined with the daily number of respiratory diseases for parameter estimation and numerical simulation. Numerical simulation results showed that respiratory diseases were easy to break out in the autumn and winter and were relatively stable in the spring and summer. Through parameter estimation, the unknown parameter value was achieved and the result was obtained that the initial number of nonclinic visits is 10-11 times that of clinic visits. Finally, the result of sensitivity analysis displayed that the proportion of the number of nonclinic visits to the total number of patients has a significant influence on the final number of patients. If persons improve their resistance so that the number of nonclinic visits increases, the total number of patients will be reduced or even reduced to zero. Besides, reducing contact infection rate of disease and increasing the cure rate can also reduce the final total number of patients.

Multiple infection leads to backward bifurcation for a schistosomiasis model.

Based on years of experience in schistosomiasis prevention and treatment, one of the typical features of schistosomiasis is multiple infection of a human host by parasites, which may dramatically a ect the host's infectivity. In this paper we establish a schistosomiasis model that takes into consideration multiple infection by separating humans with single and multiple infectious. The disease free equilibrium is shown to be globally asymptotically stable under certain condition. The model analysis suggests that a backward bifurcation may occur if the transmission rate from multiple infected humans to snails is high. This conclusion has not been seen in previous models of schistosomiasis. Such backward bifurcation is not possible without considering multiple infections. This conclusion may provide a new threshold theory for the prevention and treatment of schistosomiasis. Furthermore, numerical simulations suggest that e ective treatment of humans with multiple infection is important to control schistosomiasis. Especially, prevention of multiple infection may be critical.

Parameter estimation of modeling schistosomiasis transmission for four provinces in China.

According to monitoring data of Anhui, Jiangxi, Hubei, Jiangsu Provinces, in this paper the transmission of schistosomiasis is studied based on Barbour's mathematical model. The values of the basic reproduction number and key parameters are obtained with two methods. The first method is to calculate directly by using parameter values in references. The second one is to estimate parameter values by the methods of noise measurement and data smoothing and then to obtain new values of basic reproduction number. Comparing these two methods, we found the second method is good to fit the data. This parameter values can be used as reference values in other provinces. Finally, some numerical simulations are carried out to discuss the development trend of prevalence of humans and snails in each province. It is found that schistosomiasis in four provinces is expected to be eliminated with the improvement or maintenance of the standards of prevention and control. Furthermore, the time needed is different in the different four provinces.

Schistosomiasis Transmission Model and its Control in Anhui Province.

National Bureau of Statistics of China reports that the incidence of schistosomiasis has been increasing in recent years. To study dynamic behaviors of schistosomiasis transmission, based on practical experience of staff in Anhui Institute of Schistosomiasis, a mathematical schistosomiasis model with reinfection of recovered people is established in this paper. Metzler matrix theory and center manifold theorem are used to analyze stability of equilibria. Parameter estimation has been performed by combining model and monitoring data. It is found that the basic reproduction number is different every year. The most concern of Institute of Schistosomiasis is whether or when to kill snails every year. To answer this question, threshold value of snail density can be obtained. Once the snail density exceeds the threshold, the staff will need to kill snails. To find the best control measures, sensitivity analysis is used to find out sensitive parameters, and then control measures can be obtained by optimization control measures. The results show that combination of spraying molluscicide, publicity and education, improving the health facilities, and large-scale treatment of patient groups have the best effect. In additional, it is found that the number of patients does not change much when the reinfection rate of recovered people is very small. However, when the reinfection rate is slightly larger, the number of patients will suddenly increase to a large value.