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.