Mathematical Models Of Schistosomiasis Epidemic And The Simulation Of Applications In Practical

Schistosomiasis is a serious infectious and parasitic disease transmitted through the medium of water, with great influence on human health, social stability and economic development. It mainly prevails in 381 counties (cities, districts) of 12 provinces, autonomous regions, municipalities along and to the south of the Yangtze River valley, and above 100 million people become the victims of schistosomiasis. Often two methods are taken to control epidermic situation according to the situation of our country: mass human and buffalo synchronous chemotherapy and focal snail control. Statistics by year show that mass human and buffalo synchronous chemotherapy is extensively adopted, but these measures will not be long sustained. In recent years, a number of long-term mechanism on the prevention and treatment of China's schistosomiasis have been proposed, such as building latrines on places like sand beach, stable cattle breeding and using tractors to replace the work of farm cattle.According to the actual data of the morbidity rate in six villages of Hunan and Hubei provinces between 1990 and 1998, as well as understanding on the parameters of the Barbour's two-host model, by the way of adding the equations, this dissertation improve the Barbour's two-host model. At the same time, the improved simulation model is used to simulate the morbidity rate of human and buffalo under the measures of mass human and buffalo synchronous chemotherapy, building latrines and substitution for farm cattle, among which the latter two measures have not yet been systematically studied through numerical simulation by experts at home and abroad.In this article, the conclusion has been achieved through numerical simulation and comparison that:To build latrines is a long-term mechanism, whose main role is to control human environmental pollution. Under its influence, we selected six villages, while all of theoverall basic reproduction rate through the two-host transmission R_o" are less than 1,and tend to reach the disease-free equilibrium.Mass human and buffalo synchronous chemotherapy is a short-term mechanism, which can only reduce morbidity rate of human and buffalo in a short period of time. The higher the strength is, and the longer time is required to bounce back. Under its influence, all of the overall basic reproduction rate R_o" of two-host transmission inour calculation of six villages in Hunan, Hubei Provinces are more than 1. In the mathematical sense, schistosomiasis tends to be an endemic disease in these villages.Substitution for farm cattle is also a long-term mechanism, which has particularly obvious effects on the control over the morbidity rate of buffalo, while the control over the morbidity rate of human has moderate effects. By the means of substitutionfor farm cattle, all values of R_o~" are less than 1, which tend to reach the disease-freeequilibrium. It can be taken as a long-term control measure to play roles throughout the substitution periods, and the persistent effects make it possible to achieve the eradication of schistosomiasis along with long-term usage.A wide range of mass human and buffalo synchronous chemotherapy measures are still taken in China's affected areas of schistosomiasis, while in ralation to Hunan Province, farm cattle are grazed in the wilds in most regions, the morbidity rate of buffalo is relatively higher. The buffalo plays a comparatively important role in the spreading factor of schistosomiasis, and the high morbidity rate of buffalo is a big threat to disease control. In these areas, mass human and buffalo synchronous chemotherapy can first be adopted to reduce the morbidity of human and buffalo to a lower level, and then the further control of the morbidity of buffalo can be appropriately supplemented by long-term mechanisms like substitution for farm cattle to confine the morbidity of human and buffalo to the national epidemic control standards.To sum up, when the morbidity rate of human and buffalo is relatively moderate or low, mass human and buffalo synchronous chemotherapy is a much better choice; when the morbidity of cattle is relatively high and the morbidity rate of human is moderate, substitution for farm cattle has comparatively benefits; when the positive rate of human excrement influences on environment pollution to a certain degree, the measures of building latrines can take advantages. That is why we have to take different measures in the light of local conditions. Finally, according to the author's research on the Barbour's two-host model parameters in accordance with the actual situation of stratification based on the study of schistosomiasis in China, a hierarchical model is constructed. Subsequently, exemplified by the instances of dividing Liupo Villige in Guichi City of Anhui Province into three lines, some assumed models are applied to simplify the equations, and calculations are made based on the morbidity rate of human in different years and on differnt lines as well as the overall morbidity rate of buffalo, then a brief hierarchical model is thus summarized.