埃博拉病毒传播问题的数学模型研究

In this paper in order to exterminate Ebola virus epidemic in West Africa, we establish four models. In model 1, we collect the number of total cases and deaths of Ebola in Guinea, Liberia and Sierra Leone from WHO's website. There is no vaccine or medication which can protect people from the disease in this period, so in order to describe the spread of Ebola virus accurately, we build improved SI epidemic model to estimate how many cases of Ebola will exist in these countries when the epidemic has been controlled. In model 2, the medication is widely used to fight against Ebola, and we take patients in the incubation period into consideration. So we build improved SEIR epidemic model to estimate how many people will be cured and the quantity of the medicine needed. We use the iterative method to obtain the numerical solution for its nonlinearity. For example, we estimate that 11271 people in Guinea will suffer from the disease, 6071 of them will be cured. It means those 11271 people need medicine (it can be equivalent to 8904 adults). In model 3, we build a PSO optimization model. At first we find there are 10 Ebola treatment centers (ETC) in Guinea and get the coordinates of them from Global Ebola Response Monitoring and Mapping System. Then we investigate the traffic conditions and epidemic situation around them.Finally we use PSO algorithm based on the goal to minimize the time to determine the optimal location of the delivery center. Its coordinate is (-10.599,9.043). In model 4, we develop a mixed model by combining the previous three models. We build a complete system in the axle of time to estimate speed of manufacturing of the medicine, which we can use to forecast, estimate and delivery. For instance, we estimate that we need 356 days to control the epidemic via using improved SI epidemic model. Then we do a sensitivity analysis and find that the model is sensitive to recovery rate, but it isn't sensitive to morbidity.