Modeling the Impact of Medication on Ebola 数学建模-美赛-2015-A题.docVIP

For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ Team Control Number38915 ? Problem ChosenA For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ 2015 Mathematical Contest in Modeling (MCM) Summary Sheet Modeling the Impact of Medication on Ebola Ebola virus disease is spreading in West African countries. As the medication for Ebola has been developed, we manage to offer an optimal plan for controlling the spread of Ebola. At first, we consider the situation without intervention. Based on SEIR model, we formulate an epidemic model (SEIQFR) with time-lag to simulate the future situation of Ebola. Referring to the data from the WHO early period, we fit the unknown parameters with the least square method. Implementing our model with the data of Sierra Leone, we give a future prediction of Ebola epidemic situation with Runge Kutta method. The result suggests that all compartments become stable in the end, which means an equilibrium point is reached. As for intervention involved situation, we build a non-liner programming model to generate a distribution plan of medication. Based on the first model, we add intervention of vaccine. Assisted with modified Particle Swarm Optimization algorithm, we reach to a solution leading to fewer infected population in Sierra Leone after 4 days with a steady manufacture speed of vaccine. We find the infected people will decrease by 80, therefore proves that vaccine is able to ease the epidemic. Then, we develop a liner programming model to provide a delivery system with the least cost. According to the results in distribution model, we get this solution system for Sierra Leone. Our sensitivity analysis considers influence of other factors. Situations with contact rate changes are tested. The results suggest that the contact rate between infected and susceptible people has the most impact. Our SEIQFR model considers the effect of time-