2014 HiMCM B题特等奖学生论文下载4880

2014 HiMCM B题特等奖学生论文下载4880

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论文摘要如下：

17th Annual High School Mathematical Contest in Modeling (HiMCM)

Summary Sheet (Please attach a copy of this page to your Solution Paper.)

Team Control Number: 4880

Problem Chosen: B

Please type a summary of your results on this page. Please remember not to include the name of your school, advisor, or team members on this page.

SUMMARY:

In order to determine how severe the spread of the disease is, we began by classifying the disease based on its mode of transmission. This was done by researching the respective reproductive rates (R0) of representative diseases for each major mode of transmission and matching the range of values found with the R0 of the unknown disease based on the data given in the problem. Using this method, we determined the disease to be transmitted primarily through air, with a R0 of 1.79, meaning that on average an infected person will pass it on to 1.79 other people. Using this value, we also determined that the disease is not contained since the number of infected individuals is still increasing since R0 is greater than 1. If R0 is less than 1, then the number of cases will slowly decrease and the disease will slowly disappear from the system because infected individuals are not generating enough new cases.

To model the spread of the disease through the population, we modified the SIR model to include a new factor E, which represents the number of individuals in the ‘latency phase’, which means that they are exposed and infected by the disease but are not showing symptoms yet. This model is known as the SEIR model. Since most diseases have an incubation period before symptoms are manifested, it is necessary to consider E when modeling the spread of the disease.

To determine the appropriate measures to be taken on the island, we first defined 6 different stages of a disease to match appropriate reactions and resource allocations. These stages are closely related to the variables in our SEIR model. I1 represents the number of individuals that are not showing symptoms (S and E); I6 represents the number of individuals that have died as a result of the disease (R); I2, I3, I4, and I5 represent the four stages of visible illness which have varying degrees of severity (I).

 

 

2014 HiMCM特等奖论文完整版 下载链接