2014 HiMCM B题特等奖学生论文下载5325

ExecutiveSummary

As the world population grows and its distribution changes over time, mathematically modeling the spread of disease is an increasingly important means of developing rapid and effective response measures in diverse areas of the world. Quantitative knowledge of factors related to the spread of disease can be used to influence public policy to determine the best allocation of scarce medical resources to best combat disease. Given this need to address the spread of an unknown disease in a small village on an island in Indonesia, we have created a series of models that, when combined, can both predict the progression of said disease over time and recommend the necessary preventative measures.

Our first model uses a typical SIR model to provide an initial, simplified prediction of how the disease might spread over time absent any preventative measures. From this foundation, we then modified the SIR model into the SIRD model, which accounts specifically for deaths over time and contains a modification that allows for modeling the spread of the disease given some relative abundance of vaccines that have an average protection rate (i.e. the chance that a vaccine has of making an individual immune to said disease). Our third model is a decision tree that categorizes the severity of the disease based on quantitative thresholds of individual and community risk. The model then recommends treatment measures based on the category said disease falls under.

In a real world situation, all three of the previously discussed models would be used in conjunction to ascertain an appropriate response to the disease and adjust it over time. The three models all start with the same initial input of known disease characteristics, and result in a categorization of severity from the Decision Tree Model and an estimation of the progression of the disease from the SIR and the SIRD model. Appropriate treatment measures would likely be determined by adjusting the prescriptions of the Decision Tree using conclusions that can be drawn from the other two models. The interconnectivity between the models means that the effectiveness of the implemented treatment measure can be evaluated by re-running the SIRD model with data from the situation where treatment measures are in effect. If the effects of the disease are shown as being significantly mitigated, the effectiveness of the treatment has been confirmed; otherwise, a re-categorization of the disease and a change in the way resources are allocated may be appropriate. Therefore, the interconnectivity of the models serves as a way to confirm the effectiveness of our response.