发布时间 : 星期二 文章数学建模 美赛 2015 A题更新完毕开始阅读
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Fig 10: Comparison of different intervention time
Seen from the figure above, the case without intervention has the highest peak and earliest peak time. The earlier the intervention happens, the lower the peak will be, and the later the peak will arrive. Therefore, the conclusion for this is : a sooner intervention of quarantine can reduce the severity of epidemic, as well as delay the coming of epidemic peak.
V. Conclusions
5.1 Conclusions of the problem
We eventually work out proper solution for Sierra Leone, and the delivery plan is illustrated in table 6. When solving the problem, we split it into three parts: the simulation part without intervention, the distribution part concluded medication intervention and the delivery part based on former results.
Therefore, we have solid reasons to suggest the infected individuals being quarantined and offering medicine as quickly as possible, so as to limit the chances of normal people getting infected. Focusing on the parameters, other factors like transformation of lifestyle can influence the contact rate thereby reduce the severity of the disease. 5.2 Strengths and weaknesses
Like any other models, ours have strengths as well as weaknesses, which is listed below. 5.2.1 Strengths
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? The SEIQFR model yields satisfying results
? We take infection from quarantined and buried individuals into consideration, alone with the latent period and time-lag. Therefore the model suits the real world better.
? In the Sierra Leone case, we are aware of the stage differences among districts. And our
results reflect this feature clearly.
? Our model is samely effective in other infected country cases. For the basic model remains
the same, and the only alteration is initial values of the city. 5.2.2 Weaknesses
? Due to a lack of data, we have to adopt national parameters in district simulation, which
will affect the accuracy of the results. ? We leave out some factors, such as the mutation of the virus and the flow of the population. VI. Future Work
? It is more appropriate to use ETU sites as the receiving locations. As the World Health
Organization suggests, there are about 21 ETUs (Ebola treatment unit) and more to be built, the locations and numbers of which are generally decided by the ratios of infected population. Because that the function of ETU is to provide medical assistance for resisting Ebola, the medication should be delivered to those sites as soon and much as possible.
Fig 11: ETU sites location
The figure above is extracted from the World Heath Organization website[9]. It illustrates the ETUs distribution in the three countries. The green ones are opening sites, while the yellow ones are under construction. And one unit in the figure equals to 34610 meters (1: 34610).
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Placed in a Cartesian coordinate system, the coordinates of each site is easy to get, so as the relative distances among them.
? The definition of parameters can involve the effect of time. It is more realistic if the
parameters change with time.
? The calculation of medicine can also be addressed. The medicine will reduce I, so as to
bring contact rates down. The impact of medicine may be more impressive than vaccine.
VII. References
[1] Astacio, J., Briere, D., Guillen, M., Martinez, J., Rodriguez, F., & Valenzuela-Campos, N. (1996). MATHEMATICAL MODELS TO STUDY THE OUTBREAKSOFEBOLA.
[2] LEGRAND, J., GRAIS, R., BOELLE, P., VALLERON, A. and FLAHAULT, A. (2006).
Understanding the dynamics of Ebola epidemics. Epidemiol. Infect., 135(04), p.610. [3] Rivers, C. M., Lofgren, E. T., Marathe, M., Eubank, S., & Lewis, B. L. (2014). Modeling
the impact of interventions on an epidemic of Ebola in Sierra Leone and Liberia. arXiv preprint arXiv:1409.4607. [4] Virginia Tech university. (2014，September 30). Ebola Modeling Update. Retrieved
February 8，2015, from http://ndssl.vbi.vt.edu/ebola/sample_locations_wa-ver1.1.html [5] Meltzer, M., Atkins, C., Santibanez, S., Knust, B., Petersen, B., Ervin, E., Nichol, S.,
Damon, I. and Washington, M. (2015). Estimating the Future Number of Cases in the Ebola Epidemic — Liberia and Sierra Leone, 2014–2015. [online] Cdc.gov. Available at: http://www.cdc.gov/mmwr/preview/mmwrhtml/su6303a1.htm#Appendix-tab4 [Accessed 9 Feb. 2015].
[6] Jing Xiang. (2011). Stability Analysis and Optimal Control for a Epidemic Model (Master's
thesis, Northeastern University).
[7] Althaus, C. L. (2014). Estimating the reproduction number of Zaire Ebola virus (EBOV)
during the 2014 outbreak in West Africa. arXiv preprint arXiv:1408.3505.
[8] Jiang Wei, Peng Xinyi, & Zhou Yuren. (2009). Reconstruction Method of Gene Regulatory
Network Based on Modified Particle Swarm Optimization. Computer Engineering , 35(20), 181-183. [9] (n.d.). WHO. Global Ebola Response Monitoring and Mapping System. Retrieved February
8, 2015, from http://maps.who.int/MapGallery/
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VIII. Memo
In response to the question regarding controlling the spread of Ebola epidemic and meditation delivery, we are writing to offering a general introduction of our work.
Focusing on Ebola virus disease, we first worked on the estimation of later epidemic situation and reached desirable result. The model is based on the early data of Ebola cases provided by the World Heath Organization, then it can generate an assemble curve based on the real initial data. Thus the trend of the spreading is simulated and the values of case in the future is illustrated by the curve we get. Then we consider the intervention of vaccine. When the delivery plan changes, the possible trend changes with it. So we find a proper plan to reduce the overall infected number. Also, assuming the delivery happens between national airports and capitals of the district, we are able to produce a vaccine delivery plan with the least cost.
Our model is flexible permitting various input of overall population and initial situation of the outbreak. That means the model can be used in other infected countries, as long as the basic information is available.
Referring to the analysis of our results, we highly suggest the infected individuals being quarantined and offering medicine as quickly as possible, so as to limit the chances of normal people getting infected. Besides, a higher level of quarantine and scientific burial also helps to ease the epidemic. The upgrade of resisting system should be done soon, for another finding in our paper is that Ebola will not stop by itself, unless we take enough measurements to control it. To eradicate Ebola, people in infected countries shall hold together, and ready for a long period of change in lifestyle. During our research, we notice there still remains unhealthy customs, some of them are even hazardous. So the advocation of government is necessary to correct those customs, like cremation. Taking account of the countries situation, we propose more countries and institutions to get involved, which can definitely boost the pace of eradicating Ebola therefore create a more healthy environment for the prosperity worldwide. The content above is a brief description of our work and advices. And wish our work can make a difference in the battle against Ebola.