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Mathematical Epidemiology: Past Findings and Future Possibilities

By: Madhav Parthasarathy

Have you ever wondered how and why diseases spread? Well, the answer to that is Mathematical Epidemiology! Mathematical Epidemiology is the mathematical modeling of diseases to determine the rate at which people become infected with diseases. The study of infectious disease data began with the work of John Graunt in his 1662 book “Natural and Political Observations made upon the Bills of Mortality,” which lists weekly records of numbers and causes of death in the London parishes. These records began in 1592 and were kept continuously since 1603. Graunt analyzed the different causes of death and created a method of estimating the risks of dying from different diseases. This was the first approach used to analyze data to determine the various risks of the disease. Now, what I just talked about was the first study of infectious disease data, but the first model in mathematical epidemiology was the work of Daniel Bernoulli on inoculation against smallpox. Variolation was introduced as a method to produce immunity against smallpox, with the negligible, mostly, risk of possible death. There was debate held on whether variolation was actually beneficial, and Bernoulli was told to lead the study to answer this controversial question. The approach Bernoulli used was to calculate the increase in life expectancy if smallpox were to be eliminated as one of the causes of death. This approach led to the publication of a complete exposition in 1766. These findings discussed were from many years in the past, while one of the main findings in mathematical epidemiology was the Kermack and McKendrick model in 1927:

Here x(t) is the number of people who are susceptible to the disease itself, y(t) is the number of infectious individuals, and z(t) is the number of recovered individuals.

There is a clear history of Mathematical Epidemiology that has served as a progression for epidemiologists to be able to use. However, now the challenge for epidemiological modeling would be to determine which situations would allow for slower exponential growth. This is an important direction that epidemic modeling must take, and suggestions to work past this challenge include metapopulation models with spatial structures that discuss population dynamics, such as contact rates, etc. Another direction that would be interesting for epidemic modeling to take would be researching contact rates decreasing in time because of behavioral changes within individuals in response to diseases entering the body. Contact rates are extremely important to determine whether someone will become infected or not. These are just a few of the future implications of Epidemic modeling and, I hope that all of you are as excited as I am, to see what’s in stock for the future of this unsaturated topic that is Mathematical Epidemiology.

Work Cited

Bauer, F. (2017). Mathematical epidemiology: Past, present, and future. Infectious Disease Modeling, 113–127. doi: 10.1016/j.idm.2017.02.001

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