Epidemiology and Mathematics

Mathematical Epidemiology is a growing field of study. Mathematical models can show how infectious diseases progress and deduce a likely outcome of an epidemic which in turn helps inform public health interventions. Mathematical models are created out of base level statistic collection. Further, parameters are found for the growth of infectious diseases and those parameters are used to calculate various interventions. Mathematics becomes especially important when deciding who to vaccinate when during mass vaccination programs.

John Graunt was the first scientist who systematically tried to quantify causes of death in his book Natural and Political Observations. Graunt’s work was the beginning of the ‘theory of competing risks’ which is now a well established theory among modern day epidemiologists.

In 1760, Daniel Bernoulli created a mathematical model to defend the practice of inoculating against smallpox.The model’s calculations l showed that universal inoculation against smallpox would increase life expectancy from 26 years 7 months to 29 years 9 months.

There are two types of epidemic models, Stochastic and Deterministic. “Stochastic” means having a random variable. A stochastic model is used to estimate distributions of potential outcomes with the use of random variables at different junctures of calculation. Stochastic models depend on the chance variations in risk of exposure, disease etc. “Deterministic” models are used for larger populations, this is based on a set number of assumptions.

The most common variable in mathematical epidemiology is the basic reproduction number, also known as R0, it is a measure of how transferable a disease is. Further there are variables such as L (life expectancy), S (populations that are susceptible) , A (average age of infection).

While epidemics are chaotic, mathematics can help determine a lot of the trajectory of an epidemic even if not all of it. With the growth of science and mathematical understandings, while dealing with epidemic outbreaks, mathematical models have become crucial in determining proper intervention.