There are many forms of mathematical modeling but the one I'm going to talk about is called Queueing Theory. Basically, this field is concerned with planing and optimizing waiting times, e.g., for surgeries in a hospital.

By planing I refer to scheduling the shifts of the medical personnel, or efficiently using the available resources (e.g., beds, rooms). Doing this simply based on 'intuition' can be subjective and/or misleading. A mathematical model can incorporate the statistics observed over previous years of operation and tries to predict future demand to simplify the planing decisions named above.

Optimizing waiting times is another challenge where Queueing Theory can be helpful. Imagine your hospital has ten rooms for surgery (some being larger, being equipped with specialized tools etc.). How do you assign surgery cases to these rooms? Again, one might make a first guess - however, queueing theorists haven proven various cases in which our first intuition is misleading. A simple instance is the difference between A) making the decision which surgery takes place in which of the ten rooms upfront as far into the future as possible and B) having a central queue of planned surgeries for all ten room together. How much of a difference can it make, do you say? Well this simple case is well known as the difference between 10 M/M/1 queues (A) and a single M/M/10 queue (B) and it makes a huge difference: you should always choose strategy B! It'll make everything a lot faster and fairer for your patients!

Obviously, my examples only scratched the surface and were overly simplistic. There is a vast amount of literature and scheduling surgeries is not the only example for the applicability of Queueing Theory in public health. And, at last, Queueing Theory is just one of many mathematical modeling tools. Another tool that come to my head would be graph-theoretic models to track, predict, and stop the spread of illness like the flu (checkout the Google Flu Trends link I posted below).

For further reading on the planing of surgeries I also added a link to a corresponding survey paper.

In my research I used to use mathematical modeling to research Chronic Obstructive Pulmonary Disease at the German Cancer Research Center (statistical models for detecting the disease). Nowadays, I work in a completely different field and use mathematical modeling to study content delivery (websites, photos, videos) on the Internet.

http://www.google.org/flutrends/

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1072083/

There are many forms of mathematical modeling but the one I'm going to talk about is called Queueing Theory. Basically, this field is concerned with planing and optimizing waiting times, e.g., for surgeries in a hospital.

By planing I refer to scheduling the shifts of the medical personnel, or efficiently using the available resources (e.g., beds, rooms). Doing this simply based on 'intuition' can be subjective and/or misleading. A mathematical model can incorporate the statistics observed over previous years of operation and tries to predict future demand to simplify the planing decisions named above.

Optimizing waiting times is another challenge where Queueing Theory can be helpful. Imagine your hospital has ten rooms for surgery (some being larger, being equipped with specialized tools etc.). How do you assign surgery cases to these rooms? Again, one might make a first guess - however, queueing theorists haven proven various cases in which our first intuition is misleading. A simple instance is the difference between A) making the decision which surgery takes place in which of the ten rooms upfront as far into the future as possible and B) having a central queue of planned surgeries for all ten room together. How much of a difference can it make, do you say? Well this simple case is well known as the difference between 10 M/M/1 queues (A) and a single M/M/10 queue (B) and it makes a huge difference: you should always choose strategy B! It'll make everything a lot faster and fairer for your patients!

Obviously, my examples only scratched the surface and were overly simplistic. There is a vast amount of literature and scheduling surgeries is not the only example for the applicability of Queueing Theory in public health. And, at last, Queueing Theory is just one of many mathematical modeling tools. Another tool that come to my head would be graph-theoretic models to track, predict, and stop the spread of illness like the flu (checkout the Google Flu Trends link I posted below).

For further reading on the planing of surgeries I also added a link to a corresponding survey paper.

In my research I used to use mathematical modeling to research Chronic Obstructive Pulmonary Disease at the German Cancer Research Center (statistical models for detecting the disease). Nowadays, I work in a completely different field and use mathematical modeling to study content delivery (websites, photos, videos) on the Internet.

http://www.google.org/flutrends/

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1072083/

Epidemic modelling is another well developed field. Basically it involves the solution of non linear differentiale equations, for which many packages are available.

This technique enables infectious disease control workers to better predict the course of epidemics, given vector control, biological control, treatment etc.

Mathematical modelling is the process of  explaining or representing a system in terms mathematical concepts and language. Most of the real life situations (in any fields) can be represented using mathematical models and can find out a suitable solution for them in an easier and logical way. A couple of interesting writes up on mathematical modelling are attached herewith.  Another interesting book on Mathematical Modelling is  Mathematical Modelling Handbook published by The Consortium for Mathematics and Its Applications, Bedford, in 2012.

Regarding its roles public health affairs, a beautiful slide presentation prepared by Mr. Larry Svenson is also attached herewith.  I also hope that the other links attached will also be helpful to you.

http://www.sfu.ca/~vdabbagh/Chap1-modeling.pdf

http://www.maths.bris.ac.uk/~madjl/course_text.pdf

http://www.healthknowledge.org.uk/public-health-textbook/health-information/3c-applications/mathematical-modelling

http://www.scor.com/en/sgrc/life/pandemic/item/1683-the-role-of-mathematical-modelling-in-public-health-planning-and-decision-making/1683-the-role-of-mathematical-modelling-in-public-health-planning-and-decision-making.html

http://www.math.ualberta.ca/~irl/summer_school/2012/lecture_notes/larry_svenson.pdf