Introduction Throughout the earth, diseases affect people from all walks of life. People from different races, religions, age groups and socio-economics classes can all be susceptible to various diseases. Thus mankind as a whole endures great suffering, as hundreds of millions are painfully afflicted and many lose their lives to a foe much stronger than themselves. The struggle is greatest in third world countries, where malnutrition is typical and health standards are, as a rule, dismal. Sadly, infants and children are the most vulnerable, and worst affected by disease. Every year 11 million children aged five or under due from diseases that could easily have been prevented. This equates to the unnecessary death of one one child every 3.5 seconds. These figures cannot possibly be received comfortably when it is also known that the cost of immunising a child against these diseases is merely a few cents.
So what can be done to ease this burden from the weary backs of so many? How can mathematics help to provide the answers?
By effectively modelling the disease mathematically, the model can be used to predict the behaviour of the disease, that is, the occurrence and severity of epidemics, the long term fraction of the population that is infected and the possibility of the disease being eradicated. From this data decisions can be made about treatment and vaccination, so that infections are minimised in the most cost effective manner, saving both people from harm and resources for aid organisations.
Over the past semester I have been looking at some simple ways of modelling diseases and using the models to analyse the behaviour of the diseases, and the affect this has on the population.