IntroductionAt the moment, we are at the edge of a possible biological trouble.Some people say that the 19 th century was the century of chemistry, the 20 th was the century of physics, and they say that the 21 st will be the century of biology.If we think, the advances in the biological field in the recent years have been incredible, and like the physics and its atomic bomb, with biology could create global epidemics diseases.Also the climate change could produce a new virus better than the existing virus, creating an atmosphere of panic, such as the influenza A (H1N1) in recent years or Malaria who still killing people.To go a step further, we use computer science in the improvement of disease prevention (Baker, 2007; Magal & Rouen, 2008).For beginning, we mention quickly some plagues in history such as the Black Death as an example of Bubonic plague, and we present from their basic concepts the most common classical epidemic models.We present a transmission malaria model with inhomogeneities in a human population, which is proposed in terms of SIR coupled models for human and mosquitoes, which are described by differential equations.The human population is considered divided into several groups depending on genetics profiles, social condition, differentiation between rural or urban people, etc.Within malaria model we consider that mosquitoes bite humans in a differentiated way in accordance with the inhomogeneity.We use an algorithm for the analysis from local stability of the infection-free equilibrium and that algorithm is implemented on Maple™.This algorithm consists on determinate the characteristic polynomial from Jacobian matrix of the model and the analysis of their eigenvalues using Routh-Hurwitz theorem.As a result we obtain the basic reproductive number for malaria (R o ) and the threshold condition for a malaria epidemic triggering (R o >1).From this result we can derivate effective control measures for avoiding malaria outbreaks and determinate the minimum level of income for a community becomes free of malaria infection.This work pretend to show the symbolic computing potential from CAS (Computer Algebra Systems), in our case Maple™, for analysing automatically complex epidemic models and the usefulness of them for designing and implementing public health politics. Historical survey of epidemiological modelsIn this first part of the chapter, we are going to mention two aspects to capture your attention, the first one is a little tour for history where we refer to some of the most tragic www.intechopen.com Advances in Computer Science and Engineering 38plagues, but we just pretend to show some examples of diseases for that reason it is not all the history of each plague, and the second one is a presentation of the most common models used in epidemics problems such as SIS, SIR and SEIR models, trying to explain their dynamics.This model models can be used in other sciences such as economics, biology, etc. (Perthame, 2007) Epidemic infectionsIt's true that in our time, every year is more difficult to find an outbreak in the developed countries, but it isn't the same situation in the developing countries, in which the epidemics problems appear frequently (Porta, 2008).Initially, human diseases began with the change of their way to live, the first change was when humans learnt the agriculture which made possible that more people could live in the same place, this situation produced problems on healthiness and then, the diseases started.The next step in the change of life was domesticating animals, which gave us some disease because of their genetic changes.Some of the diseases that we have thanks to animals are Measles, Tuberculosis, Smallpox, Influenza, Malaria, between others.We introduce the Bubonic Plague who had his biggest spreading with the name Black Death in mid-fourteenth century, it received his name because of the black skin that people had when they were dying.This plague is spread by vectors that could be rats and other small m a m m a l s , a n d t h e i r f l e a s .S o m e c a s e s o f t h i s p l a g u e w e r e r e p o r t e d i n A t h e n s i n t h e Peloponnesian War, and after the 14 th century, in the World War II, Japan spread infected fleas over some cities in China (Christakos et al., 2005;Gottfried, 1983).Now we talk about Malaria and Yellow Fever, both diseases are transmitted by flies and it for that reason that these diseases are very dangerous because his range of spread could be extremely wide.In the case of the Malaria the historians believe that its beginning was in the apes in Africa, this disease is also called Burning Ague because of intermittent painful fevers.The Yellow Fever is called "Yellow Jack", the name yellow is for the colour that people have with this illness.These diseases are described even in the bible, the old testament, Leviticus 26:16, "then I will do this to you: I will visit you with panic, with wasting disease and fever that consume the eyes and make the heart ache..." and Deuteronomy 28:22, "The LORD will strike you with wasting disease and with fever, inflammation and fiery heat..." And in present days still happen even more in countries near to the equatorial line because the mosquitoes find ideal conditions to survive, temperature between 20°C and 30°C, and humidity over 60%.As a final example of infections, we bring the Smallpox and Measles, which are the most severe example of how humans appear the diseases, and these diseases have the highest fatality rate in the history, surpassing even the medieval Black Death.The Smallpox was widely used in the process of America's conquest with the intension of decimate the native population.With the last phrase we note the human intention to use biological weapons, and it's worrying to think in the biological weapon that we could have with the actual technologies (Bollet, 2004). Models usedNow, we talk about some models used to predict the behaviour of the population along an infection.The models we show here are classical in epidemiology and they are differential equations systems (Stewart, 2002).We won't show the equations systems because they depend on the characteristics of the epidemic, but we will show some diagrams.If you want www.intechopen.com