The natural history of an infectious disease can be described by the so-called SEIR model: susceptible individuals (S) become exposed and acquire the infection (E). After a latent period, they become infectious (I) and pass on the infection. If they survive the disease, they will acquire a permanent immunity (R). Furthermore, we can adopt a slightly more sophisticated model where we split the infectious state into three different compartments according to different symptoms. Infectious cases can remain asymptomatic or they can develop mild or severe disease. Infectious individuals of these three states may differ in their biological contagiousness and in their ability to contact and infect others. Severely ill cases may stay at home or are transferred to a hospital where they can only infect people that are regarded as “close contacts”. Asymptomatic and mildly ill cases, on the other hand, retain most of their mobility and can also infect “casual contacts”. The recognition of symptoms may also influence the individual’s and the public health system’s ability to intervene against further spreading the disease by targeted application of drugs or vaccinations. Prophylactic use of drugs or vaccination can modify the infection process and the natural history of disease. Prophylaxis can reduce the susceptibility to infection and the treatment of cases can reduce their infectivity. Even though prophylactic drug use may not always prevent infection, it can effect the development of symptoms, so that a larger fraction of infected cases will remain asymptomatic or develop only mild symptoms.