SIR Model

The diseases we are discussing have been classified as microparasitic. Examples of microparasitic diseases are chicken pox, measles, HIV/AIDS, influenza and tuberculosis. Diseases due to worms, for example, are called macroparasitic. Other than the size of the infecting agent, the main distinction is that the microparasites reproduce within their hosts and are transmitted directly from one host to another. Most macroparasites, on the other hand, have a somewhat more complicated life cycle, often with a secondary host or carrier. Schistosomiasis is an example of a macroparasitic disease. Schistosomiasis is passed only through contact with water in which live snails that can incubate the disease causing helminths. In reality, the distinction between microand macro-parasitic diseases is not always clear and there is a range of infecting agents and transmission paths. In the case of malaria, the disease is not passed from human to human but through the anopheline mosquitoes, but some of the parasite’s life cycle occurs in the mosquito and some in humans. When a mosquito bites an infected individual, it sucks the gametocytes, the sexual forms of the parasite, along with blood. These gametocytes continue the sexual phase of the cycle within the mosquito gut and the sporozoites that develop then fill the salivary glands of the infested mosquito. When this female mosquito bites another human for a blood meal, the sporozoites are inoculated into the blood stream of the fresh victim, thus spreading the infection. Microparasitic diseases (viral or bacterial) can pass through a population like a flame through fuel, and useful analogies have been made between epidemics and chemical reactions. A theory of these epidemics was derived by W.O. Kermack, a chemist, and A. G. McKendrick, a physician, working at the Royal College of Surgeons in Edinburgh between 1900 and 1930. The simple model we considered this morning, is based on their work. One important result of theirs is that an infection determines a threshold size for the susceptible population, above which an epidemic will propagate. Their theoretical epidemic threshold is observed in practice,