SIR Model

The SIR models variables between three states: susceptible (S), infected (I) and resistant (R). Each of these variables represents the number of people, objects, or quantities of the variable in those groups. The alpha and beta parameters partially control the rate at which the variable changes from susceptible to infected (alpha) and from infected to resistant (beta). The SIR model is used to model parameters that interfere with one another directly (eg through a disease vector, such as a mosquito). An individual who recovers from the disease is also modeled to have perfect immunity to the disease after that. Contact between people is also modeled to be random. The rate at which people are infected is proportional to the number of people infected and the number of people susceptible.

If there are many people infected, the chances of a susceptible person coming into contact with someone infected are high. Likewise, if there are very few people who are susceptible, the chances of a susceptible person coming into contact with an infected person is less (since most of the contact would be between non-susceptible people - infected or resistant). This is an ordinary differential equation model, described by the following equation:

Note: The SIR model will be one of the ways used to model population growth and to relate to other variables that are directly linked. In the next posts, the other modeling methodologies will be presented, such as exponential population growth, malthusia theory and the implementation of such equations in Matlab Software.