Mathematical model in epidemiology
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The spread of disease in humans and animals can be modeled by systems of differential equations. The total population is subdivided into three categories: Susceptible (S), infective (I) and Recovered (R) i.e. N= S(t) + I(t) + R(t). R0 is a parameter that measures the initial growth rate. A system with R <10 is considered not to result in an epidemic whereas when R >1, the system will result into an epidemic. We will consider three 0models. The first and simplest ignores vital dynamics like births and deaths; it is appropriate for studying “short term” diseases. The second model takes account of those vital dynamics needed for an effective analysis of diseases taking a longer time to sweep through the population. More refined dynamics allowed in the third model take the transmission process of a disease into account.