Practical utilization SIR model
With limited research capacity, mathematical modeling of infectious diseases has yet to be sufficiently implemented in Japan. However in many countries, it has become essential to consider vaccination policies. Out of many mathematical models, the SIR model is the most basic model, allowing to explain the transmission dynamics of certain infectious diseases. The SIR model consists 3 compartments, susceptible, infectious, and recovered. The rate of change of each compartment is described using differential equations, and each compartment is parameterized the demographic change, the transmission rate of disease, recovery rate of infected, or the intensity of the control.
In the example below, we introduce a simple example of the application of SIR model which compare the effect of two vaccination strategies: vaccination against new born babies and vaccination against any susceptible individuals.
Reference: Keeling, Matt, et al. “The mathematics of vaccination.” Math. Today 49 (2013): 40-43.