Deterministic and stochastic SIS and SIR models, comparison and analysis with Matlab - Couderc, Antoine (2020)
An epidemic is the rapid spread of an infectious disease within a population or community, making a large number of infected individuals in a short period of time. These may ultimately die, or become permanently incapacitated. Infectious diseases that can be responsible for an epidemic outbreak include well nown diseases such as HIV, Small-pox, SARS and (H1N1) influenza, among others. Mathematical modelling of an epidemic, or epidemic modelling, aims to understand the spreading process of an infectious disease and to predict its future course. This information is of vital importance to the implementation of strategies to control the spread of the epidemic. For instance, mathematical models allow to estimate several effects of an epidemic, like the total number of infected people or the duration of the epidemic, and how and when to use prevention methods such as education, immunization or isolation, just to name the most common prevention strategies. In this work we make a simulation of two models: SIS (susceptible-infected-susceptible) and SIR (susceptible-infected-susceptible). The implementation is done in Matlab using its Deterministic and stochastic formulations and make the comparison between the two approaches.