DISCRETE TIME MARKOV CHAIN MODEL FOR SIS AND SIR EPIDEMIC MODELS - Agnesia, Yoli
In disease epidemic model, a set of populations is commonly divided into three groups: Susceptible (S), Infected (I), and Recovery (R). In this thesis, SIS and SIR epidemic models are constructed by using discrete time Markov chains in terms of a probability function for number of infected populations over time. Numerical simulations of the SIS epidemic model show that probability function of the absorbing state increases with increasing time. This means that the probability of the epidemic disease leading to a disease-free condition is close to 1. This result is also shown by spectral analysis carried out on the eigenvalues of the transition matrix. In addition, based on expected duration when the disease disappears, it is found that the smaller the initial population, the faster the disease will disappear. For the SIR epidemic model, the joint probability of two random variables is constucted. The resulted transition matrix is not as simple as in the SIS model, so a numerical approach will be appropriate for this model. SIR numerical simulations have been carried out, but the presents results are not close enough to the references results. This may be due to the lack of information of the parameter simulations that we have to set up for our simulations.