DISCRETE TIME MARKOV CHAIN MODEL FOR SIS AND SIR EPIDEMIC MODELS
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 popula...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/39175 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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