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Hermite Polynomial Closure Approximations for Stochastic Epidemic Models
| Content Provider | Semantic Scholar |
|---|---|
| Author | Pender, Jamol |
| Copyright Year | 2014 |
| Abstract | Moment closure approximations have been developed to provide simple approximations to non-linear stochastic models. They can give tremendous insight into the qualitative and quantitative behavior of stochastic models. They are also important because they can be used to mimic behavior observed in simulation studies, or in some cases, validate the dynamics of rigorous limit theorems. In most stochastic epidemic models, most researchers tend to focus on the mean and the variance of the model. This is because of rigorous limit theorems such as the strong law of large numbers and the central limit theorem. As a result, much of the literature tends to focus on the mean and variance and neglect the importance of higher moments, which may provide valuable information about the stochastic dynamics. Understanding the higher moments are crucial since many of the populations models have extinction, which tend to skew the distributions to absorbing states. In this paper, we address this problem by exploring the skewness of our Markovian (susceptible-infected-susceptible) SIS model via expanding our SIS model in terms of Hermite polynomials. We then use this finite Hermite expansion to develop first, second, and third order approximations for our stochastic population model. Using methods developed in the queueing theory literature, we also derive closed form expressions for the cumulative density function (cdf) and probability density function (pdf) of our approximate model. Finally, we show through simulations that our method is better at approximating of real behavior of the stochastic model, especially the asymmetry in the empirical distributions for high values of skewness. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://people.orie.cornell.edu/jpender/SIS_Skew.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
