Estimating Vital Parameters for SVIR Epidemic Models. Case Study- Influenza
Abstract or Description
Virtual presentation given at 2020 SIAM Conference on the Life Sciences
Deriving a robust statistical scheme to approximate important epidemiological control parameters such as the basic reproduction number (BRN), the probability of no spread of a disease etc. is a very important first step in determining the prognosis of diseases. In this talk, a discrete time Markov chain (DTMC) model for influenza epidemics with vaccination and removed states is derived and studied in a novel framework, where the various compartments of the infectious and vaccinated states of the system are generated over the infectious and immunity periods. The DTMC model consists of trinomial transition probabilities, and they are also derived under special assumptions of correlated vaccination and infection probabilities at any instant. The techniques of maximum likelihood estimation (MLE), and expectation maximization (EM) algorithm are applied to find estimates for the SVIR model parameters and the BRN. The algorithm is tested on influenza data for Georgia, USA, and the numerical results are presented and interpreted. Also, the diffusion approximation of the DTMC model to stochastic differential equations is discussed.
2020 SIAM Conference on the Life Sciences
"Estimating Vital Parameters for SVIR Epidemic Models. Case Study- Influenza."
Department of Mathematical Sciences Faculty Presentations.