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Innovative Approaches in Epidemic Modeling and Sampling Using Markov Chain Monte Carlo Methods
We present a novel way to model the spread of a multi-strain epidemic in a population as well as an alternative approach to understanding the dynamics of a Markov chain in multi-dimensional parameter space in the context of Bayesian estimation. A modified Susceptible-Infected-Recovered (SIR) epidemic compartmental model is constructed to describe the emergence of a new viral strain in a population dealing with an existing strain. The emergent strain is assumed to be resistant to the immunity against the existing strain built through vaccination and recovery from infection. Deterministic and probabilistic simulations of the epidemic model showed the existence of isolated and endemic equilibrium points and the short-term domination of either strain in the infected population. The modified multi-strain SIR model is applied to the weekly influenza incidence data of the A(H1N1)pdm09 virus in 2009. The Bayesian estimation of the multi-strain SIR model parameters is performed using the Hamiltonian Monte Carlo (HMC) method, and the values are compared to the estimates from the single-strain SIR models. The transition coefficients and effective reproduction number estimates for the A(H1N1)pdm09 strain and the non-A(H1N1)pdm09 strains obtained from the multi-strain model are close to the estimates obtained from running two separate single-strain models. Unlike the single-strain model, the multi-strain model is able to estimate the initial size of the emergent A(H1N1)pdm09 strain in the total infected population. We also introduce the path integral formulation to describe the path taken by different stochastic processes in the parameter space. The equation of motion for the Wiener process is proven to be equivalent to the update equations of existing Markov Chain Monte Carlo samplers, while the Cauchy flight was determined to have different modes of motion with different dynamics. The Cauchy Flight Lagrangian Monte Carlo (CFLMC) algorithm was developed as a prototype of a multimodal sampler based on the path integral formulation of the Cauchy process. Experimental results showed that the sampler yielded samples with unbiased estimates. The CFLMC was implemented to sample from a bimodal Gamma mixture distribution and yielded results comparable to that of Tempered MCMC.
Statistics|Systematic biology|Epidemiology|Statistical physics|Biostatistics
Fudolig, Miguel Antonio, "Innovative Approaches in Epidemic Modeling and Sampling Using Markov Chain Monte Carlo Methods" (2022). ETD collection for University of Nebraska - Lincoln. AAI29257027.