Differential Equations Seminar: S. Gutowska and M. Yu (UMBC)
Monday, May 10, 2021 · 11 AM - 12 PM
Sylvia Gutowska
Title: PrEP and Partnerships: The effects of treatment on the spread of HIV among the MSM partners
Abstract: A classic approach for modeling the spread of the sexually transmitted diseases is to assume a zero inherent length infection contact. However, in the population with long-term partnerships, the infection status of the partners, the length of the partnership, and the exclusivity of the partnership, all affect the rate of infection. Additionally, the presence of the pre exposure prophylaxis (PrEP) will also impact the dynamics of the disease. The goal of this project is to develop a compartmental model that accounts for various partnership scenarios as well as the uptake and adherence to the PrEP treatment. Sensitivity and PRCC analysis are performed on the parameters to determine the best interventions in the fight against the HIV epidemic.
Mingkai Yu
Abstract: We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species. In some applications, only a small number of key species could be observed, which gives rise to the problem of estimating the copy number of the unobserved species. We provide a novel particle filter method for state and parameter estimation based on exact observation of the copy number of some of the species in continuous time. The conditional probability distribution of the copy numbers of the unobserved species is shown to satisfy a system of differential equations with jumps. We provide a method of simulating a process that is a proxy for the vector copy number of the unobserved species along with a weight. The resulting weighted Monte Carlo simulation is then used to compute the conditional probability distribution of the unobserved species. We also show how our algorithm can be adapted for a Bayesian estimation of parameters and for the estimation of a past state value based on observations up to a future time.
Title: State and Parameter Estimation from Exact Partial State Observation in Stochastic Reaction Networks
Abstract: We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species. In some applications, only a small number of key species could be observed, which gives rise to the problem of estimating the copy number of the unobserved species. We provide a novel particle filter method for state and parameter estimation based on exact observation of the copy number of some of the species in continuous time. The conditional probability distribution of the copy numbers of the unobserved species is shown to satisfy a system of differential equations with jumps. We provide a method of simulating a process that is a proxy for the vector copy number of the unobserved species along with a weight. The resulting weighted Monte Carlo simulation is then used to compute the conditional probability distribution of the unobserved species. We also show how our algorithm can be adapted for a Bayesian estimation of parameters and for the estimation of a past state value based on observations up to a future time.
