### Parameter estimation in deterministic and stochastic models of viral infection

Ankur Gupta
Fifth-year Graduate Student (co-advised by Prof. John Yin)
Email: gupta25@wisc.edu
Office: Room 2009/2011 EH
Phone: 608-265-8607

Research
Viruses cause deadly diseases which can be prevented, treated or cured by studying the process of viral infection. Mathematical modeling of viruses allows us to systematically study complicated viral infection processes. My research focuses on two approaches to mathematical modeling of viral infection -- deterministic and stochastic. Deterministic models (for example: traditional ordinary and partial differential equations, difference equations) do not involve any randomness and are used to model processes which have -- (a) large number of molecules of all the species, (b) experimental data without noise. Stochastic models (for example: Markov chains, stochastic differential equations) are used to describe the inherent randomness of viral processes. The choice of models depends both on the research question one wants to answer and the kind of experimental data obtained from the experiment.

Parametric models are of limited use unless values of the model parameters are estimated. My research focuses on the estimation of parameters and confidence intervals for the both stochastic and deterministic viral models using experimental data obtained in Yin Group. Yin Group performs experiments to study and understand viral spread and replication of viruses like Influenza A and Vesicular Stomatitis Virus (VSV). The process of modeling and parameter estimation is a challenging problem for two reasons -- (a) relatively sparse experimental data does not allow parameter estimation in detailed mechanistic models, and (b) parameter estimation in stochastic models is computationally expensive. I attempt to solve these problems by building mathematical (stochastic and deterministic) models of reasonable size which allow parameter estimation and developing new approaches to perform stochastic parameter estimation with much less computational cost.

Mathematical tools used in my research: Numerical/analytical solution to ODEs, Markov chains, stochastic simulation algorithms, Bayesian Inference, Monte Carlo simulations, Nonlinear optimization.