Applications of jump processes in epidemiology and neuroscience

This thesis concerns novel applications of jump processes in epidemiology and neuroscience. A jump process is a stochastic process that models the occurrence of discrete events over time. In epidemiology, the events correspond to catching an infection, recovering from a disease, etc. In neuroscience, the spike train of a neuron can be described as a jump process. The first contribution of this thesis is a data-informed approach for analysis, validation and identification of compartmental models in epidemiology. We propose that the ad-hoc process of building compartmental models can be improved by a framework grounded in the continuous-time Markov chains underlying these models. In particular, we use the available COVID-19 data on individuals' transition (jump) times between different compartments and argue that these times must be exponentially distributed. In case the transition times between two compartments are not exponentially distributed, there must be some hidden states between the two. The second contribution extends the existing mean-field game (MFG) literature to analyze the presymptomatic and asymptomatic agents' decision-making under uncertainty during an epidemic. The resulting model explores how partial information influences individual decision-making and examines the collective impact of these decisions on the spread of a virus. The research is motivated by the presymptomatic and asymptomatic transmission of COVID-19, where individuals unknowingly contribute to spreading the virus. The findings reveal that even when agents are highly altruistic and act rationally, asymptomatic individuals' unwitting spreading of the virus may still cause an epidemic. Finally, the third contribution of this thesis focuses on questions in system neuroscience, which are motivated by the experiments conducted by Oliver Qu in Prof. Howard Gritton's lab at the UIUC College of Veterinary Medicine. We seek to understand how the location of a sound is encoded and decoded in the mouse auditory cortex. To this end, we claim that the spike-trains of the auditory cortical neurons can be modeled as non-stationary Poisson processes. Based on this insight, we propose a maximum likelihood decoder. The proposed decoder can decode non-stationary neural responses in real time. We also propose a model for binaural hearing, which can be used to extend the maximum likelihood decoder to arbitrary stimuli.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Olmez, Yagiz

Contributors dc:contributor

• Mehta, Prashant G
• Salapaka, Srinivasa M
• Sadaghiani, Sepideh
• Gritton, Howard
• Dayanikli, Gokce

• Jump processes
• Stochastic processes
• Epidemiology
• Neuroscience
• Compartmental models
• Continuous-time Markov chains
• COVID-19
• Mean-field games
• Asymptomatic agents
• Decision-making under uncertainty
• Spike trains
• Poisson processes
• Maximum likelihood decoder
• Auditory cortex
• Binaural hearing
• System neuroscience
• Data-informed modeling

Statement dc:rights

• Copyright 2025 Yagiz Olmez

Language dc:language

en

Handle dc:identifier

https://hdl.handle.net/2142/132730

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/132730