My research interests include building a solid mathematical foundation for difference approximations to partial differential equations and using mathematical models to better understand and predict the spread of epidemics.
Statistical and Numerical Analysis:
My research is the creation and analysis of more accurate and efficient numerical algorithms to characterize multivariate functions when we have the ability to sample the function at a very few data points. My approach is to adaptively quantify the uncertainty in the desired quantities of interest, such as the approximation, integration, or optimization of the unknown function, as a function of the sample points. That is, a desired distribution of sample points is adaptively updated during the sampling process based on the existing sample values. Low-discrepancy algorithms are used to generate the future sample points based on both the current and desired sample distributions.
We create, and analyze, mathematical models that can capture the role of heterogeneity in disease transmission and impact of disease mitigations on its spread. My research includes the mathematical analysis of small-scale compartmental differential equation transmission models, risk-based transmission models, and large-scale (millions of agents) individual-based models, such as the Los Alamos EpiSimS code. The goal of these efforts has always been to create mathematical models that can help the public health community understand and anticipate the spread of an infection and evaluate the potential effectiveness of different approaches for bringing it under control.
A key aspect of my research is to identify effective approaches to quantify uncertainty in forecasts as a function of the model assumptions. The epidemiological data for disease outbreaks are incomplete and inaccurate. Infection forecasts based on inaccurate data are useless unless the uncertainties in the predictions can be quantified in terms of the available data and the model assumptions, such as the behavior of the infected population. These techniques can help identify which data would be most useful in estimating the current prevalence, the risk of infection, and the effectiveness of potential mitigation programs.
Areas of Expertise (6)
Courant Institute of Mathematical Sciences: Ph.D., Mathematics 1976
Courant Institute of Mathematical Sciences: M.S., Computer Science and Mathematics 1974
Tulane University: B.S., Physics 1972
Tulane University: B.S., Mathematics 1972
A novel sub-epidemic modeling framework for short-term forecasting epidemic wavesBMC Medicine
Gerardo Chowell, Amna Tariq, James M Hyman
2019 Simple phenomenological growth models can be useful for estimating transmission parameters and forecasting epidemic trajectories. However, most existing phenomenological growth models only support single-peak outbreak dynamics whereas real epidemics often display more complex transmission trajectories.
Generating a Hierarchy of Reduced Models for a System of Differential Equations Modeling the Spread of Wolbachia in MosquitoesSIAM Journal on Applied Mathematics
Zhuolin Qu, James M Hyman
2019 We create and analyze a hierarchy of reduced order models for the spread of a Wolbachia bacteria infection in mosquitoes. Mosquitoes that are infected with some strains of the Wolbachia bacteria are much less effective at transmitting zoonotic diseases, including Zika, chikungunya, dengue fever, and other mosquito-borne diseases.
Quantification of human-mosquito contact rate using surveys and its application in determining dengue viral transmission riskbioRxiv
Panpim Thongsripong, Zhuolin Qu, Joshua O Yukich, James M Hyman, Dawn M Wesson
2019 Aedes-borne viral diseases, including dengue fever, chikungunya, and Zika, have been surging in incidence and spreading to new areas where their mosquito vectors thrive. To estimate viral transmission risks, availability of accurate local transmission parameters is essential. One of the most important parameters to determine infection risk is the human-mosquito contact rate.