My current research interests are in the fields of mathematical biology and other applications of dynamical systems.
- Parameter estimation for epidemiological models of influenza. Studying the time-dependent transmission rate in stochastic and deterministic epidemic models.
- Statistical inference for discrete and continuous Markov chain models of disease spread.
- Modeling the Midwestern United States prairie ecosystem using ordinary differential equations, using data to estiamte model parameters, and sensitivity and uncertainty analysis.
Selected Past Projects
- Modeling a pandemic flu outbreak focusing on determining why 2009 pandemic H1N1 flu has two peaks in the number of infected individuals, while seasonal flu only has one peak, using agent-based modeling. This project is part of the Marshall BioM2 project (NSF – UBM grant).
- Modeling the influence of isolation and other mandates on controlling outbreaks of infectious diseases, with a focus on optimal control measures.
- Modeling the influence of media intervention on the severity of disease epidemics.
- Discretizing the SI (susceptible-infected) epidemic model.
- Modeling super-spreading events of infectious diseases, with a focus on SARS.
- Modeling reslin in insect joints. This project is part of the Marshal BioM2 project (NSF – UBM grant).
- Analysis of respiratory rates in freshwater mussels. This project is part of the Marshal BioM2 project (NSF – UBM grant).
- Modeling antibiotic resistant bacteria in rivers.
- Examining projective conics on the sphere.
- Berger, Meyer, Mummert, Tirado, Saucedo, Longstreet, Van Arsdale, and Williams. (accepted 2020). Land use dynamics within the Tallgrass Prairie ecosystem: the case for the Conservation Reserve Program (CRP). Theoretical Ecology.
- Mummert and Otunuga. 2019. Parameter Identification for a Stochastic SEIRS Epidemic Model: Case Study Influenza. Journal of Mathematical Biology. Volume 79, Issue 2, Pages 705-729. doi: 10.1007/s00285-019-01374-z.
- Mummert and Weiss. 2017. Controlling viral outbreaks: Quantitative strategies. PLoS ONE. 12(2): e171199. doi.org/10.1371/journal.pone.0171199.
- Mummert and Weiss. 2013. Get the News Out Loudly and Quickly: Modeling the Influence of the Media on Limiting Infectious Disease Outbreaks. PLoS ONE. 8(8): e71692. doi: 10.1371/journal.pone.0071692.
- Mummert. 2013. Studying the Recovery Proceedure for the Time-dependent Transmission Rate(s) in Epidemic Models. Journal of Mathematical Biology. Volume 67, Issue 3, Pages 483-507. doi:10.1007/s00285-012-0558-1.
- Mummert, Weiss, Long, Amigo, and Wan. 2013. A Perspective on Multiple Waves of Influenza Pandemics. PLoS ONE. 8(4): e60343. doi:10.1371/journal.pone.0060343.
- Mummert. 2007. A Variational Principle for Discontinuous Potentials, Ergodic Theory and Dynamical Systems, Volume 27, Number 2.
- Mummert. 2006. A Thermodynamic Formalism for Almost-additive Sequences, Discrete and Continuous Dynamical Systems, Volume 15, Number 2, October.
- Sutton. 2014. Discretizing the SI Epidemic Model. Rose-Hulman Institute of Technology Undergraduate Math Journal. Volume 15, Issue 1, Article 12. Available at https://scholar.rose-hulman.edu/rhumj/vol15/iss1/12.
- Mkhatshwa and Mummert. 2011. Modeling Super-spreading Events for Infectious Diseases: Case Study SARS. IAENG International Journal of Applied Mathematics. Volume 41, Issue 2, 24 May 2011.