{"id":8,"date":"2019-08-20T20:12:15","date_gmt":"2019-08-20T20:12:15","guid":{"rendered":"https:\/\/mupages.marshall.edu\/sites\/mummerta\/?page_id=8"},"modified":"2020-01-10T14:58:51","modified_gmt":"2020-01-10T14:58:51","slug":"about-me","status":"publish","type":"page","link":"https:\/\/mupages.marshall.edu\/mummerta\/about-me\/","title":{"rendered":"Research"},"content":{"rendered":"<p>My current research interests are in the fields of mathematical biology and other applications of dynamical systems.<\/p>\n<h3>Epidemiological Modeling<\/h3>\n<ul>\n<li>Parameter estimation for epidemiological models of influenza. Studying the time-dependent transmission rate in stochastic and deterministic epidemic models.<\/li>\n<li>Statistical inference for discrete and continuous Markov chain models of disease spread.<\/li>\n<\/ul>\n<h3>Ecological Modeling<\/h3>\n<ul>\n<li>Modeling the Midwestern United States prairie ecosystem using ordinary differential equations, using data to estiamte model parameters, and sensitivity and uncertainty analysis.<\/li>\n<\/ul>\n<h3>Selected Past Projects<\/h3>\n<ul>\n<li>Epidemiology:\n<ul>\n<li>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 &#8211; UBM grant).<\/li>\n<li>Modeling the influence of isolation and other mandates on controlling outbreaks of infectious diseases, with a focus on optimal control measures.<\/li>\n<li>Modeling the influence of media intervention on the severity of disease epidemics.<\/li>\n<li>Discretizing the SI (susceptible-infected) epidemic model.<\/li>\n<li>Modeling super-spreading events of infectious diseases, with a focus on SARS.<\/li>\n<\/ul>\n<\/li>\n<li>Biological:\n<ul>\n<li>Modeling reslin in insect joints.\u00a0 This project is part of the Marshal BioM2 project (NSF &#8211; UBM grant).<\/li>\n<li>Analysis of respiratory rates in freshwater mussels.\u00a0 This project is part of the Marshal BioM2 project (NSF &#8211; UBM grant).<\/li>\n<li>Modeling antibiotic resistant bacteria in rivers.<\/li>\n<\/ul>\n<\/li>\n<li>Geometry:\n<ul>\n<li>Examining projective conics on the sphere.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3 class=\"w3-center\">Publications<\/h3>\n<ol class=\"spaced\">\n<li>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).\u00a0 Theoretical Ecology.<\/li>\n<li>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.\u00a0 doi: 10.1007\/s00285-019-01374-z.<\/li>\n<li>Mummert and Weiss. 2017. Controlling viral outbreaks: Quantitative strategies. PLoS ONE. 12(2): e171199. doi.org\/10.1371\/journal.pone.0171199.<\/li>\n<li>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.<\/li>\n<li>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.<\/li>\n<li>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.<\/li>\n<li>Mummert. 2007. A Variational Principle for Discontinuous Potentials, Ergodic Theory and Dynamical Systems, Volume 27, Number 2.<\/li>\n<li>Mummert. 2006. A Thermodynamic Formalism for Almost-additive Sequences, Discrete and Continuous Dynamical Systems, Volume 15, Number 2, October.<\/li>\n<\/ol>\n<h5 class=\"w3-center\">Student Publications<\/h5>\n<ol class=\"spaced\">\n<li>Sutton. 2014. Discretizing the SI Epidemic Model. Rose-Hulman Institute of Technology Undergraduate Math Journal. Volume 15, Issue 1, Article 12. Available at <a href=\"https:\/\/scholar.rose-hulman.edu\/rhumj\/vol15\/iss1\/12\">https:\/\/scholar.rose-hulman.edu\/rhumj\/vol15\/iss1\/12<\/a>.<\/li>\n<li>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.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>My current research interests are in the fields of mathematical biology and other applications of dynamical systems. Epidemiological Modeling 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. Ecological Modeling Modeling the Midwestern United [&hellip;]<\/p>\n","protected":false},"author":28,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-8","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/mupages.marshall.edu\/mummerta\/wp-json\/wp\/v2\/pages\/8","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mupages.marshall.edu\/mummerta\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mupages.marshall.edu\/mummerta\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mupages.marshall.edu\/mummerta\/wp-json\/wp\/v2\/users\/28"}],"replies":[{"embeddable":true,"href":"https:\/\/mupages.marshall.edu\/mummerta\/wp-json\/wp\/v2\/comments?post=8"}],"version-history":[{"count":29,"href":"https:\/\/mupages.marshall.edu\/mummerta\/wp-json\/wp\/v2\/pages\/8\/revisions"}],"predecessor-version":[{"id":76,"href":"https:\/\/mupages.marshall.edu\/mummerta\/wp-json\/wp\/v2\/pages\/8\/revisions\/76"}],"wp:attachment":[{"href":"https:\/\/mupages.marshall.edu\/mummerta\/wp-json\/wp\/v2\/media?parent=8"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}