The 10th anniversary of MBI’s 2013 Workshop for Young Researchers in Mathematical Biology

Hayriye Gulbudak

University of Louisiana at Lafayette (Mathematics)

"A delay model for persistent viral infections in replicating cells"

Persistently infecting viruses remain within infected cells for a prolonged period of time without killing the cells and can reproduce via budding virus particles or passing on to daughter cells after division. The ability for populations of infected cells to be long-lived and replicate viral progeny through cell division may be critical for virus survival in examples such as HIV latent reservoirs, tumor oncolytic virotherapy, and non-virulent phages in microbial hosts. We consider a model for persistent viral infection within a replicating cell population with time delay in the eclipse stage prior to infected cell replicative form. We obtain reproduction numbers that provide criteria for the existence and stability of the equilibria of the system and provide bifurcation diagrams illustrating transcritical (backward and forward), saddle-node, and Hopf bifurcations, and provide evidence of homoclinic bifurcations and a Bogdanov–Takens bifurcation. We investigate the possibility of long term survival of the infection (represented by chronically infected cells and free virus) in the cell population by using the mathematical concept of robust uniform persistence. Using numerical continuation software with parameter values estimated from phage-microbe systems, we obtain two parameter bifurcation diagrams that divide parameter space into regions with different dynamical outcomes. We thus investigate how varying different parameters, including how the time spent in the eclipse phase, can influence whether or not the virus survives.
Additional authors: Paul Salceanu, University of Louisiana at Lafayette; Gail Wolkowicz, McMaster University

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Amy Buchmann

University of San Diego (Mathematics)

"A decade of modeling microscale biofluids"

One area of research within mathematical biology is computational biofluids. This includes understanding the mechanics of biological fluid flow systems in the human body (the circulatory and respiratory systems), cells, and microorganism motility. I became interested in biofluids right around the time that I attended the Workshop for Young Researchers in Mathematical Biology in 2013, and have spent most of my career working in this area focusing on microscale biofluids. In this talk, I will discuss several of my collaborative projects that study microorganisms by modeling the interactions between elastic structures in a viscous fluid.

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Reginald McGee

College of the Holy Cross (Mathematics and Computer Science)

"Towards A Modeling Framework For Pediatric Sickle Cell Pain"

Sickle cell pain presents in acute episodes in pediatric patients, as opposed to the chronic pain observed in adults. The episodic nature of pain events in pediatric patients necessitates a distinct approach from what has been used to mathematically model pain severity levels in adults. Statistical studies have examined interactions between sleep actigraphy measurements --- like sleep quality and sleep efficiency --- and pain levels in pediatric populations, and we propose a framework for modeling pediatric pain dynamics that incorporates the effects of sleep actigraphy and electronic survey data over varying time windows. We hypothesize that cumulative effects of these measurements will be more important than daily measurements in both replicating pain severity levels and determining markers of a pain episode. The ability to identify markers preceding the onset of a pain episode will be crucial in improving patient quality of life. We present work in progress towards developing this modeling framework.
Additional authors: Angela Reynolds (Virginia Commonwealth University); Quindel Jones (Virginia Commonwealth University); Rebecca Segal (Virginia Commonwealth University); Cecelia Valrie (Virginia Commonwealth University); Wally Smith (Virginia Commonwealth University)

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Michael A. Robert

Virginia Tech (Department of Mathematics)

"Investigating impacts on malaria transmission of altered bioamine levels in Anopheles mosquitoes"

Malaria is caused by Plasmodium species that are transmitted to humans primarily by Anopheles mosquitoes. Currently, over half of the world’s population is at risk of malaria, and after decades of progress towards eradication led to declines in cases reported globally, cases have increased since 2020, with 247 million cases and 619,000 deaths reported in 2021. Malaria infection is known to influence levels of biogenic amines in human blood. Specifically, individuals with severe malaria may exhibit increased concentrations of histamine and/or decreased concentrations of serotonin. The altered amine levels may also impact the biology and behavior of Anopheles mosquitoes that ingest them in bloodmeals, but it remains to be seen what role these changes may have on mosquito population dynamics and malaria transmission. We developed a stage-structured discrete time mathematical model of mosquito population dynamics coupled with population-level malaria transmission dynamics to investigate how these altered amine levels may play a role in the malaria transmission cycle. We incorporated demographic, behavioral, and parasite reproduction data into the model and explored scenarios that consider different possible concentrations of histamine and serotonin in bloodmeals and different effects thereof by studying differences in mosquito population size and malaria incidence and prevalence. We explore different possible extensions of the model and discuss our findings in the context of malaria control as well as future experimental work.

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