Fox Infectious Disease Modeling Lab
Interested in Math Bio or disease modeling? Contact Prof. Fox!
Confidence in Calculus I is recommended.
Email: foxl@eckerd.edu
Find Out More
Ways To Get Involved
Projects
What is Mathematical Biology?
What is disease modeling?
Watch my Research Bites video
Explore my past and on-going projects
Take my Mathematical Biology course (MA 303)
Check out my First-Year Student Research Associateship project
Check out the EC-INSPIRED website
Email me: foxl@eckerd.edu
Resistance to Disinfectants (2021-23)
Mariana Olivares-Cely ('25), Prof. Fox
& Karin Ebey ('25)
Optimal Control Theory to Mitigate the Effects of Resistance to Disinfectants
Abstract: This study explores how resistance to disinfectants affects disease transmission in long term care facilities and the best disinfectant use strategy. A compartmental model was created, using a system of ordinary differential equations, describing the transmission of two strains of a pathogen, resistant and susceptible to disinfectants with transmission through direct and surface contact, and evolution of resistance through mutation and horizontal gene transfer. An optimal control problem was set up to determine the best disinfectant use strategy under different cost schemes and resistance levels to minimize costs and cases. The disinfectant strategy depends on whether the system is open or closed and the cost scheme. The epidemic dies out in the closed system, but becomes endemic in the open system. The amount of disinfectant used is directly related to the cost of disinfectant. More people become infected at higher levels of resistance. These results have implications for infection management.
Presented at:
Apr. 2023: Math Seminar class
Mar. 2023: Eckerd College Research Symposium (poster)
Feb. 2023: Annual meeting of the Florida Section of the Mathematical Association of America
Mar. 2022: Eckerd College Research Symposium (poster)
⭐︎ Winner of a poster award! ⭐︎
Feb. 2022: Annual meeting of the Florida Section of the Mathematical Association of America
Koi Herpesvirus (2021-23)
Optimal Harvesting in an Epidemic Model of Koi Herpesvirus (KHV)
Abstract: Koi herpesvirus (KHV) is a highly transmissible disease that can infect common carp (Cyprinus carpio) and fancy carp, also known as koi, which are carp that have been selectively bred for aesthetics. Due to the high mortality of the virus (80-100%), ornamental fisheries can suffer from significant economic losses if an outbreak of KHV occurs. In this study we use ordinary differential equations to model the transmission dynamics of KHV within and between two pools of koi fish: a juvenile pool, which contain fish too young, and therefore too small, to be sold, and a market pool, which contain fish that are mature/large enough to be sold and can be used for breeding. In each pool we include four classes to describe the disease status of the fish population, as well as an environmental reservoir. Since seasonal water temperature plays a vital role in KHV outbreaks and disease severity, many of the disease-related transition rates are dependent on time and temperature. Further, we consider an optimal fishery harvesting problem during an outbreak of KHV.
Presented at:
Apr. 2023: Thesis defense
Mar. 2023: Math Seminar class
Mar. 2023: Eckerd College Student Research Symposium (poster)
Feb. 2023: Annual meeting of the Florida Section of the Mathematical Association of America
⭐︎ Honorable Mention for Best Student Presentation! ⭐︎
Jan. 2023: Joint Math Meetings, Boston, MA
Susan Krage ('23) visiting Imperial Tropicals in Lakeland, FL
Kelsey Weeden ('23), Payton Bivens ('24)
& Prof. Fox
Mathematically Modeling the Transmission of Koi Herpesvirus in Common Carp
Abstract: Koi herpesvirus (KHV) is an extremely contagious virus that affects common carp. The virus is transmitted through direct contact with infected fish, contaminated fluids, or other contaminated vectors. In this study, we constructed an epidemiological model that uses a system of ordinary differential equations to describe the transmission dynamics of KHV. Classes include susceptible, exposed, infectious, ailing, and recovered. Some parameters of the model fluctuate with water temperature: the rate of progression through the exposed and infected compartments. Between five degrees celsius and twenty-eight degrees celsius, these progression rates are the highest corresponding to when the virus is active. We also study the effects of harvesting from an ornamental fishery in which KHV is present. We seek to find the optimal harvesting rate to maximize revenue while also minimizing the number of cases.
Presented at:
C. difficile and Healthcare Workers (2021-22)
Mathematically modeling the role of healthcare workers in the environmental transmission of C. difficile
Abstract: Clostridioides difficile is the leading cause of infectious diarrhea and one of the most common healthcare-acquired infections in United States hospitals. C. difficile persists well in healthcare environments because it forms spores that can survive for long periods of time and can be transmitted to susceptible patients through contact with contaminated hands and surfaces that can harbor infectious agents, called fomites. This study explores an alteration of a previous model to include healthcare workers as a transmission vector in conjunction with high-touch and low-touch fomites. The transmission is described by a system of ordinary differential equations representing four patient classes, two pathogen environmental reservoirs, and two healthcare worker groupings. Parameters have a significant effect on the incidence and three different parameter scenarios were explored. The goal of this study was to successfully alter the pre-existing model to encompass the healthcare workers as a transmission vector.
Presented at:
Mar. 2022: Eckerd College Student Research Symposium (poster)
Feb. 2022: Annual meeting of the Florida Section of the Mathematical Association of America
⭐︎ Winner of Best Student Poster Presentation! ⭐︎
Kath Fillman ('22), Isaac Blackburn ('22) & Prof. Fox
COVID-19 at Eckerd College (2020-21)
Prof. Fox, Alyssa Bernstein ('24)
& Madyson Woodburn ('24)
Mathematically modeling the transmission of COVID-19 at Eckerd College
Abstract: The COVID-19 pandemic has posed many challenges for colleges and universities around the world. Schools must maintain their academic standards while also implementing a strong response to the virus. In particular, small liberal arts colleges, such as Eckerd College in St. Petersburg, FL, have limited housing space available but must provide enough quarantine beds to support a small outbreak. In this study, we constructed an epidemiological model that uses a system of ordinary differential equations to describe the dynamics of transmission of COVID-19 on Eckerd College’s campus. The classes of the model include susceptible, asymptomatic, infectious, and recovered, as well as three different quarantine classes used to incorporate Eckerd’s testing approach. The goal of the model is to estimate the number of quarantine beds Eckerd College will need.
Presented at:
Mar. 2021: Eckerd College Student Research Symposium (poster)
Feb. 2021: Annual meeting of the Florida Section of the Mathematical Association of America