Fox Infectious Disease Modeling Lab

Interested in Math Bio or disease modeling? Contact Prof. Fox!

Confidence in Calculus I is recommended.


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Ways To Get Involved


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:

⭐︎ Winner of a poster award! ⭐︎

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:

⭐︎ Honorable Mention for Best Student Presentation! ⭐︎

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:

⭐︎ 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.

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