A mathematical model of <i>Clostridioides difficile</i> transmission in long-term care facilities

Priscilla Doran; Natsuka Hayashida; Kristen Joyner; Grace Moberg; Austin Kind; Matthew Senese; Brittany Stephenson; Cara Jill Sulyok; Priscilla Doran; Natsuka Hayashida; Kristen Joyner; Grace Moberg; Austin Kind; Matthew Senese; Brittany Stephenson; Cara Jill Sulyok

doi:10.3934/mbe.2025118

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 12: 3201-3235. doi: 10.3934/mbe.2025118

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A mathematical model of Clostridioides difficile transmission in long-term care facilities

1.
Department of Mathematics, University of Tennessee, Knoxville, TN, USA
2.
Department of Mathematics, Brown University, Providence, RI, USA
3.
Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO, USA
4.
Department of Engineering, Computing, and Mathematical Sciences, Lewis University, Romeoville, IL, USA
5.
Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA
6.
Department of Mathematics and Statistics, Villanova University, Villanova, PA, USA
^† These authors contributed equally to this work and are joint first authors.

Received: 22 August 2025 Revised: 27 September 2025 Accepted: 22 October 2025 Published: 11 November 2025

Clostridioides difficile, also known as C. difficile, is a prevalent cause of infectious diarrhea in United States healthcare facilities. Spread through the fecal-oral route and often through contact with spores on contaminated surfaces, C. difficile can cause severe diarrhea, stomach pain, and colitis. Most individuals can mount an effective immune response, but older populations, immunocompromised individuals, and those taking antibiotics have a higher risk of being colonized by C. difficile. While extensive research has been conducted in hospital-based settings to improve understanding of the transmission of this bacteria, few studies apply mathematical models in the context of long-term care facilities. This work introduced a mathematical model using a system of ordinary differential equations to represent C. difficile transmission dynamics in assisted living facilities, with their interactive nature and high risk factors. The equations included four resident classes (susceptible, colonized, diseased, and isolated) and three pathogen-carrying classes (high-traffic areas, low-traffic areas, and healthcare workers' hands) to simultaneously capture the movement between classes and track spore density on environmental reservoirs and healthcare workers' hands, including their contributions to disease spread. Parameter estimation using data from the Emerging Infections Program at the Centers for Disease Control and Prevention was completed and was followed by sensitivity analyses to quantify the impact of varying these parameters and their impact on incidence. Mitigation strategies, including frequent disinfection, increased healthcare worker hand hygiene compliance, a lower ratio between residents and healthcare workers, and increased resident screening had the greatest impact on reducing the incidence of C. difficile.
- Clostridioides difficile,
- ordinary differential equations,
- environmental transmission,
- colony-forming units,
- sensitivity analysis,
- parameter estimation,
- mathematical model
Citation: Priscilla Doran, Natsuka Hayashida, Kristen Joyner, Grace Moberg, Austin Kind, Matthew Senese, Brittany Stephenson, Cara Jill Sulyok. A mathematical model of Clostridioides difficile transmission in long-term care facilities[J]. Mathematical Biosciences and Engineering, 2025, 22(12): 3201-3235. doi: 10.3934/mbe.2025118

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Abstract

Clostridioides difficile, also known as C. difficile, is a prevalent cause of infectious diarrhea in United States healthcare facilities. Spread through the fecal-oral route and often through contact with spores on contaminated surfaces, C. difficile can cause severe diarrhea, stomach pain, and colitis. Most individuals can mount an effective immune response, but older populations, immunocompromised individuals, and those taking antibiotics have a higher risk of being colonized by C. difficile. While extensive research has been conducted in hospital-based settings to improve understanding of the transmission of this bacteria, few studies apply mathematical models in the context of long-term care facilities. This work introduced a mathematical model using a system of ordinary differential equations to represent C. difficile transmission dynamics in assisted living facilities, with their interactive nature and high risk factors. The equations included four resident classes (susceptible, colonized, diseased, and isolated) and three pathogen-carrying classes (high-traffic areas, low-traffic areas, and healthcare workers' hands) to simultaneously capture the movement between classes and track spore density on environmental reservoirs and healthcare workers' hands, including their contributions to disease spread. Parameter estimation using data from the Emerging Infections Program at the Centers for Disease Control and Prevention was completed and was followed by sensitivity analyses to quantify the impact of varying these parameters and their impact on incidence. Mitigation strategies, including frequent disinfection, increased healthcare worker hand hygiene compliance, a lower ratio between residents and healthcare workers, and increased resident screening had the greatest impact on reducing the incidence of C. difficile.

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