Department
Mathematics
Document Type
Article
Publication Date
Spring 4-18-2025
Embargo Period
4-30-2025
Abstract
Legionnaires' disease (LD) is a largely understudied and underreported pneumonic environmentally transmitted disease caused by the bacteria \textit{Legionella}. It primarily occurs in places with poorly maintained artificial sources of water. There is currently a lack of mathematical models on the dynamics of LD. In this paper, we formulate a novel ordinary differential equation-based susceptible-exposed-infected-recovered (SEIR) model for LD. One issue with LD is the difficulty in its detection, as the majority of countries around the world lack the proper surveillance and diagnosis methods. Thus, there is not much publicly available data or literature on LD. We use parameter estimation for our model with one of the few outbreaks with time series data from Murcia, Spain in 2001. Furthermore, we apply a global sensitivity analysis to understand the contributions of parameters to our model output. To consider managing LD outbreaks, we explore implementing sanitizing individual sources of water by constructing an optimal control problem. Using our fitted model and the optimal control problem, we analyze how different parameters and controls might help manage LD outbreaks in the future.
Journal Title
Mathematical Biosciences and Engineering
Journal ISSN
1551-0018
Volume
22
Issue
5
First Page
1226
Last Page
1242
Digital Object Identifier (DOI)
10.3934/mbe.2025045
Included in
Control Theory Commons, Dynamic Systems Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Life Sciences Commons
Comments
This article received funding through Kennesaw State University's Faculty Open Access Publishing Fund, supported by the KSU Library System and KSU Office of Research.