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

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.

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