Work

Using mathematical modeling to study the dynamics of Legionnaires' disease and consider management options

Year: 2025

Type: article

Abstract: Legionnaires' disease (LD) is a largely understudied and underreported pneumonic environmentally transmitted disease caused by the bacteria 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.

Source: Mathematical Biosciences & Engineering

DOI: 10.3934/mbe.2025045

Authors: Mark Z. Wang, Christina J. Edholm, Lihong Zhao

Institutions: Pitzer College, Scripps College, Kennesaw State University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

SDGs: Good health and well-being, Clean water and sanitation

Open Access status: gold

Estimated APC paid: $1,000