<abstract xmlns="http://www.w3.org/1999/xhtml">A mathematical model for transmission dynamics of tuberculosis among healthcare workers is formulated. Tuberculosis is an airborne disease caused by Mycobacterium tuberculosis bacteria that affect the lungs of a host. Previous research had concentrated on mathematical modeling of transmission dynamics of tuberculosis without considering the impact of compliance rate to particulate respirator by healthcare workers on the transmission. Therefore, how compliance rate to particulate respirator reduces the transmission of tuberculosis is an active question, and we develop a new system of ordinary differential equations that explicitly explores the impact of compliance rate to particulate respirator by healthcare workers upon transmission. Rigorous analysis of the model shows that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number, <italic>Ro</italic> &lt; 1. This is established through the analysis of characteristic equation. Basic reproduction, <italic>Ro</italic> is the number of new cases that an existing case generates on average over the infectious period in a susceptible population. We also show that the endemic equilibrium point is locally asymptotically stable for <italic>Ro</italic> > 1, by using Routh-Hurwitz criteria for stability. Sensitivity analysis is carried out to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is β (Human-to-human transmission rate), followed by Λ (Human recruitment rate). Also, the result shows that increase in <italic>ψ</italic> (compliance rate to particulate respirator by healthcare workers) leads to decrease in <italic>Ro</italic> which reduces tuberculosis spread among healthcare workers.</abstract>

A mathematical model for transmission dynamics of tuberculosis among healthcare workers is formulated. Tuberculosis is an airborne disease caused by Mycobacterium tuberculosis bacteria that affect the lungs of a host. Previous research had concentrated on mathematical modeling of transmission dynamics of tuberculosis without considering the impact of compliance rate to particulate respirator by healthcare workers on the transmission. Therefore, how compliance rate to particulate respirator reduces the transmission of tuberculosis is an active question, and we develop a new system of ordinary differential equations that explicitly explores the impact of compliance rate to particulate respirator by healthcare workers upon transmission. Rigorous analysis of the model shows that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number, Ro < 1. This is established through the analysis of characteristic equation. Basic reproduction, Ro is the number of new cases that an existing case generates on average over the infectious period in a susceptible population. We also show that the endemic equilibrium point is locally asymptotically stable for Ro > 1, by using Routh-Hurwitz criteria for stability. Sensitivity analysis is carried out to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is β (Human-to-human transmission rate), followed by Λ (Human recruitment rate). Also, the result shows that increase in ψ (compliance rate to particulate respirator by healthcare workers) leads to decrease in Ro which reduces tuberculosis spread among healthcare workers.

Modeling Tuberculosis Among Healthcare Workers

Department of Mathematics, African Institute for Mathematical Sciences

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Modeling Tuberculosis Among Healthcare Workers"}

A mathematical model for transmission dynamics of tuberculosis among healthcare workers is formulated. Tuberculosis is an airborne disease caused by Mycobacterium tuberculosis bacteria that affect the lungs of a host. Previous research had concentrated on mathematical modeling of transmission dynamics of tuberculosis without considering the impact of compliance rate to particulate respirator by healthcare workers on the transmission. Therefore, how compliance rate to particulate respirator reduces the transmission of tuberculosis is an active question, and we develop a new system of ordinary differential equations that explicitly explores the impact of compliance rate to particulate respirator by healthcare workers upon transmission. Rigorous analysis of the model shows that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number, Ro  1, by using Routh-Hurwitz criteria for stability. Sensitivity analysis is carried out to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is β (Human-to-human transmission rate), followed by Λ (Human recruitment rate). Also, the result shows that increase in ψ (compliance rate to particulate respirator by healthcare workers) leads to decrease in Ro which reduces tuberculosis spread among healthcare workers.

A mathematical model for transmission dynamics of tuberculosis among healthcare workers is formulated. Tuberculosis is an airborne disease caused by...

Modeling Tuberculosis Among Healthcare Workers

Published Online: Jan 24, 2020

Page range: 186 - 196

Received: Apr 27, 2019

Accepted: Nov 28, 2019

DOI: https://doi.org/10.2478/mjpaa-2019-0014

Keywords
Tuberculosis, Respirator, Basic Reproduction Number, Stability, Sensitivity Analysis

© 2019 T.S. Faniran et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Modeling Tuberculosis Among Healthcare Workers

Published Online: Jan 24, 2020

Page range: 186 - 196

Received: Apr 27, 2019

Accepted: Nov 28, 2019

DOI: https://doi.org/10.2478/mjpaa-2019-0014

KeywordsTuberculosis, Respirator, Basic Reproduction Number, Stability, Sensitivity Analysis

© 2019 T.S. Faniran et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Tuberculosis, Respirator, Basic Reproduction Number, Stability, Sensitivity Analysis