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Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures

Vaccination and treatment are the most effective ways of controlling the transmission of most infectious diseases. While vaccination helps susceptible individuals to build either a long-term immunity or short-term immunity, treatment reduces the number of disease-induced deaths and the number of inf...

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Autores principales: Asamoah, Joshua Kiddy K., Nyabadza, Farai, Seidu, Baba, Chand, Mehar, Dutta, Hemen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5892307/
https://www.ncbi.nlm.nih.gov/pubmed/29780431
http://dx.doi.org/10.1155/2018/2657461
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author Asamoah, Joshua Kiddy K.
Nyabadza, Farai
Seidu, Baba
Chand, Mehar
Dutta, Hemen
author_facet Asamoah, Joshua Kiddy K.
Nyabadza, Farai
Seidu, Baba
Chand, Mehar
Dutta, Hemen
author_sort Asamoah, Joshua Kiddy K.
collection PubMed
description Vaccination and treatment are the most effective ways of controlling the transmission of most infectious diseases. While vaccination helps susceptible individuals to build either a long-term immunity or short-term immunity, treatment reduces the number of disease-induced deaths and the number of infectious individuals in a community/nation. In this paper, a nonlinear deterministic model with time-dependent controls has been proposed to describe the dynamics of bacterial meningitis in a population. The model is shown to exhibit a unique globally asymptotically stable disease-free equilibrium ℰ(0), when the effective reproduction number ℛ(VT) ≤ 1, and a globally asymptotically stable endemic equilibrium ℰ(1), when ℛ(VT) > 1; and it exhibits a transcritical bifurcation at ℛ(VT) = 1. Carriers have been shown (by Tornado plot) to have a higher chance of spreading the infection than those with clinical symptoms who will sometimes be bound to bed during the acute phase of the infection. In order to find the best strategy for minimizing the number of carriers and ill individuals and the cost of control implementation, an optimal control problem is set up by defining a Lagrangian function L to be minimized subject to the proposed model. Numerical simulation of the optimal problem demonstrates that the best strategy to control bacterial meningitis is to combine vaccination with other interventions (such as treatment and public health education). Additionally, this research suggests that stakeholders should press hard for the production of existing/new vaccines and antibiotics and their disbursement to areas that are most affected by bacterial meningitis, especially Sub-Saharan Africa; furthermore, individuals who live in communities where the environment is relatively warm (hot/moisture) are advised to go for vaccination against bacterial meningitis.
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spelling pubmed-58923072018-05-20 Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures Asamoah, Joshua Kiddy K. Nyabadza, Farai Seidu, Baba Chand, Mehar Dutta, Hemen Comput Math Methods Med Research Article Vaccination and treatment are the most effective ways of controlling the transmission of most infectious diseases. While vaccination helps susceptible individuals to build either a long-term immunity or short-term immunity, treatment reduces the number of disease-induced deaths and the number of infectious individuals in a community/nation. In this paper, a nonlinear deterministic model with time-dependent controls has been proposed to describe the dynamics of bacterial meningitis in a population. The model is shown to exhibit a unique globally asymptotically stable disease-free equilibrium ℰ(0), when the effective reproduction number ℛ(VT) ≤ 1, and a globally asymptotically stable endemic equilibrium ℰ(1), when ℛ(VT) > 1; and it exhibits a transcritical bifurcation at ℛ(VT) = 1. Carriers have been shown (by Tornado plot) to have a higher chance of spreading the infection than those with clinical symptoms who will sometimes be bound to bed during the acute phase of the infection. In order to find the best strategy for minimizing the number of carriers and ill individuals and the cost of control implementation, an optimal control problem is set up by defining a Lagrangian function L to be minimized subject to the proposed model. Numerical simulation of the optimal problem demonstrates that the best strategy to control bacterial meningitis is to combine vaccination with other interventions (such as treatment and public health education). Additionally, this research suggests that stakeholders should press hard for the production of existing/new vaccines and antibiotics and their disbursement to areas that are most affected by bacterial meningitis, especially Sub-Saharan Africa; furthermore, individuals who live in communities where the environment is relatively warm (hot/moisture) are advised to go for vaccination against bacterial meningitis. Hindawi 2018-03-27 /pmc/articles/PMC5892307/ /pubmed/29780431 http://dx.doi.org/10.1155/2018/2657461 Text en Copyright © 2018 Joshua Kiddy K. Asamoah et al. https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Asamoah, Joshua Kiddy K.
Nyabadza, Farai
Seidu, Baba
Chand, Mehar
Dutta, Hemen
Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures
title Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures
title_full Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures
title_fullStr Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures
title_full_unstemmed Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures
title_short Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures
title_sort mathematical modelling of bacterial meningitis transmission dynamics with control measures
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5892307/
https://www.ncbi.nlm.nih.gov/pubmed/29780431
http://dx.doi.org/10.1155/2018/2657461
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