Mathematical modelling of bacterial meningitis transmission dynamics with control measures
type: Item
instance of: scholarly article
title: Mathematical modelling of bacterial meningitis transmission dynamics with control measures
zbMATH Open document ID: 1411.92264
DOI: 10.1155/2018/2657461
author: Joshua Kiddy K. Asamoah
author: Farai Nyabadza
author: Baba Seidu
author: Mehar Chand
author: Hemen Dutta
published in: Computational \& Mathematical Methods in Medicine
publication date: 2019-03-27T00:00:00Z
review text: Summary: 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 \(\mathcal{E}_0\), when the effective reproduction number \(\mathcal{R}_{\text{VT}} \leq 1\), and a globally asymptotically stable endemic equilibrium \(\mathcal{E}_1\), when \(\mathcal{R}_{\text{VT}} > 1\); and it exhibits a transcritical bifurcation at \(\mathcal{R}_{\text{VT}} = 1\). 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.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 49N90
zbMATH DE Number: 7042931
zbMATH Keywords: bacterial meningitis
zbMATH Keywords: transmission dynamics
zbMATH Keywords: vaccination and treatment
zbMATH Keywords: optimal control
Wikidata QID: Q55022086
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/2657461
OpenAlex ID: W2794679918
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description: scientific article; zbMATH DE number 7042931