A Mathematical Model to Study the Meningococcal Meningitis

Martínez, María José Fresnadillo; Merino, Enrique; Sánchez, Enrique García; Sánchez, José Elías García; Rey, Ángel Martín del; Sánchez, Gerardo Rodríguez

doi:10.1016/j.procs.2013.05.426

Cited by 17 publications

(19 citation statements)

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“…We found papers modeling a theoretical grid [ 83 , 85 , 96 ] or a generic “low income setting” [ 89 ]. The study population of the other papers did not exceed a single country, and ranged from a North American [ 23 , 24 , 80 , 86 , 90 , 92 , 94 , 101 ] to a European [ 84 , 87 , 88 , 95 , 97 – 100 , 102 , 103 ] or African [ 91 , 93 ] country.…”

Section: Resultsmentioning

confidence: 99%

“…The dynamics regarding age and social mixing in the population were modeled static (i.e. constant) [ 85 ] or dynamic (with ageing, mortality, newborns, weddings) [ 92 , 100 ]. Ajelli and Merler [ 103 ] were exceptional in that they provided an explicit approach to model household dynamics over time to enable IBM simulations on long time-scales.…”

Section: Resultsmentioning

confidence: 99%

“…We distinguished a category of papers using mathematical software such as MATLAB ®; [ 102 ] and Mathematica ®; [ 85 ]. Others used more explicit modeling platforms for IBMs such as NetLogo [ 23 , 90 ], RepastS [ 24 ] and AnyLogic ®; [ 94 ].…”

Section: Resultsmentioning

confidence: 99%

“…We discerned 3 main reasons for choosing an IBM for these childhood diseases. Firstly, to model heterogeneous between-host interactions regarding social mixing behavior, age, demography, clustering, compliance to mitigation strategies and spatial distribution (e.g., [ 85 , 88 , 91 ]). Secondly, to model heterogeneous within-host processes in combination with between-host interactions (e.g., [ 87 , 98 , 99 ]).…”

Section: Resultsmentioning

confidence: 99%

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Lessons from a decade of individual-based models for infectious disease transmission: a systematic review (2006-2015)

et al. 2017

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BackgroundIndividual-based models (IBMs) are useful to simulate events subject to stochasticity and/or heterogeneity, and have become well established to model the potential (re)emergence of pathogens (e.g., pandemic influenza, bioterrorism). Individual heterogeneity at the host and pathogen level is increasingly documented to influence transmission of endemic diseases and it is well understood that the final stages of elimination strategies for vaccine-preventable childhood diseases (e.g., polio, measles) are subject to stochasticity. Even so it appears IBMs for both these phenomena are not well established. We review a decade of IBM publications aiming to obtain insights in their advantages, pitfalls and rationale for use and to make recommendations facilitating knowledge transfer within and across disciplines.MethodsWe systematically identified publications in Web of Science and PubMed from 2006-2015 based on title/abstract/keywords screening (and full-text if necessary) to retrieve topics, modeling purposes and general specifications. We extracted detailed modeling features from papers on established vaccine-preventable childhood diseases based on full-text screening.ResultsWe identified 698 papers, which applied an IBM for infectious disease transmission, and listed these in a reference database, describing their general characteristics. The diversity of disease-topics and overall publication frequency have increased over time (38 to 115 annual publications from 2006 to 2015). The inclusion of intervention strategies (8 to 52) and economic consequences (1 to 20) are increasing, to the detriment of purely theoretical explorations. Unfortunately, terminology used to describe IBMs is inconsistent and ambiguous. We retrieved 24 studies on a vaccine-preventable childhood disease (covering 7 different diseases), with publication frequency increasing from the first such study published in 2008. IBMs have been useful to explore heterogeneous between- and within-host interactions, but combined applications are still sparse. The amount of missing information on model characteristics and study design is remarkable.ConclusionsIBMs are suited to combine heterogeneous within- and between-host interactions, which offers many opportunities, especially to analyze targeted interventions for endemic infections. We advocate the exchange of (open-source) platforms and stress the need for consistent “branding”. Using (existing) conventions and reporting protocols would stimulate cross-fertilization between research groups and fields, and ultimately policy making in decades to come.Electronic supplementary materialThe online version of this article (doi:10.1186/s12879-017-2699-8) contains supplementary material, which is available to authorized users.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Lessons from a decade of individual-based models for infectious disease transmission: a systematic review (2006-2015)

et al. 2017

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“…Bacterial meningitis is common in children and young adults. This disease mostly spreads in communities/societies that live in close quarters (e.g., police staff, police cells, college students, military staff, and prisons) [ 2 ]. Bacterial meningitis is generally caused by germs such as Listeria monocytogenes , Streptococcus pneumoniae , Group B Streptococcus , Neisseria meningitidis , and Haemophilus influenzae , which spreads from one person to another [ 3 ].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures

Asamoah

Nyabadza

Seidu

et al. 2018

Computational and Mathematical Methods in Medicine

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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 ℰ0, when the effective reproduction number ℛVT ≤ 1, and a globally asymptotically stable endemic equilibrium ℰ1, when ℛVT > 1; and it exhibits a transcritical bifurcation at ℛVT = 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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A spatiotemporal model of meningococcal meningitis with direct and indirect transmission

Zorom

Andrianisa

Dorville³

et al. 2020

Math Methods in App Sciences

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We extend an ordinary differential equation (ODE) model for the meningococcal meningitis disease to a partial differential equation (PDE). This extension istwofold: (i) consideration of two modes of contamination, namely through a direct transmission (human to human) and an indirect transmission (via free‐living bacteria). (ii) consideration of the human movement and the dispersal of bacteria in a heterogeneous environment. Furthermore we show the existence of the solutions and define the basic reproduction number scriptR0 for the model. Additionally, the existence and the stability of both disease‐free and endemic equilibria were investigated. The sensitivity of scriptR0 and the endemic state with respect of the model parameters were studied. Numerical computations of the spreading bacteria are carried out to illustrate our mathematical results.

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A Mathematical Model to Study the Meningococcal Meningitis

Cited by 17 publications

References 5 publications

Lessons from a decade of individual-based models for infectious disease transmission: a systematic review (2006-2015)

Lessons from a decade of individual-based models for infectious disease transmission: a systematic review (2006-2015)

Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures

A spatiotemporal model of meningococcal meningitis with direct and indirect transmission

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