Mathematical Modeling of Bacterial Resistance to Antibiotics by Mutations and Plasmids

Ibargüen-Mondragón, Eduardo; Romero–Leiton, Jhoana P.; Esteva, Luis; Burbano-Rosero, Edith Mariela

doi:10.1142/s0218339016500078

Cited by 24 publications

(23 citation statements)

References 23 publications

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“…For this reason in this work, we define some control variables, and we formulate an optimal control problem defined by (3), (2) and (4). The qualitative analysis of (2) can be made following a process similar as in [2,3,6,7,8],…”

Section: Discussionmentioning

confidence: 99%

An optimal control problem applied to malaria disease in Colombia

Romero–Leiton¹,

Montoya-Aguilar²,

Ibargüen-Mondragón³

2018

ams

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In Colombia, malaria is a public health problem that affects a large part of its population. Above motivated us to formulate an optimal control problem considering the following control variables: bed nets (BN), intermittent prophylactic treatment in pregnancy (IPTp) and prompt and effective case management (PECM). The results reveal the importance of congenital transmission and death due to disease in the infection outcome. It is imperative that strategies be defined to reduce these risk factors.

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Section: Discussionmentioning

confidence: 99%

An optimal control problem applied to malaria disease in Colombia

Romero–Leiton¹,

Montoya-Aguilar²,

Ibargüen-Mondragón³

2018

ams

Self Cite

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“…Inversely, the remaining eight studies [32,55,58,60,[63][64][65]69] attempted to place at least some of their results in a public health setting by, for example, quantifying the impact of transfer on the incidence of multidrug-resistant bacteria infection in humans [32,69]. In accordance with this previous point, almost half of the studies (20/43) modelled bacteria exclusively in culture [33][34][35][36][37][38][39][40][41][42]47,49,50,52,53,58,59,66,70,71], and only seven modelled bacteria in humans [30,32,55,60,63,65,69] (figure 3). In the remaining studies, seven did not specify an environment for their bacteria [31,48,56,57,61,62,67].…”

Section: Resultsmentioning

confidence: 95%

“…Sensitivity analysis is extremely important in any case since a small change in parameter value can lead to a greater change in the results. Despite this, nine studies exclusively relied on a deterministic model without sampling parameters or performing sensitivity analyses [30,36,40,42,48,54,55,58,68]. Interestingly, five of these nine studies also generated their own parameter values experimentally [36,40,42,54,68].…”

Section: Discussionmentioning

confidence: 99%

Mathematical modelling to study the horizontal transfer of antimicrobial resistance genes in bacteria: current state of the field and recommendations

Leclerc

Lindsay

Knight

2019

J. R. Soc. Interface.

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Antimicrobial resistance (AMR) is one of the greatest public health challenges we are currently facing. To develop effective interventions against this, it is essential to understand the processes behind the spread of AMR. These are partly dependent on the dynamics of horizontal transfer of resistance genes between bacteria, which can occur by conjugation (direct contact), transformation (uptake from the environment) or transduction (mediated by bacteriophages). Mathematical modelling is a powerful tool to investigate the dynamics of AMR; however, the extent of its use to study the horizontal transfer of AMR genes is currently unclear. In this systematic review, we searched for mathematical modelling studies that focused on horizontal transfer of AMR genes. We compared their aims and methods using a list of predetermined criteria and used our results to assess the current state of this research field. Of the 43 studies we identified, most focused on the transfer of single genes by conjugation in Escherichia coli in culture and its impact on the bacterial evolutionary dynamics. Our findings highlight the existence of an important research gap in the dynamics of transformation and transduction and the overall public health implications of horizontal transfer of AMR genes. To further develop this field and improve our ability to control AMR, it is essential that we clarify the structural complexity required to study the dynamics of horizontal gene transfer, which will require cooperation between microbiologists and modellers.

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“…The test can be used to verify the equilibrium solution of different models such as those developed in [4,5,6,7,8,9,10,11,12,13,14,15,16,17]. However, in this section we will analyze the stability of the SEIR model, a multi-patch model and a model on immunology of tuberculosis.…”

Section: Application Of Main Resultsmentioning

confidence: 99%

A stability test for non linear systems of ordinary differential equations based on the Gershgorin circles

Bejarano¹,

Ibargüen-Mondragón²,

Gómez-Hernández³

2018

ces

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The Gershgorin Circles Theorem (GCT) is a very useful tool to characterize the regions of the complex plane in which the eigenvalues of a matrix are found. Within the analysis of local stability to equilibrium solutionx of a system of ordinary differential equations is vital to determine the sign of the real part of the eigenvalues of the Jacobian matrix evaluated inx. For this reason, a local stability test is formulated for equilibrium solutions, based on the indirect method of Lyapunov and GCT.

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Mathematical Modeling of Bacterial Resistance to Antibiotics by Mutations and Plasmids

Cited by 24 publications

References 23 publications

An optimal control problem applied to malaria disease in Colombia

An optimal control problem applied to malaria disease in Colombia

Mathematical modelling to study the horizontal transfer of antimicrobial resistance genes in bacteria: current state of the field and recommendations

A stability test for non linear systems of ordinary differential equations based on the Gershgorin circles

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