Mathematical modeling on bacterial resistance to multiple antibiotics caused by spontaneous mutations

Optimal control strategies for mitigating antibiotic resistance: Integrating virus dynamics for enhanced intervention design

Given the global increase in antibiotic resistance, new effective strategies must be developed to treat bacteria that do not respond to first or second line antibiotics. One novel method uses bacterial phage therapy to control bacterial populations. Phage viruses replicate and infect bacterial cells and are regarded as the most prevalent biological agent on earth. This paper presents a comprehensive model capturing the dynamics of wild-type bacteria (S), antibiotic-resistant bacteria (R), and virus-infected (I) bacteria population, incorporating virus inclusion. Our model integrates biologically relevant parameters governing bacterial birth rates, death rates, mutation probabilities and incorporates infection dynamics via contact with a virus. We employ an optimal control approach to study the influence of virus inclusion on bacterial population dynamics. Through numerical simulations, we establish insights into the stability of various system equilibria and bacterial population responses to varying infection rates. By examining the equilibria, we reveal the impact of virus inclusion on population trajectories, describe a medical intervention for antibiotic-resistant bacterial infections through the lense of optimal control theory, and discuss how to implement it in a clinical setting. Our findings underscore the necessity of considering virus inclusion in antibiotic resistance studies, shedding light on subtle yet influential dynamics in bacterial ecosystems.

A within-host model on the interactions of sensitive and resistant Helicobacter pylori to antibiotic therapy considering immune response

In this work, we formulated a mathematical model to describe growth, acquisition of bacterial resistance, and immune response for Helicobacter pylori (H. pylori). The qualitative analysis revealed the existence of five equilibrium solutions: (ⅰ) An infection-free state, in which the bacterial population and immune cells are suppressed, (ⅱ) an endemic state only with resistant bacteria without immune cells, (ⅲ) an endemic state only with resistant bacteria and immune cells, (ⅳ) an endemic state of bacterial coexistence without immune cells, and (ⅴ) an endemic coexistence state with immune response. The stability analysis showed that the equilibrium solutions (ⅰ) and (ⅳ) are locally asymptotically stable, whereas the equilibria (ⅱ) and (ⅲ) are unstable. We found four threshold conditions that establish the existence and stability of equilibria, which determine when the populations of sensitive H. pylori and resistant H. pylori are controlled or eliminated, or when the infection progresses only with resistant bacteria or with both bacterial populations. The numerical simulations corroborated the qualitative analysis, and provided information on the emergence of a limit cycle that breaks the stability of the coexistence equilibrium. The results revealed that the key to controlling bacterial progression is to keep bacterial growth thresholds below 1; this can be achieved by applying an appropriate combination of antibiotics and correct stimulation of the immune response. Otherwise, when bacterial growth thresholds exceed 1, the bacterial persistence scenarios mentioned above occur.

Modeling the impact of urban and hospital eco-exposomes on antibiotic-resistance dynamics in wastewaters

The emergence and selection of antibiotic resistance is a major public health problem worldwide. The presence of antibiotic-resistant bacteria (ARBs) in natural and anthropogenic environments threatens the sustainability of efforts to reduce resistance in human and animal populations. Here, we use mathematical modeling of the selective effect of antibiotics and contaminants on the dynamics of bacterial resistance in water to analyze longitudinal spatio-temporal data collected in hospital and urban wastewater between 2012 and 2015. Samples were collected monthly during the study period at four different sites in Haute-Savoie, France: hospital and urban wastewater, before and after water treatment plants. Three different categories of exposure variables were collected simultaneously: 1) heavy metals, 2) antibiotics and 3) surfactants for a total of 13 drugs/molecules; in parallel to the normalized abundance of 88 individual genes and mobile genetic elements, mostly conferring resistance to antibiotics. A simple hypothesis-driven model describing weekly antibiotic resistance gene (ARG) dynamics was proposed to fit the available data, assuming that normalized gene abundance is proportional to antibiotic resistant bacteria (ARB) populations in water. The detected compounds were found to influence the dynamics of 17 genes found at multiple sites. While mercury and vancomycin were associated with increased ARG and affected the dynamics of 10 and 12 identified genes respectively, surfactants antagonistically affected the dynamics of three genes. The models proposed here make it possible to analyze the relationship between the persistence of resistance genes in the aquatic environment and specific compounds associated with human activities from longitudinal data. Our analysis of French data over 2012-2015 identified mercury and vancomycin as co-selectors for some ARGs.

Mathematical modelling of antibiotic interaction on evolution of antibiotic resistance: an analytical approach

Background

The emergence and spread of antibiotic-resistant pathogens have led to the exploration of antibiotic combinations to enhance clinical effectiveness and counter resistance development. Synergistic and antagonistic interactions between antibiotics can intensify or diminish the combined therapy's impact. Moreover, these interactions can evolve as bacteria transition from wildtype to mutant (resistant) strains. Experimental studies have shown that the antagonistically interacting antibiotics against wildtype bacteria slow down the evolution of resistance. Interestingly, other studies have shown that antibiotics that interact antagonistically against mutants accelerate resistance. However, it is unclear if the beneficial effect of antagonism in the wildtype bacteria is more critical than the detrimental effect of antagonism in the mutants. This study aims to illuminate the importance of antibiotic interactions against wildtype bacteria and mutants on the deacceleration of antimicrobial resistance.

Methods

To address this, we developed and analyzed a mathematical model that explores the population dynamics of wildtype and mutant bacteria under the influence of interacting antibiotics. The model investigates the relationship between synergistic and antagonistic antibiotic interactions with respect to the growth rate of mutant bacteria acquiring resistance. Stability analysis was conducted for equilibrium points representing bacteria-free conditions, all-mutant scenarios, and coexistence of both types. Numerical simulations corroborated the analytical findings, illustrating the temporal dynamics of wildtype and mutant bacteria under different combination therapies.

Results

Our analysis provides analytical clarification and numerical validation that antibiotic interactions against wildtype bacteria exert a more significant effect on reducing the rate of resistance development than interactions against mutants. Specifically, our findings highlight the crucial role of antagonistic antibiotic interactions against wildtype bacteria in slowing the growth rate of resistant mutants. In contrast, antagonistic interactions against mutants only marginally affect resistance evolution and may even accelerate it.

Conclusion

Our results emphasize the importance of considering the nature of antibiotic interactions against wildtype bacteria rather than mutants when aiming to slow down the acquisition of antibiotic resistance.

Dynamic analysis of a bacterial resistance model with impulsive state feedback control

Bacterial resistance caused by prolonged administration of the same antibiotics exacerbates the threat of bacterial infection to human health. It is essential to optimize antibiotic treatment measures. In this paper, we formulate a simplified model of conversion between sensitive and resistant bacteria. Subsequently, impulsive state feedback control is introduced to reduce bacterial resistance to a low level. The global asymptotic stability of the positive equilibrium and the orbital stability of the order-1 periodic solution are proved by the Poincaré-Bendixson Theorem and the theory of the semi-continuous dynamical system, respectively. Finally, numerical simulations are performed to validate the accuracy of the theoretical findings.

Identification of the elements of models of antimicrobial resistance of bacteria for assessing their usefulness and usability in One Health decision making: a protocol for scoping review

INTRODUCTION

Antimicrobial resistance (AMR) is a complex problem that requires the One Health approach, that is, a collaboration among various disciplines working in different sectors (animal, human and environment) to resolve it. Mathematical and statistical models have been used to understand AMR development, emergence, dissemination, prediction and forecasting. A review of the published models of AMR will help consolidate our knowledge of the dynamics of AMR and will also facilitate decision-makers and researchers in evaluating the credibility, generalisability and interpretation of the results and aspects of AMR models. The study objective is to identify and synthesise knowledge on mathematical and statistical models of AMR among bacteria in animals, humans and environmental compartments.

METHODS AND ANALYSIS

Eligibility criteria: Original research studies reporting mathematical and statistical models of AMR among bacteria in animal, human and environmental compartments that were published until 2022 in English, French and Spanish will be included in this study.

SOURCES OF EVIDENCE

Database of PubMed, Agricola (Ovid), Centre for Agriculture and Bioscience Direct (CABI), Web of Science (Clarivate), Cumulative Index to Nursing and Allied Health Literature (CINAHL) and MathScinet. Data charting: Metadata of the study, the context of the study, model structure, model process and reporting quality will be extracted. A narrative summary of this information, gaps and recommendations will be prepared and reported in One Health decision-making context.

ETHICS AND DISSEMINATION

Research ethics board approval was not obtained for this study as neither human participation nor unpublished human data were used in this study. The study findings will be widely disseminated among the One Health Modelling Network for Emerging Infections network and stakeholders by means of conferences, and publication in open-access peer-reviewed journals.

A MODEL ON BACTERIAL RESISTANCE CONSIDERING A GENERALIZED LAW OF MASS ACTION FOR PLASMID REPLICATION

Bacterial plasmids play a fundamental role in antibiotic resistance. However, a lack of knowledge about their biology is an obstacle in fully understanding the mechanisms and properties of plasmid-mediated resistance. This has motivated investigations of real systems in vitro to analyze the transfer and replication of plasmids. In this work, we address this issue with mathematical modeling. We formulate and perform a qualitative analysis of a nonlinear system of ordinary differential equations describing the competition dynamics between plasmids and sensitive and resistant bacteria. In addition, we estimated parameter values from empirical data. Our model predicts scenarios consistent with biological phenomena. The elimination or spread of infection depends on factors associated with bacterial reproduction and the transfer and replication of plasmids. From the estimated parameters, three bacterial growth experiments were analyzed in vitro. We determined the experiment with the highest bacterial growth rate and the highest rate of plasmid transfer. Moreover, numerical simulations were performed to predict bacterial growth.

Modification of empirical antimicrobial regimens in large animal medicine

BACKGROUND

Empirical antimicrobial regimens can be modified following new diagnostic information or when empirical treatment fails. Little is known about the frequency or clinical context in which these modifications occur. We characterised these modifications in a large animal hospital to identify when antimicrobial use could be optimised.

METHODS

Chart reviews were performed for all inpatients and outpatients administered antimicrobials at a large animal veterinary referral and teaching hospital in 2017-2018 (n=1163 visits) to determine when and why empirical regimens were modified. Multinomial logistic regression was performed to identify factors associated with reasons for modification.

RESULTS

Empirical antimicrobial regimens were modified in 17.3 per cent of visits. The main reasons were parenteral-oral conversions in horses and failure of disease prevention or treatment in ruminants. Empirical therapy for disease prevention was more likely to be modified because of complications in ruminants and in animals on the emergency/critical care service. Empirical therapy for disease treatment was more often modified for reasons other than de-escalation in ruminants and in animals with longer lengths of stay.

CONCLUSIONS

Empirical antimicrobial regimens were modified infrequently and mostly for purposes of parenteral-oral conversion in horses and lack of response in ruminants. De-escalation of antimicrobials administered for disease treatment, when guided by diagnostics, is a major tenet of judicious antimicrobial use. However, more research is needed to determine when and how antimicrobial regimens administered for disease prevention should be modified.

A survey of within-host and between-hosts modelling for antibiotic resistance

Antibiotic resistance is a global public health problem which has the attention of many stakeholders including clinicians, the pharmaceutical industry, researchers and policy makers. Despite the existence of many studies, control of resistance transmission has become a rather daunting task as the mechanisms underlying resistance evolution and development are not fully known. Here, we discuss the mechanisms underlying antibiotic resistance development, explore some treatment strategies used in the fight against antibiotic resistance and consider recent findings on collateral susceptibilities amongst antibiotic classes. Mathematical models have proved valuable for unravelling complex mechanisms in biology and such models have been used in the quest of understanding the development and spread of antibiotic resistance. While assessing the importance of such mathematical models, previous systematic reviews were interested in investigating whether these models follow good modelling practice. We focus on theoretical approaches used for resistance modelling considering both within and between host models as well as some pharmacodynamic and pharmakokinetic approaches and further examine the interaction between drugs and host immune response during treatment with antibiotics. Finally, we provide an outlook for future research aimed at modelling approaches for combating antibiotic resistance.

Dynamic analysis of conversion from a drug-sensitivity strain to a drug-resistant strain

In this paper, a mathematical model of conversion from a drug-sensitivity strain to a drug-resistant strain is given to investigate how antibiotic usage may be optimized to preserve or restore antibiotic effectiveness. This novel theoretical framework could result in an optimal criterion on how to reduce the drug resistance to a reasonable range by using the antibiotic dressing strategy. The sufficient conditions of existence of order-1 periodic solution are obtained in view of the geometrical theory of the semi-continuous dynamical system and the qualitative properties of the corresponding continuous system. The stability of the order-1 periodic solution is proved by means of [H. J. Guo, L. S. Chen and X. Y. Song, Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property, Appl. Math. Comput. 271 (2015) 905–922]. Finally, our results are confirmed by means of numerical simulations.

Send more data: a systematic review of mathematical models of antimicrobial resistance

Background

Antimicrobial resistance is a global health problem that demands all possible means to control it. Mathematical modelling is a valuable tool for understanding the mechanisms of AMR development and spread, and can help us to investigate and propose novel control strategies. However, it is of vital importance that mathematical models have a broad utility, which can be assured if good modelling practice is followed.

Objective

The objective of this study was to provide a comprehensive systematic review of published models of AMR development and spread. Furthermore, the study aimed to identify gaps in the knowledge required to develop useful models.

Methods

The review comprised a comprehensive literature search with 38 selected studies. Information was extracted from the selected papers using an adaptation of previously published frameworks, and was evaluated using the TRACE good modelling practice guidelines.

Results

None of the selected papers fulfilled the TRACE guidelines. We recommend that future mathematical models should: a) model the biological processes mechanistically, b) incorporate uncertainty and variability in the system using stochastic modelling, c) include a sensitivity analysis and model external and internal validation.

Conclusion

Many mathematical models of AMR development and spread exist. There is still a lack of knowledge about antimicrobial resistance, which restricts the development of useful mathematical models.

THE MATHEMATICAL ANALYSIS OF THE MODEL OF ANTIBIOTIC-RESISTANT BACTERIA AND THE IMMUNE CELLS

Currently, World Health Organization (WHO) report confirms that the antibiotic-resistant infections are the greatest threat to health. Despite the new therapeutic strategies, the bacteria develop mechanisms to defend themselves against antibiotics. In this paper, we propose a mathematical model describing the dynamics of resistant bacteria, non-resistant bacteria and immune cells exposed to an antibiotic. The global stability of equilibria is performed by using Lyapunov functions.

Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma

In this work we formulate a model for the population dynamics of Mycobacterium tuberculosis (Mtb), the causative agent of tuberculosis (TB). Our main interest is to assess the impact of the competition among bacteria on the infection prevalence. For this end, we assume that Mtb population has two types of growth. The first one is due to bacteria produced in the interior of each infected macrophage, and it is assumed that is proportional to the number of infected macrophages. The second one is of logistic type due to the competition among free bacteria released by the same infected macrophages. The qualitative analysis and numerical results suggests the existence of forward, backward and S-shaped bifurcations when the associated reproduction number R0 of the Mtb is less unity. In addition, qualitative analysis of the model shows that there may be up to three bacteria-present equilibria, two locally asymptotically stable, and one unstable.

In silico analysis of antibiotic-induced Clostridium difficile infection: Remediation techniques and biological adaptations

In this paper we study antibiotic-induced C. difficile infection (CDI), caused by the toxin-producing C. difficile (CD), and implement clinically-inspired simulated treatments in a computational framework that synthesizes a generalized Lotka-Volterra (gLV) model with SIR modeling techniques. The gLV model uses parameters derived from an experimental mouse model, in which the mice are administered antibiotics and subsequently dosed with CD. We numerically identify which of the experimentally measured initial conditions are vulnerable to CD colonization, then formalize the notion of CD susceptibility analytically. We simulate fecal transplantation, a clinically successful treatment for CDI, and discover that both the transplant timing and transplant donor are relevant to the the efficacy of the treatment, a result which has clinical implications. We incorporate two nongeneric yet dangerous attributes of CD into the gLV model, sporulation and antibiotic-resistant mutation, and for each identify relevant SIR techniques that describe the desired attribute. Finally, we rely on the results of our framework to analyze an experimental study of fecal transplants in mice, and are able to explain observed experimental results, validate our simulated results, and suggest model-motivated experiments.

Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection

Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung.

Mathematical modelling of bacterial resistance to multiple antibiotics and immune system response

Resistance of developed bacteria to antibiotic treatment is a very important issue, because introduction of any new antibiotic is after a little while followed by the formation of resistant bacterial isolates in the clinic. The significant increase in clinical resistance to antibiotics is a troubling situation especially in nosocomial infections, where already defenseless patients can be unsuccessful to respond to treatment, causing even greater health issue. Nosocomial infections can be identified as those happening within 2 days of hospital acceptance, 3 days of discharge or 1 month of an operation. They influence 1 out of 10 patients admitted to hospital. Annually, this outcomes in 5000 deaths only in UK with a cost to the National Health Service of a billion pounds. Despite these problems, antibiotic therapy is still the most common method used to treat bacterial infections. On the other hand, it is often mentioned that immune system plays a major role in the progress of infections. In this context, we proposed a mathematical model defining population dynamics of both the specific immune cells produced according to the properties of bacteria by host and the bacteria exposed to multiple antibiotics synchronically, presuming that resistance is gained through mutations due to exposure to antibiotic. Qualitative analysis found out infection-free equilibrium point and other equilibrium points where resistant bacteria and immune system cells exist, only resistant bacteria exists and sensitive bacteria, resistant bacteria and immune system cells exist. As a result of this analysis, our model highlights the fact that when an individual’s immune system weakens, he/she suffers more from the bacterial infections which are believed to have been confined or terminated. Also, these results was supported by numerical simulations.

MATHEMATICAL MODELING OF BACTERIAL RESISTANCE TO ANTIBIOTICS BY MUTATIONS AND PLASMIDS

Diversity of drugs against bacterial infections, and development of resistance to such drugs are increasing. We formulate and analyze a deterministic model for the population dynamics of sensitive and resistant bacteria to multiple bactericidal and bacteriostatic antibiotics, assuming that drug resistance is acquired through mutations and plasmid transmission. Model equilibria are determined from qualitative analysis, and numerical simulations are used to assess temporal dynamics of sensitive and drug-resistant bacteria. The model presents three possibilities: elimination of bacteria, persistence of only resistant bacteria, or coexistence of sensitive and resistant bacteria. Evolution to one of these scenarios depends on thresholds numbers involving sensitive and resistant bacteria.

Antibiotic resistance monitoring in Vibrio spp. isolated from rearing environment and intestines of abalone Haliotis diversicolor

546 Vibrio isolates from rearing seawater (292 strains) and intestines of abalone (254 strains) were tested to ten antibiotics using Kirby-Bauer diffusion method. Resistant rates of abalone-derived Vibrio isolates to chloramphenicol (C), enrofloxacin (ENX) and norfloxacin (NOR) were <28%, whereas those from seawater showed large fluctuations in resistance to each of the tested antibiotics. Many strains showed higher resistant rates (>40%) to kanamycin (KNA), furazolidone (F), tetracycline (TE), gentamicin (GM) and rifampin (RA). 332 isolates from seawater (n=258) and abalone (n=74) were resistant to more than three antibiotics. Peaked resistant rates of seawater-derived isolates to multiple antibiotics were overlapped in May and August. Statistical analysis showed that pH had an important effect on resistant rates of abalone-derived Vibrio isolates to RA, NOR, and ENX. Salinity and dissolved oxygen were negatively correlated with resistant rates of seawater-derived Vibrio isolates to KNA, RA, and PG.