Bifurcation analysis and global dynamics of a mathematical model of antibiotic resistance in hospitals

A fractional-order model for nosocomial infection caused by Pseudomonas aeruginosa in Northern Cyprus

Pseudomonas aeruginosa, a resilient gram-negative bacterium, poses a persistent threat as a leading cause of nosocomial infections, particularly in resource-constrained regions. Despite existing treatment and control measures, the bacterium continues to challenge healthcare systems, especially in developing nations. This paper introduces a fractional-order model to elucidate the dynamic behavior of nosocomial infections caused by P. aeruginosa and to compare the efficacy of carbapenems and aminoglycosides in treatment. The model's existence and uniqueness are established, and both global and local stability are confirmed. The effective reproduction number is computed, revealing an epidemic potential with a value of 1.02 in Northern Cyprus. Utilizing real-life data from a university hospital and employing numerical simulations, our results indicate that patients exhibit higher sensitivity and lower resistance to aminoglycoside treatment compared to carbapenems. Aminoglycosides consistently outperform carbapenems across key metrics, including the reduction of susceptible population, infection numbers, treatment efficacy, total infected population, hospital occupancy, and effective reproduction number. The fractional-order approach emerges as a suitable and insightful tool for studying the transmission dynamics of the disease and assessing treatment effectiveness. This research provides a robust foundation for refining treatment strategies against P. aeruginosa infections, contributing valuable insights for healthcare practitioners and policymakers alike.

A stochastic dynamical model for nosocomial infections with co-circulation of sensitive and resistant bacterial strains

Nosocomial infections (hospital-acquired) has been an important public health problem, which may make those patients with infections or involved visitors and hospital personnel at higher risk of worse clinical outcomes or infection, and then consume more healthcare resources. Taking into account the stochasticity of the death and discharge rate of patients staying in hospitals, in this paper, we propose a stochastic dynamical model describing the transmission of nosocomial pathogens among patients admitted for hospital stays. The stochastic terms of the model are incorporated to capture the randomness arising from death and discharge processes of patients. Firstly, a sufficient condition is established for the stochastic extinction of disease. It shows that introducing randomness in the model will result in lower potential of nosocomial outbreaks. Further, we establish a threshold criterion on the existence of stationary distribution and ergodicity for any positive solution of the model. Particularly, the spectral radius form of stochastic threshold value is calculated in the special case. Moreover, the numerical simulations are conducted to both validate the theoretical results and investigate the effect of prevention and control strategies on the prevalence of nosocomial infection. We show that enhancing hygiene, targeting colonized and infected patients, improving antibiotic treatment accuracy, shortening treatment periods are all crucial factors to contain nosocomial infections.

Mathematical Modeling and Analysis of Tumor Chemotherapy

Cancer diseases lead to the second-highest death rate all over the world. For treating tumors, one of the most common schemes is chemotherapy, which can decrease the tumor size and control the progression of cancer diseases. To better understand the mechanisms of chemotherapy, we developed a mathematical model of tumor growth under chemotherapy. This model includes both immune system response and drug therapy. We characterize the symmetrical properties and dynamics of this differential equation model by finding the equilibrium points and exploring the stability and symmetry properties in a range of model parameters. Sensitivity analyses suggest that the chemotherapy drug-induced tumor mortality rate and the drug decay rate contribute significantly to the determination of treatment outcomes. Numerical simulations highlight the importance of CTL activation in tumor chemotherapy.

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.

Modeling Antibiotic Use Strategies in Intensive Care Units: Comparing De-escalation and Continuation

Antimicrobial de-escalation refers to the treatment mechanism of switching from empiric antibiotics with good coverage to alternatives based on laboratory susceptibility test results, with the aim of avoiding unnecessary use of broad-spectrum antibiotics. In a previous study, we have developed multi-strain and multi-drug models in an intensive care unit setting, to evaluate the benefits and trade-offs of de-escalation in comparison with the conventional strategy called antimicrobial continuation. Our simulation results indicated that for a large portion of credible parameter combinations, de-escalation reduces the use of the empiric antibiotic but increases the probabilities of colonization and infections. In this paper, we first simplify the previous models to compare the long-term dynamical behaviors between de-escalation and continuation systems under a two-strain scenario. The analytical results coincide with our previous findings in the complex models, indicating the benefits and unintended consequences of de-escalation strategy result from the nature of this treatment mechanism, not from the complexity of the high-dimensional systems. By extending the models to three-strain scenarios, we find that de-escalation is superior than continuation in preventing outbreaks of invading strains that are resistant to empiric antibiotics. Thus decisions on antibiotic use strategies should be made specifically according to ICU conditions and intervention objectives.

Computational Health Engineering Applied to Model Infectious Diseases and Antimicrobial Resistance Spread

Infectious diseases are the primary cause of mortality worldwide. The dangers of infectious disease are compounded with antimicrobial resistance, which remains the greatest concern for human health. Although novel approaches are under investigation, the World Health Organization predicts that by 2050, septicaemia caused by antimicrobial resistant bacteria could result in 10 million deaths per year. One of the main challenges in medical microbiology is to develop novel experimental approaches, which enable a better understanding of bacterial infections and antimicrobial resistance. After the introduction of whole genome sequencing, there was a great improvement in bacterial detection and identification, which also enabled the characterization of virulence factors and antimicrobial resistance genes. Today, the use of in silico experiments jointly with computational and machine learning offer an in depth understanding of systems biology, allowing us to use this knowledge for the prevention, prediction, and control of infectious disease. Herein, the aim of this review is to discuss the latest advances in human health engineering and their applicability in the control of infectious diseases. An in-depth knowledge of host–pathogen–protein interactions, combined with a better understanding of a host’s immune response and bacterial fitness, are key determinants for halting infectious diseases and antimicrobial resistance dissemination.