Miller Cerón Gómez

In order to advance in the fight against plasmid-mediated resistance, it is necessary to deepen our understanding of the role played by these DNA molecules. In this sense, the achievements obtained from experimentation validated by mathematical models have contributed to the discovery of key properties in the dynamics of antibiotic resistance. In this work, we attempt to characterize some of these properties through nonlinear functional responses of both plasmid replication and plasmid transfer. The results of the mathematical modeling performed here suggest that the emergence of antibiotic resistance in an individual due to the transfer of plasmid-borne resistance genes is directly associated with the production capacity of both recipient and donor bacteria. Whereas for persistence, in addition to bacterial replication, specific properties associated with plasmid replication and transfer are required.

We present a mathematical model of pathogenic bacteria and bacteriophages, incorporating an abortive infection as a mechanism of bacterial protection against viral infection. We identified three equilibria: the extinction equilibrium point, the bacteriophages extinction equilibrium, and the coexistence equilibrium. The stability of these equilibria is determined by thresholds. We found that the extinction equilibrium point is always unstable, while the bacteriophages extinction equilibrium is globally asymptotically stable. The stability of the coexistence equilibrium varies, being unstable, locally asymptotically stable, or globally asymptotically stable depending on certain thresholds. We conclude that bacterial extinction is not possible, possibly due to the inclusion of the abortive infection, but it is feasible to maintain a low level of pathogenic bacteria.

We present a mathematical model employing ordinary differential equations to model the interaction dynamics between bacterial pathogens and Bacteriophages. Our model incorporates a non-linear function with inhibitory effects to describe the infection dynamics within these populations. By utilizing the Lyapunov theory and the second additive compound matrix, we analyze the stability of the model. Additionally, a global sensitivity analysis is conducted to identify the most influential parameters. Parameter estimation is performed using growth data of Escherichia coli (E. coli) bacteria in the presence of Coliphages, which are bacteriophages targeting E. coli, at various levels of multiplicity of infection. Our findings reveal a critical threshold that determines whether bacteriophage concentration will lead to coexistence with the bacterium or extinction of the phages. The coexistence equilibrium is found to be locally asymptotically stable, while the phages extinction equilibrium is globally asymptotically stable, contingent upon the magnitude of this threshold. Furthermore, our analysis indicates that the infection rate of bacteria and the half-saturation phage density significantly influence the dynamics of the model. Importantly, our parameter estimation demonstrates the effectiveness of all multiplicities of infection in eliminating infected bacteria, albeit with smaller multiplicities resulting in a higher residual population of bacteriophages post-elimination.

This work investigates the dynamical consequences of a nonlinear functional response in a predator–prey system. The model exhibits three equilibria: total extinction, predator extinction, and coexistence. Stability analysis shows that the total extinction equilibrium is inherently unstable, while the predator‐extinction equilibrium achieves global asymptotic stability if the functional response is increasing. The coexistence equilibrium, however, can exhibit distinct regimes—local stability, global stability, or oscillatory dynamics via a Hopf bifurcation. A key result demonstrates that a strictly increasing functional response is necessary but insufficient for global stability of the coexistence equilibrium. Conversely, Hopf bifurcation arises under two critical conditions: (1) prey density at coexistence remains below half the carrying capacity, and (2) the functional response’s growth rate at equilibrium does not exceed the prey’s intrinsic growth rate. These findings highlight how the curvature of the functional response governs bifurcation structures and long‐term ecological dynamics.

Lake Guamuez is the second largest lake in Colombia and economically supports hundreds of families in the area. The main activities carried out in the region have focused on tourism, agriculture, livestock, and rainbow trout production; however, these activities have been associated with contamination of the lake. This research aimed to evaluate the water quality of Lake Guamuez using somatic coliphages (SCs) as bioindicators. For this purpose, periodic sampling was carried out for 6 months at nine strategic points of the lake. For the detection of SCs, the method described in 9211 D of the Standard Methods for the Examination of Water and Wastewater was used. The genomic variability and presence of virulence genes in the isolated SCs were determined. Water contamination in the lake is evident, and the SCs titer is greater in areas with a high flow of anthropogenic activities. An important degree of genetic diversity and a high prevalence of virulence genes could be observed among the SCs analyzed. The results when compared with guidelines and water quality standards from various countries showed concentrations of SCs higher than those allowed. The high prevalence of gastrointestinal diseases in the region suggests a link to water contamination.

In this paper, we proposed a generalization for a model that considers Susceptible, Infected, Carrier, and Recovered by introducing a general incidence rate and considering migration in all its populations. This model has the characteristic that carriers and infected can transmit the disease, besides it has not a disease-free equilibrium point and no basic reproductive number. The focus of this study is to show a generalized model and the conditions required to analyze the equilibrium point stability. Using an appropriate Lyapunov function and with suitable conditions on the functions involved in the general incidence, we showed that the disease equilibrium point is globally asymptotically stable. Also, we presented numerical simulations of two applications to illustrate the results obtained from the analytical part.

A model with multiple disease stages is discussed; its main feature is that it considers a general incidence rate, functions for death and immigration rates in all populations. We show via a suitable Lyapunov function that the unique endemic equilibrium is globally asymptotically stable. We conclude that, in order to obtain the existence and global stability of the equilibrium point of general models, conditions must be imposed on the functions present in the model. In addition, the model has no basic reproduction number due to the constant flow of infected people, which makes its eradication impossible; therefore, there is no equilibrium point free of infection.

We propose a mathematical model based in ordinary differential equations between bacterial pathogen and Bacteriophages to describe the infection dynamics of these populations, for which we use a nonlinear function with an inhibitory effect. We study the stability of the model using the Lyapunov theory and the second additive compound matrix and perform a global sensitivity analysis to elucidate the most influential parameters in the model, besides we make a parameter estimation using growth data of Escherichia coli (E.coli) bacteria in presence of Coliphages (bacteriophages that infect E.coli) with different multiplicity of infection. We found a threshold that indicates whether the bacteriophage concentration will coexist with the bacterium (the coexistence equilibrium) or become extinct (phages extinction equilibrium), the first equilibrium is locally asymptotically stable while the other is globally asymptotically stable depending on the magnitude of this threshold. Beside we found that the dynamics of the model is particularly affected by infection rate of bacteria and Half-saturation phages density. Parameter estimation show that all multiplicities of infection are effective in eliminating infected bacteria but the smaller one leaves a higher number of bacteriophages at the end of this elimination.