Mathematical modelling of MS2 virus inactivation by Al/Fe-PILC-activated catalytic wet peroxide oxidation (CWPO).

Catalytic wet peroxide oxidation (CWPO) is a novel, alternative technology to conventional disinfection methods that are widely used to control microbial parameters in drinking water. To assess its effectiveness, new studies revealing the kinetics of MS2 coliphage inactivation by CWPO technology are required. This investigation therefore aimed to perform mathematical modelling of MS2 inactivation through CWPO technology activated by an Al/Fe-pillared clay catalyst (Al/Fe-PILC) in the presence of a synthetic surrogate of dissolved natural organic matter. The inactivation constant was obtained from two different statistical approaches, and the experimental data were better fitted to the pseudo-first-order Chick-Watson model in which the inactivation rate is constant. For this model, the maximum inactivation rate was k = 0.1648 min-1, which was achieved in the MS2-3 catalytic test using an initial mass ratio of peroxide to active iron (Feact) of 1.2 mg H2O2/mg Feact. To estimate the inactivation rate due to reactive oxygen species (ROS), we supposed that the inactivation constant depends on both ROS and Feact. In this case, the maximum inactivation rate due to ROS was kr = 2.4 × 10-9 min-1 (using 1.17 mg H2O2/mg Feact), which was achieved in the MS2-10 trial; both cases led to the conclusion that the optimal initial ratio of peroxide to active Fe in the catalyst in CWPO activated by Al/Fe-PILC was close to 1.2 mg H2O2/mg Feact. These kinetic studies showed that rapid inactivation takes place very early in the reaction, followed by slow inactivation during the remaining period of the recorded reaction time. This research revealed the strong potential of CWPO technology to improve microbiological parameters in drinking water due to the high catalytic performance in the heterogeneous Fenton reaction displayed by Fe sites incorporated in the Al/Fe-PILCs.

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.

Eficiencia en la reducción de Cromo por una bacteria silvestre en un tratamiento tipo Batch utilizando como sustrato agua residual del municipio de Pasto, Colombia / Efficiency in the reduction of chromium by a wild bacterium in a Batch treatment type using residual water substrate from the municipality of Pasto, Colombia

Resumen Objetivo: Evaluar la eficiencia en la reducción de Cromo en un tratamiento tipo Batch, utilizando como sustrato agua residual municipal inoculada con una bacteria silvestre. Materiales y métodos: Se verificó a escala de laboratorio el porcentaje de reducción de Cromo hexavalente de tres bacterias silvestres previamente aisladas de agua residual del Río Pasto (Bacillus thuringiensis, Bacillus amyloliquefaciens y Paenibacillus sp.); se seleccionó el aislado que presentó mayor porcentaje de reducción de Cr y fue sometido a diferentes tratamientos. El análisis de los resultados se hizo mediante estadística descriptiva. Resultados: B. thuringiensis, B. amyloliquefaciens, y Paenibacillus sp., presentaron porcentajes de reducción de Cr (VI) de 82,01%; 80,85% y 79,27%, respectivamente. Se determinó que el tercer tratamiento (agua sin esterilizar del Río Pasto con B. thuringiensis) presentó diferencias significativas respecto a los demás (p = 0,0001 α = 0,05), concluyendo que B. thuringiensis reduce en mayor proporción el Cr (VI), los resultados encontrados en esta investigación son promisorios en el campo de la biorremediación de efluentes contaminados con Cromo ya que pueden ser tomados como base para implementar estrategias de biorremediación a gran escala. Conclusión: La bacteria B. thuringiensis presentó alta eficiencia en la reducción de Cromo hexavalente (99,42%), cuando fue implementada en un tratamiento a escala de laboratorio de agua residual sin esterilizar.

Abstract Objective: To evaluate the efficiency in the reduction of chromium in a Batch treatment type, using municipal residual water substrate inoculated with a wild bacterium. Materials and methods: The reduction percentage of hexavalent chromium of three wild bacteria previously isolated from residual water from the Pasto River was verified at laboratory scale (Bacillus thuringiensis, Bacillus amyloliquefaciens and Paenibacillus sp.); the isolated that showed the highest percentage of reduction of Cr was selected and was subjected to different treatments. The analysis of results was done using descriptive statistics. Results: B. thuringiensis, B. amyloliquefaciens, and Paenibacillus sp., presented percentages of reduction of Cr (VI) of 82,01%; 80,85% and 79,27%, respectively. It was determined that the third treatment (nonsterile water from the Pasto River with B. thuringiensis) presented significant differences with regard to the other (p = 0.0001 α = 0.05), concluding that B. thuringiensis reduces in greater proportion the Cr (VI). The results found in this research are promising in the field of bioremediation of contaminated effluents with Chrome since they may be taken as the basis for implementing strategies of bioremediation on a large scale. Conclusion: The bacteria B. thuringiensis presented high efficiency in the reduction of hexavalent chromium (99.42%) when implemented in a treatment at laboratory scale of residual nonsterile water.

Elementos para la modelación matemática de la epidemiología de la neumonía / Elements for mathematical modeling in pneumonia epidemiology

La neumonía es una infección respiratoria aguda (IRA) que afecta a los pulmones, se considera como la segunda causa de muerte asociada a infecciones respiratorias a nivel global. En Colombia hay reportes de aproximadamente 120.000 consultas anuales y 50.000 egresos hospitalarios en niños menores de 5 años. En particular, en el municipio de San Juan de Pasto se presentaron 65 muertes asociadas a esta enfermedad en 2010. A través de la modelación matemática sobre la epidemiología de la neumonía se puede aportar de manera directa al estudio de la distribución, la causalidad y la prevención de dicha enfermedad. El propósito de este artículo es relacionar la epidemiología de la neumonía con la modelación matemática.

Pneumonia is an acute respiratory infection (ARI) which affects the lungs. It is considered as the second cause of death associated with respiratory infections globally. In Colombia, there are reports of approximately 120,000 consultations per year and 50,000 hospital discharges in children under 5. In particular, in the municipality of San Juan de Pasto, there were 65 deaths associated with this disease in 2010. It can be contributed directly to the study of the distribution, causation and prevention of the disease through mathematical modeling about pneumonia epidemiology. The purpose of this review is to relate pneumonia epidemiology with mathematical modeling.

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

We formulate a mathematical model that describes the population dynamics of bacteria exposed to multiple antibiotics simultaneously, assuming that acquisition of resistance is through mutations due to antibiotic exposure. Qualitative analysis reveals the existence of a free-bacteria equilibrium, resistant-bacteria equilibrium and an endemic equilibrium where both bacteria coexist.

On the interactions of sensitive and resistant Mycobacterium tuberculosis to antibiotics.

In this work we propose a system of non linear ordinary differential equations for the dynamics of Mycobacterium tuberculosis (Mtb) within the host, in order to study the role of macrophages, T cells and antibiotics in the control of sensitive and resistant Mtb. Conditions for the persistence of sensitive and resistant bacteria are given in terms of the secondary infections produced by bacteria and macrophages, the immune response, and the antibiotic treatment. Model analysis predicts backward bifurcations for certain values of the parameters. In this case, the dynamics is characterized by the coexistence of two infection states with low and high bacteria load, respectively.

A mathematical model for cellular immunology of tuberculosis.

Tuberculosis (TB) is a global emergency. The World Health Organization reports about 9.2 million new infections each year, with an average of 1.7 million people killed by the disease. The causative agent is Mycobacterium tuberculosis (Mtb), whose main target are the macrophages, important immune system cells. Macrophages and T cell populations are the main responsible for fighting the pathogen. A better understanding of the interaction between Mtb, macrophages and T cells will contribute to the design of strategies to control TB. The purpose of this study is to evaluate the impact of the response of T cells and macrophages in the control of Mtb. To this end, we propose a system of ordinary differential equations to model the interaction among non-infected macrophages, infected macrophages, T cells and Mtb bacilli. Model analysis reveals the existence of two equilibrium states, infection-free equilibrium and the endemically infected equilibrium which can represent a state of latent or active infection, depending on the amount of bacteria.