Estrategias construidas para la división de fracciones

Este trabajo recoge un estudio sobre las estrategias de cálculo desarrolladas por estudiantes de sexto año de educación primaria y por maestros, el cual reveló el uso de métodos de dos etapas para problemas de división de fracciones cuotitiva y partitiva. Estos métodos añaden un paso más a las estrategias de un solo paso desarrolladas para la división de números enteros; el paso adicional convierte unidades por medio de multiplicación (la unitización). También se observa el uso de las unidades de co-medida, y algunos errores comunes

Influence of Vectors' Risk-Spreading Strategies and Environmental Stochasticity on the Epidemiology and Evolution of Vector-Borne Diseases: The Example of Chagas' Disease

Insects are known to display strategies that spread the risk of encountering unfavorable conditions, thereby decreasing the extinction probability of genetic lineages in unpredictable environments. To what extent these strategies influence the epidemiology and evolution of vector-borne diseases in stochastic environments is largely unknown. In triatomines, the vectors of the parasite Trypanosoma cruzi, the etiological agent of Chagas' disease, juvenile development time varies between individuals and such variation most likely decreases the extinction risk of vector populations in stochastic environments. We developed a simplified multi-stage vector-borne SI epidemiological model to investigate how vector risk-spreading strategies and environmental stochasticity influence the prevalence and evolution of a parasite. This model is based on available knowledge on triatomine biodemography, but its conceptual outcomes apply, to a certain extent, to other vector-borne diseases. Model comparisons between deterministic and stochastic settings led to the conclusion that environmental stochasticity, vector risk-spreading strategies (in particular an increase in the length and variability of development time) and their interaction have drastic consequences on vector population dynamics, disease prevalence, and the relative short-term evolution of parasite virulence. Our work shows that stochastic environments and associated risk-spreading strategies can increase the prevalence of vector-borne diseases and favor the invasion of more virulent parasite strains on relatively short evolutionary timescales. This study raises new questions and challenges in a context of increasingly unpredictable environmental variations as a result of global climate change and human interventions such as habitat destruction or vector control.Centro de Estudios Parasitológicos y de Vectore

Influence of Vectors' Risk-Spreading Strategies and Environmental Stochasticity on the Epidemiology and Evolution of Vector-Borne Diseases: The Example of Chagas' Disease

Insects are known to display strategies that spread the risk of encountering unfavorable conditions, thereby decreasing the extinction probability of genetic lineages in unpredictable environments. To what extent these strategies influence the epidemiology and evolution of vector-borne diseases in stochastic environments is largely unknown. In triatomines, the vectors of the parasite Trypanosoma cruzi, the etiological agent of Chagas' disease, juvenile development time varies between individuals and such variation most likely decreases the extinction risk of vector populations in stochastic environments. We developed a simplified multi-stage vector-borne SI epidemiological model to investigate how vector risk-spreading strategies and environmental stochasticity influence the prevalence and evolution of a parasite. This model is based on available knowledge on triatomine biodemography, but its conceptual outcomes apply, to a certain extent, to other vector-borne diseases. Model comparisons between deterministic and stochastic settings led to the conclusion that environmental stochasticity, vector risk-spreading strategies (in particular an increase in the length and variability of development time) and their interaction have drastic consequences on vector population dynamics, disease prevalence, and the relative short-term evolution of parasite virulence. Our work shows that stochastic environments and associated risk-spreading strategies can increase the prevalence of vector-borne diseases and favor the invasion of more virulent parasite strains on relatively short evolutionary timescales. This study raises new questions and challenges in a context of increasingly unpredictable environmental variations as a result of global climate change and human interventions such as habitat destruction or vector control.Centro de Estudios Parasitológicos y de Vectore

Model Parameters and Outbreak Control for SARS

Control of the 2002–2003 severe acute respiratory syndrome (SARS) outbreak was based on rapid diagnosis coupled with effective patient isolation. We used uncertainty and sensitivity analysis of the basic reproductive number R0 to assess the role that model parameters play in outbreak control. The transmission rate and isolation effectiveness have the largest fractional effect on R0. We estimated the distribution of the reproductive number R0 under perfect isolation conditions. The distribution lies in the interquartile range 0.19–1.08, with a median of 0.49. Even though the median of R0 is \u3c1, we found that 25% of our R0 distribution lies at R0 \u3e 1, even with perfect isolation. This implies the need to simultaneously apply more than one method of control

Influence of Vectors' Risk-Spreading Strategies and Environmental Stochasticity on the Epidemiology and Evolution of Vector-Borne Diseases: The Example of Chagas' Disease

Insects are known to display strategies that spread the risk of encountering unfavorable conditions, thereby decreasing the extinction probability of genetic lineages in unpredictable environments. To what extent these strategies influence the epidemiology and evolution of vector-borne diseases in stochastic environments is largely unknown. In triatomines, the vectors of the parasite Trypanosoma cruzi, the etiological agent of Chagas' disease, juvenile development time varies between individuals and such variation most likely decreases the extinction risk of vector populations in stochastic environments. We developed a simplified multi-stage vector-borne SI epidemiological model to investigate how vector risk-spreading strategies and environmental stochasticity influence the prevalence and evolution of a parasite. This model is based on available knowledge on triatomine biodemography, but its conceptual outcomes apply, to a certain extent, to other vector-borne diseases. Model comparisons between deterministic and stochastic settings led to the conclusion that environmental stochasticity, vector risk-spreading strategies (in particular an increase in the length and variability of development time) and their interaction have drastic consequences on vector population dynamics, disease prevalence, and the relative short-term evolution of parasite virulence. Our work shows that stochastic environments and associated risk-spreading strategies can increase the prevalence of vector-borne diseases and favor the invasion of more virulent parasite strains on relatively short evolutionary timescales. This study raises new questions and challenges in a context of increasingly unpredictable environmental variations as a result of global climate change and human interventions such as habitat destruction or vector control.Centro de Estudios Parasitológicos y de Vectore

Who Says We R(o) Ready for Change?

18 pages, 1 article*Who Says We R(o) Ready for Change?* (Crisosto, Nicolas M.; Castillo-Chavez, Carlos; Kribs-Zaleta, Christopher; Wirkus, Stephen) 18 page

Estimating Contact Process Saturation in Sylvatic Transmission of Trypanosoma cruzi in the United States

Although it has been known for nearly a century that strains of Trypanosoma cruzi, the etiological agent for Chagas' disease, are enzootic in the southern U.S., much remains unknown about the dynamics of its transmission in the sylvatic cycles that maintain it, including the relative importance of different transmission routes. Mathematical models can fill in gaps where field and lab data are difficult to collect, but they need as inputs the values of certain key demographic and epidemiological quantities which parametrize the models. In particular, they determine whether saturation occurs in the contact processes that communicate the infection between the two populations. Concentrating on raccoons, opossums, and woodrats as hosts in Texas and the southeastern U.S., and the vectors Triatoma sanguisuga and Triatoma gerstaeckeri, we use an exhaustive literature review to derive estimates for fundamental parameters, and use simple mathematical models to illustrate a method for estimating infection rates indirectly based on prevalence data. Results are used to draw conclusions about saturation and which population density drives each of the two contact-based infection processes (stercorarian/bloodborne and oral). Analysis suggests that the vector feeding process associated with stercorarian transmission to hosts and bloodborne transmission to vectors is limited by the population density of vectors when dealing with woodrats, but by that of hosts when dealing with raccoons and opossums, while the predation of hosts on vectors which drives oral transmission to hosts is limited by the population density of hosts. Confidence in these conclusions is limited by a severe paucity of data underlying associated parameter estimates, but the approaches developed here can also be applied to the study of other vector-borne infections

Backward bifurcation in neutrophil-pathogen interaction

Bacterial infections elicit immune responses including neutrophils, whose recruitment is stimulated by the bacteria’s presence but which die after eliminating those bacteria. This dual interaction between bacteria and neutrophil concentrations, more complicated than the simple predator-prey relationship that describes macrophage-bacteria interactions, creates an environment in which neutrophils may only be able to clear sufficiently small infections. This study describes this relationship using a simple nonlinear dynamical system which exhibits bistability behavior known as a backward bifurcation. Bacterial growth is assumed limited by a key nutrient. In contrast to a previous study which held neutrophil and nutrient levels constant and required saturation terms to produce bistability, our model shows that simple bilinear terms support bistability when nutrient and neutrophil densities are allowed to vary in response to bacterial density. An example application involving Borrelia burgdorferi, which feeds on manganese, illustrates why neutrophils’ rapid response is key to their ability to contain bacterial infections.Las infecciones bacterianas provocan respuestas inmunitarias, incluyendo neutrófilos, cuyo reclutamiento es estimulado por la presencia de la bacteria pero que muere después de eliminar esas bacterias. Esta doble interacción entre las concentraciones de bacterias y neutrófilos, más complicada que la simple relación depredador-presa que describe las interacciones entre bacterias y macrófagos, crea un ambiente en el que los neutrófilos tal vez sólo puedan despejar infecciones suficientemente pequeñas. Este estudio describe esta relación utilizando un sistema dinámico no lineal sencillo que exhibe un comportamiento de biestabilidad conocido como una bifurcación hacia atrás. El crecimiento bacteriano se supone limitado por un nutriente clave. En contraste con un estudio anterior que mantuvo los niveles de neutrófilos y nutrientes constantes y requería términos de saturación para producir la biestabilidad, nuestro modelo muestra que los términos bilineales sencillos fomentan la biestabilidad cuando las densidades de nutrientes y neutrófilos pueden variar en respuesta a la densidad bacteriana. Un ejemplo aplicado a la bacteria Borrelia burgdorferi, que se alimenta de manganeso, ilustra por qué la respuesta rápida de los neutrófilos es clave para su capacidad de contener las infecciones bacterianas