A discrete model of competing species sharing a parasite

In this work we develop a discrete model of competing species affected by a common parasite. We analyze the influence of the fast development of the shared disease on the community dynamics. The model is presented under the form of a two time scales discrete system with four variables. Thus, it becomes analytically tractable with the help of the appropriate reduction method. The 2-dimensional reduced system, that has the same the asymptotic behaviour of the full model, is a generalization of the Leslie-Gower competition model. It has the unfrequent property in this kind of models of including multiple equilibrium attractors of mixed type. The analysis of the reduced system shows that parasites can completely alter the outcome of competition depending on the parasite's basic reproductive number R0. In some cases, initial conditions decide among several exclusion or coexistence scenarios

Discrete-time staged progression epidemic models

In the Staged Progression (SP) epidemic models, infected individuals are classified into a suitable number of states. The goal of these models is to describe as closely as possible the effect of differences in infectiousness exhibited by individuals going through the different stages. The main objective of this work is to study, from the methodological point of view, the behavior of solutions of the discrete time SP models without reinfection and with a general incidence function. Besides calculating $\mathcal{R}_{0}$, we find bounds for the epidemic final size, characterize the asymptotic behavior of the infected classes, give results about the final monotonicity of the infected classes, and obtain results regarding the initial dynamics of the prevalence of the disease. Moreover, we incorporate into the model the probability distribution of the number of contacts in order to make the model amenable to study its effect in the dynamics of the disease

Discrete epidemic models with two time scales

The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could represent movements between spatial locations, changes of individual activities or behaviours, or others. To include a sufficiently general disease model, we first build up from first principles a discrete-time Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS) model and characterize the eradication or endemicity of the disease with the help of its basic reproduction number R0. Then, we propose a general full model that includes sequentially the two processes at different time scales, and proceed to its analysis through a reduced model. The basic reproduction number R0 of the reduced system gives a good approximation of the R0 of the full model since it serves at analyzing its asymptotic behaviour. As an illustration of the proposed general framework, it is shown that there exist conditions under which a locally endemic disease, considering isolated patches in a metapopulation, can be eradicated globally by establishing the appropriate movements between patches

The Catalonian Conflict : an Interpretive Structural Model

The methodology ISM (Interpretive Structural Modeling) is used to study the conflict in Catalonia, listing a listof factors and the influences between them, building from them the Matrix of Influences and the Matrix of Scope, fromwhich they classify the factors into levels and a flow diagram is drawn up, concluding what the possible paths of evolutionof said conflict would b

Non-linear population discrete models with two time scales: re-scaling of part of the slow process

In this work we present a reduction result for discrete time systems with two time scales. In order to be valid, previous results in the field require some strong hypotheses that are difficult to check in practical applications. Roughly speaking, the iterates of a map as well as their differentials must converge uniformly on compact sets. Here, we eliminate the hypothesis of uniform convergence of the differentials at no significant cost in the conclusions of the result. This new result is then used to extend to nonlinear cases the reduction of some population discrete models involving processes acting at different time scales. In practical cases, some processes that occur at a fast time scale are often only measured at slow time intervals, notably mortality. For a general class of linear models that include such kind of processes, it has been shown that a more realistic approach requires the re-scaling of those processes to be considered at the fast time scale. We develop the same type of re-scaling in some nonlinear models and prove the corresponding reduction results. We also provide an application to a particular model of a structured population in a two-patch environment

Approximate reduction of nonlinear discrete models with two time scales

The aim of this work is to present a general class of nonlinear discrete time models with two time scales whose dynamics is susceptible of being approached by means of a reduced system. The reduction process is included in the so-called approximate aggregation of variables methods which consist of describing the dynamics of a complex system involving many coupled variables through the dynamics of a reduced system formulated in terms of a few global variables. For the time unit of the discrete system we use that of the slow dynamics and assume that fast dynamics acts a large number of times during it. After introducing a general two-time scales nonlinear discrete model we present its reduced accompanying model and the relationships between them. The main result proves that certain asymptotic behaviours, hyperbolic asymptotically stable (A.S.) periodic solutions, to the aggregated system entail that to the original system

Informalidad y evasión de impuestos de los pequeños negocios del Mercado Huamantanga, Puente Piedra 2020

La presente investigación tuvo como objetivo general determinar la relación que existe entre la informalidad y evasión de impuestos, de los pequeños negocios del mercado Huamantanga, la acción ilícita de los pequeños negocios, la fiscalización y la Administración Tributaria de los pequeños negocios del mercado Huamantanga. La metodología fue de tipo aplicada, de nivel cuantitativo y diseño no experimental. La muestra de estudio consta de 40 personas que tengan actividad comercial en el Mercado Huamantanga, los resultados de acuerdo a las estadísticas realizadas, fueron que el valor de Rho de Spearman es 0.591 lo que indica una Correlación positivo Moderada y la significancia bilateral (p= 0.00<0.01) comparado con el α = 0.05 que indica que se acepta la hipótesis alterna y se rechaza la hipótesis nula. Se concluyó que la informalidad tiene relación con la evasión de impuestos de los pequeños negocios del mercado Huamantanga Puente Piedra 2020, puesto que, al examinar el resultado se estableció que la correlación entre la informalidad y la evasión de impuestos es positiva moderada, por lo que, si existe un mayor número de comercios informales, incrementará los niveles de evasión tributaria

Guideline for dialysate quality of Spanish Society of Nephrology (second edition, 2015)

A Best Practice Guideline about Dialysis fluid purity was developed under the leadership of the Spanish Society of Nephrology in 2004. The second edition revised Guideline considered new evidences and International Standard. The Guideline has established recommen- dations for standards for preparing dialysate: water, concentrates and hemodialysis proportioning systems. This Guideline is based on the ISO 13959, European Pharmacopoeia, the Real Farmacopea Española, the AAMI Standards and Recommended Practices, Euro- pean Best Practice Guidelines for Haemodialysis, literature reviews, according to their level of evidence, and the opinion of the expert Spanish group. Two levels of quality of water were defined: purified water and high purified water (ultra pure) and for dialysate: ultra pure dialysate. Regular use of ultra pure dialysate is recom- mended for all type of hemodialysis to prevent and delay the occurrence of complications: inflammation, malnutrition, anaemia and amiloidosis. Water, concentrates and dialysate quality requirements are defined as maximum allowa- ble contaminant levels: chemicals (4.1.2), conductivity, microbial and endotoxins (4.1.1): Monitoring frequency, maintenance and corrective actions were specified. Methods of sampling and analysis were described in appendix (anexos). For microbiological monitoring, R2A medium is recommended, incubated during 7-14 days at a temperature of 17-23 °C. The dialysate quality assurance process involves all dialysis staff members and requires strict protocols. The physician in charge of hemodialysis has the ultimate responsibility for dialysate quality