The Economic Evaluation of Mastitis Control Strategies in Holstein-Friesian Dairy Herds.

The economic evaluation of mastitis control is challenging. The objective of this study was to perform the economic evaluation of mastitis control, under different intervention scenarios, quantifying the total cost of mastitis caused by S. aureus in Holstein cows in Argentina. A model was set for a dairy herd of Holstein cows endemically infected with S. aureus. A basic mastitis control plan including proper milking procedures, milking machine test, dry cow therapy, and treatment for clinical mastitis, was compared against other more complex and costly interventions, such as segregation and culling of chronically infected cows. Sensitivity analysis was performed by modifying the intramammary infection transition probabilities, economic parameters, and efficacy of treatment strategies. The basic mastitis control plan showed a median total cost of USD88.6/cow per year, which was close to the infected cows culling scenarios outputs. However, the segregation scenario was the most efficient, in which the total cost was reduced by about 50%. Such cost was more sensitive to probabilities and efficacy than the economic parameters. The model is flexible and can be customized by producers and veterinarians according to different control and herd settings.

Effects of scarcity and excess of larval food on life history traits of Aedes aegypti (Diptera: Culicidae).

Few studies have assessed the effects of food scarcity or excess on the life history traits of Aedes aegypti (L.) (Diptera: Culicidae) independently from larval density. We assessed immature survival, development time, and adult size in relation to food availability. We reared cohorts of 30 Ae. aegypti larvae from newly hatched to adult emergence with different food availability. Food conditions were kept constant by transferring larvae each day to a new food solution. Immature development was completed by some individuals in all treatments. The shortest development time, the largest adults, and the highest survival were observed at intermediate food levels. The most important effects of food scarcity were an extension in development time, a decrease in the size of adults, and a slight decrease in survival, while the most important effects of food excess were an important decrease in survival and a slight decrease in the size of adults. The variability in development time and adult size within sex and treatment increased at decreasing food availability. The results suggest that although the studied population has adapted to a wide range of food availabilities, both scarcity and excess of food have important negative impacts on fitness.

A model for the development of Aedes (Stegomyia) aegypti as a function of the available food.

We discuss the preimaginal development of the mosquito Aedes aegypti from the point of view of the statistics of developmental times and the final body-size of the pupae and adults. We begin the discussion studying existing models in relation to published data for the mosquito. The data suggest a developmental process that is described by exponentially distributed random times. The existing data show as well that the idea of cohorts emerging synchronously is verified only in optimal situations created at the laboratory but it is not verified in field experiments. We propose a model in which immature individuals progress in successive stages, all of them with exponentially distributed times, according to two different rates (one food-dependent and the other food-independent). This phenomenological model, coupled with a general model for growing, can explain the existing observations and new results produced in this work. The emerging picture is that the development of the larvae proceeds through a sequence of steps. Some of the steps depend on the available food. While food is in abundance, all steps can be thought as having equal duration, but when food is scarce, those steps that depend on food take considerably longer times. For insufficient levels of food, increase in larval mortality sets in. As a consequence of the smaller rates, the average pupation time increases and the cohort disperses in time. Dispersion, as measured by standard deviation, becomes a quadratic function of the average time indicating that cohort dispersion responds to the same causes than delays in pupation and adult emergence. During the whole developmental process the larva grows monotonically, initially at an exponential rate but later at decreasing rates, approaching a final body-size. Growth is stopped by maturation when it is already slow. As a consequence of this process, there is a slight bias favoring small individuals: Small individuals are born before larger individuals, although the tendency is very weak.

Linear processes in stochastic population dynamics: theory and application to insect development.

We consider stochastic population processes (Markov jump processes) that develop as a consequence of the occurrence of random events at random time intervals. The population is divided into subpopulations or compartments. The events occur at rates that depend linearly on the number of individuals in the different described compartments. The dynamics is presented in terms of Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously proposed, higher-order approximations are completely new. Further, we analyse a model for insect development as a sequence of E developmental stages regulated by rates that are linear in the implied subpopulations. Transition to the next stage competes with death at all times. The process ends at a predetermined stage, for example, pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time.

Dispersal of Aedes aegypti: field study in temperate areas using a novel method.

BACKGROUND & OBJECTIVES: Since Aedes aegypti was identified as vector of yellow fever and dengue, its dispersal is relevant for disease control. We studied the dispersal of Ae. aegypti in temperate areas of Argentina during egglaying, using the existing population and egg traps. METHODS: Two independent replicas of a unique experimental design involving mosquitoes dispersing from an urbanized area to adjacent non-urbanized locations were carried out and analyzed in statistical terms. RESULTS: We found relationship between stochastic variables related to the egg-laying mosquito activity (ELMA), useful to assess dispersal probabilities, despite the lack of knowledge of the total number of ovipositions in the zone. We propose to evaluate the egg-laying activity as minus the logarithm of the fraction of negative ovitraps at different distances from the buildings. INTERPRETATION & CONCLUSION: Three zones with different oviposition activity were determined, a corridor surrounding the urbanization, a second region between 10 and 25 m and the third region extending from 30 to 45 m from the urbanization. The landscape (plant cover) and the human activity in the area appear to have an influence in the dispersal of Ae. aegypti. The proposed method worked consistently in two different replicas.

Modeling dengue outbreaks.

We introduce a dengue model (SEIR) where the human individuals are treated on an individual basis (IBM) while the mosquito population, produced by an independent model, is treated by compartments (SEI). We study the spread of epidemics by the sole action of the mosquito. Exponential, deterministic and experimental distributions for the (human) exposed period are considered in two weather scenarios, one corresponding to temperate climate and the other to tropical climate. Virus circulation, final epidemic size and duration of outbreaks are considered showing that the results present little sensitivity to the statistics followed by the exposed period provided the median of the distributions are in coincidence. Only the time between an introduced (imported) case and the appearance of the first symptomatic secondary case is sensitive to this distribution. We finally show that the IBM model introduced is precisely a realization of a compartmental model, and that at least in this case, the choice between compartmental models or IBM is only a matter of convenience.

A stochastic spatial dynamical model for Aedes aegypti.

We develop a stochastic spatial model for Aedes aegypti populations based on the life cycle of the mosquito and its dispersal. Our validation corresponds to a monitoring study performed in Buenos Aires. Lacking information with regard to the number of breeding sites per block, the corresponding parameter (BS) was adjusted to the data. The model is able to produce numerical data in very good agreement with field results during most of the year, the exception being the fall season. Possible causes of the disagreement are discussed. We analyzed the mosquito dispersal as an advantageous strategy of persistence in the city and simulated the dispersal of females from a source to the surroundings along a 3-year period observing that several processes occur simultaneously: local extinctions, recolonization processes (resulting from flight and the oviposition performed by flyers), and colonization processes resulting from the persistence of eggs during the winter season. In view of this process, we suggest that eradication campaigns in temperate climates should be performed during the winter time for higher efficiency.

Blowing-up of deterministic fixed points in stochastic population dynamics.

We discuss the stochastic dynamics of biological (and other) populations presenting a limit behaviour for large environments (called deterministic limit) and its relation with the dynamics in the limit. The discussion is circumscribed to linearly stable fixed points of the deterministic dynamics, and it is shown that the cases of extinction and non-extinction equilibriums present different features. Mainly, non-extinction equilibria have associated a region of stochastic instability surrounded by a region of stochastic stability. The instability region does not exist in the case of extinction fixed points, and a linear Lyapunov function can be associated with them. Stochastically sustained oscillations of two subpopulations are also discussed in the case of complex eigenvalues of the stability matrix of the deterministic system.

A stochastic population dynamics model for Aedes aegypti: formulation and application to a city with temperate climate.

Aedes aegypti is the main vector for dengue and urban yellow fever. It is extended around the world not only in the tropical regions but also beyond them, reaching temperate climates. Because of its importance as a vector of deadly diseases, the significance of its distribution in urban areas and the possibility of breeding in laboratory facilities, Aedes aegypti is one of the best-known mosquitoes. In this work the biology of Aedes aegypti is incorporated into the framework of a stochastic population dynamics model able to handle seasonal and total extinction as well as endemic situations. The model incorporates explicitly the dependence with temperature. The ecological parameters of the model are tuned to the present populations of Aedes aegypti in Buenos Aires city, which is at the border of the present day geographical distribution in South America. Temperature thresholds for the mosquito survival are computed as a function of average yearly temperature and seasonal variation as well as breeding site availability. The stochastic analysis suggests that the southern limit of Aedes aegypti distribution in South America is close to the 15 degrees C average yearly isotherm, which accounts for the historical and current distribution better than the traditional criterion of the winter (July) 10 degrees C isotherm.

Modeling growth from the vapor and thermal annealing on micro- and nanopatterned substrates.

We propose a -dimensional mesoscopic model to describe the most relevant physical processes that take place while depositing and/or annealing micro- and nanopatterned solid substrates. The model assumes that a collimated incident beam impinges over the growing substrate; scattering effects in the vapor and reemission processes are introduced in a phenomenological way as an isotropic flow. Surface diffusion is included as the main relaxation process at the micro- or nanoscale. The stochastic model is built following population dynamics considerations; both stochastic simulations and the deterministic limit are analyzed. Numerical aspects regarding its implementation are also discussed. We study the shape-preserving growth mode, the coupling between shadowing effects and random fluctuations, and the spatial structure of noises using numerical simulations. We report important deviations from linear theories of surface diffusion when the interfaces are not compatible with the small slope approximation, including spontaneous formation of overhangs and nonexponential decay of pattern amplitudes. We discuss the dependence of stationary states with respect to the boundary conditions imposed on the system.

Probing universality classes in solid-on-solid deposition.

We consider several stochastic processes corresponding to the same physical solid-on-solid deposition problem. Simplified models presenting the same (conditional) mean and variance for each process are also introduced as well as generalizations in terms of the deposition of blobs and probabilistic deposition rules. We compare the evolution of the roughness as a function of time for a three-parameter family that includes as limit cases the Family model and the Edwards-Wilkinson equation, showing that in all cases the derived models with the same mean and variance are indistinguishable from the originating models in terms of the evolution of the roughness. Finally, we show that although all the models studied belong to the same universality class, some relevant features such as the final surface roughness are reproduced only for models within a restricted class determined by sharing the same (conditional) mean and variance.

Stochastic population dynamics: the Poisson approximation.

We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics of the populations is then the result of the projection from the space of events into the space of populations that determine the state of the system (phase space). The properties of the Poisson approximation are studied in detail. Especially, error bounds for the moment generating function and the generating function receive particular attention. The deterministic approximation for the population fractions and the Langevin-type approximation for the fluctuations around the mean value are recovered within the framework of the Poisson approximation as particular limit cases. However, the proposed framework allows to treat other limit cases and general situations with small populations that lie outside the scope of the standard approaches. The Poisson approximation can be viewed as a general (numerical) integration scheme for this family of problems in population dynamics.

Dynamics of solid growth under a gravitational field: influence of the formation of a diffusive layer.

We discuss the gravitational sedimentation of particles in terms of a stochastic model considering, in view of experimental evidence, that the aggregation to the growing surface (deposit) is mediated by the formation of a layer of suspended particles subject to gravitational forces, thermal agitation, as well as aggregation (contact) forces. The aggregation of such partially buoyant particles is ruled by the rates of occurrence of the different stochastic events: incorporation to the layer of suspended particles, sedimentation, and gravitationally biased diffusion. The model introduces bridges across different standard solid on solid deposition models which can be considered as limit cases of the present one. Analytical and numerical results show that for finite (realistic) deposits there are different regimes of aggregation including situations in which the deposit is grown completely during the transient time of the system.

Global bifurcations in a laser with injected signal: Beyond Adler's approximation.

We discuss the dynamics in the laser with an injected signal from a perturbative point of view showing how different aspects of the dynamics get their definitive character at different orders in the perturbation scheme. At the lowest order Adler's equation [Proc. IRE 34, 351 (1946)] is recovered. More features emerge at first order including some bifurcations sets and the global reinjection conjectured in Physica D 109, 293 (1997). The type of codimension-2 bifurcations present can only be resolved at second order. We show that of the two averaging approximations proposed [Opt. Commun. 111, 173 (1994); Quantum Semiclassic. Opt. 9, 797 (1997); Quantum Semiclassic. Opt. 8, 805 (1996)] differing in the second order terms, only one is accurate to the order required, hence, solving the apparent contradiction among these results. We also show in numerical studies how a homoclinic orbit of the Sil'nikov type, bifurcates into a homoclinic tangency of a periodic orbit of vanishing amplitude. The local vector field at the transition point contains a Hopf-saddle-node singularity, which becomes degenerate and changes type. The overall global bifurcation is of codimension-3. The parameter governing this transition is theta, the cavity detuning (with respect to the atomic frequency) of the laser. (c) 2001 American Institute of Physics.