Dynamics of infection with multiple transmission mechanisms in unmanaged/managed animal populations

Deterministic and stochastic models motivated by Salmonella transmission in unmanaged/managed populations are studied. The SIRS models incorporate three routes of transmission (direct, vertical and indirect via free-living infectious units in the environment). With deterministic models we are able to understand the effects of different routes of transmission and other epidemiological factors on infection dynamics. In particular, vertical transmission has little influence on this dynamics, whereas the higher the indirect (direct) transmission rate the greater the tendency to persistent oscillation (stable endemic states). We show that the sustained cycles are also prone to demographic effect, i.e., persistent oscillation becomes impossible in the managed case (in the sense of balanced recruitment and death rates) by comparing with results in unmanaged populations (exponential population dynamics). Further, approximations of quasi-stationary distributions are derived for stochastic versions of the proposed models based on a diffusion approximation to the infection process. The effect of transmission parameters on the ratio of mean to standard deviation of the approximating distribution, used to judge the validity of the approximations and the expected time until fade out of infection, is further discussed. We conclude that strengthening any route of transmission may or may not reduce the expected time to fade out of infection, depending on the population dynamics.     

Modeling the spread of methicillin-resistant Staphylococcus aureus in nursing homes for elderly

Methicillin-resistant Staphylococcus aureus (MRSA) is endemic in many hospital settings, including nursing homes. It is an important nosocomial pathogen that causes mortality and an economic burden to patients, hospitals, and the community. The epidemiology of the bacteria in nursing homes is both hospital- and community-like. Transmission occurs via hands of health care workers (HCWs) and direct contacts among residents during social activities. In this work, mathematical modeling in both deterministic and stochastic frameworks is used to study dissemination of MRSA among residents and HCWs, persistence and prevalence of MRSA in a population, and possible means of controlling the spread of this pathogen in nursing homes. The model predicts that: (i) without strict screening and decolonization of colonized individuals at admission, MRSA may persist; (ii) decolonization of colonized residents, improving hand hygiene in both residents and HCWs, reducing the duration of contamination of HCWs, and decreasing the resident∶staff ratio are possible control strategies; (iii) the mean time that a resident remains susceptible since admission may be prolonged by screening and decolonization treatment in colonized individuals; (iv) in the stochastic framework, the total number of colonized residents varies and may increase when the admission of colonized residents, the duration of colonization, the average number of contacts among residents, or the average number of contacts that each resident requires from HCWs increases; (v) an introduction of a colonized individual into an MRSA-free nursing home has a much higher probability of leading to a major outbreak taking off than an introduction of a contaminated HCW.     

Extinction risk of a meta-population: aggregation approach

Aggregation of variables of a complex mathematical model with realistic structure gives a simplified model which is more suitable than the original one when the amount of data for parameter estimation is limited. Here we explore use of a formula derived for a single unstructured population (canonical model) in predicting the extinction time for a population living in multiple habitats. In particular we focus multiple populations each following logistic growth with demographic and environmental stochasticities, and examine how the mean extinction time depends on the migration and environmental correlation. When migration rate and/or environmental correlation are very large or very small, we may express the mean extinction time exactly using the formula with properly modified parameters. When parameters are of intermediate magnitude, we generate a Monte Carlo time series of the population size for the realistic structured model, estimate the "effective parameters" by fitting the time series to the canonical model, and then calculate the mean extinction time using the formula for a single population. The mean extinction time predicted by the formula was close to those obtained from direct computer simulation of structured models. We conclude that the formula for an unstructured single-population model has good approximation capability and can be applicable in estimating the extinction risk of the structured meta-population model for a limited data set.     

The Dynamic Behavior Possibilities of Raft-Like Domains in Biological Membranes

A possible scenario of the behavior of a raft-like domain system oscillating near the phase transition point of the Verchulst transition type, when the form of the stationary distribution for the concentration of domains changes stepwise, has been considered. A stationary state of the system is also possible at the indicated phase transition point, as well as fluctuations in the state of the system between the modes of extinction and survival, if the analogy with the Verhulst model is applied. The system behavior is explored in the framework of the stochastic storage model. This model is compared with the Verhulst model of a biological population. Similarities and differences between the models are highlighted. There are no bifurcations and transition to chaos in the domain system. Other features and characteristics of the dynamic behavior and stationary states of the raft-like domain system are considered.     

Efficacy of infection control interventions in reducing the spread of multidrug-resistant organisms in the hospital setting

Multidrug-resistant organisms (MDRO) continue to spread in hospitals globally, but the population-level impact of recommended preventive strategies and the relative benefit of individual strategies targeting all MDRO in the hospital setting are unclear. To explore the dynamics of MDRO transmission in the hospital, we develop a model extending data from clinical individual-level studies to quantify the impact of hand hygiene, contact precautions, reducing antimicrobial exposure and screening surveillance cultures in decreasing the prevalence of MDRO colonization and infection. The effect of an ongoing increase in the influx of patients colonized with MDRO into the hospital setting is also quantified. We find that most recommended strategies have substantial effect in decreasing the prevalence of MDRO over time. However, screening for asymptomatic MDRO colonization among patients who are not receiving antimicrobials is of minimal value in reducing the spread of MDRO.     

Relative significance of direct and indirect effects of predation by planktivorous fish on zooplankton

One of the most obvious features of tropical lakes and reservoirs is the small body size of their zooplankton taxa. It is believed that this is the result of high and persistent predation by abundant planktivorous fish, which select large-bodied zooplankton prey thus making them more vulnerable to extinction in tropical as compared to temperate habitats. Do these extinctions result directly from fish predation? Could the high predation-induced mortality alone be responsible for an extermination of the population from a habitat? Or could indirect effects of predation be responsible? Some important indirect effects can be seen at the demographic level; these include reduced reproduction in the population resulting from higher vulnerability of ovigerous females to predation by visually oriented planktivores. Other important indirect effects can be observed at the individual level; these include shifts in behavior (from foraging to predator avoidance) and adjustments in physiology (from high to low feeding rate) in those planktonic animals which detect danger from their predators by sensing either the ‘predator odor’ or an ‘alarm substance’ originating from injured conspecific prey. Although a zooplankton species density may mostly result from the brutal force of direct predator impact on the population (mortality), it is more likely that its distribution in time and space could be attributed to a combination of indirect effects of predation on individual behavior and physiology. An example of periodicity in density and depth distribution patterns of Cahora Bassa zooplankton species and their periodic exterminations seems to confirm the role of indirect effects of predation by planktivorous fish.     

Understanding evolutionary and ecological dynamics using a continuum limit

Continuum limits in the form of stochastic differential equations are typically used in theoretical population genetics to account for genetic drift or more generally, inherent randomness of the model. In evolutionary game theory and theoretical ecology, however, this method is used less frequently to study demographic stochasticity. Here, we review the use of continuum limits in ecology and evolution. Starting with an individual‐based model, we derive a large population size limit, a (stochastic) differential equation which is called continuum limit. By example of the Wright–Fisher diffusion, we outline how to compute the stationary distribution, the fixation probability of a certain type, and the mean extinction time using the continuum limit. In the context of the logistic growth equation, we approximate the quasi‐stationary distribution in a finite population.     

Effects of directional environmental change on extinction dynamics in experimental microbial communities are predicted by a simple model

Global temperatures are expected to rise between 1.1 and 6.4°C over the next 100 years, although the exact rate will depend on future greenhouse emissions, and will vary spatially. Temperature can alter an individual's metabolic rate, and consequently birth and death rates. In declining populations, these alterations may manifest as changes in the rate of that population's decline, and subsequently the timing of extinction events. Predicting such events could therefore be of considerable use. We use a small‐scale experimental system to investigate how the rate of temperature change can alter a population's time to extinction, and whether it is possible to predict this event using a simple phenomenological model that incorporates information about population dynamics at a constant temperature, published scaling of metabolic rates, and temperature. In addition, we examine 1) the relative importance of the direct effects of temperature on metabolic rate, and the indirect effects (via temperature driven changes in body size), on predictive accuracy (defined as the proximity of the predicted date of extinction to the mean observed date of extinction), 2) the combinations of model parameters that maximise accuracy of predictions, and 3) whether substituting temperature change through time with mean temperature produces accurate predictions. We find that extinction occurs earlier in environments that warm faster, and this can be accurately predicted (R² > 0.84). Increasing the number of parameters that were temperature‐dependent increased the model's accuracy, as did scaling these temperature‐dependent parameters with either the direct effects of temperature alone, or with the direct and indirect effects. Using mean temperature through time instead of actual temperature produces less accurate predictions of extinction. These results suggest that simple phenomenological models, incorporating metabolic theory, may be useful in understanding how environmental change can alter a population's rate of extinction. Synthesis Understanding how populations will respond to future climatic change is a key goal in ecology, however the exact rate of future warming will vary both spatially and temporally. Consequently, mathematical models must be used to understand the potential range of future population dynamics under various warming scenarios. We use a combination of experimentation and modelling to show that the effects of varying rates of environmental change on population dynamics can be predicted by a simple model. However, the accuracy of these predictions depends upon, amongst other things, a detailed knowledge of how temperature will change over time, rather than approximating this change to mean temperature.     

A neutral model with fluctuating population size and its effective size

We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.     

One-stage full-mouth disinfection to overcome intra-oral transmission of periodontopathogens

The oral cavity offers a range of different niches where periodontopathogens can adhere and survive (e.g. the mucosa, the tongue, the tonsils, the saliva and all intra-oral hard surfaces such as teeth, dentures, oral implants). Transmission of bacteria from one niche to another is likely to occur. Recent studies, for example, illustrated that initially sterile abutments of oral implants were rapidly colonized by bacteria from the subgingival environment around teeth. This transmission of bacteria can occur spontaneously via the saliva, or by means of oral hygiene aids and/or dental instruments. Such an intra-oral transmission, if it occurs at a high speed, could jeopardize the outcome of periodontal therapy. To overcome a bacterial transmission, a 'one-stage full-mouth disinfection' was recently introduced for the treatment of periodontal infections. This new treatment strategy resulted in significant clinical and microbiological improvements when compared with the standard sequential treatment.     

Thresholds of color attribute differences in detecting camouflaged textures

We examined the threshold at which a camouflaged color texture pattern (target) embedded in a surrounding colored texture pattern (background) was discriminated by making the difference between their color distributions serve as a cue. The texture consisted of 900 colored disks. The color applied to the disk was chosen from a normal distribution with the mean and the standard deviation set beforehand. The mean of the background's distribution was a standard achromatic color set at L*=40, u*=0, and v*=0 of CIELUV. In experiment 1, the mean of the target's color distribution was shifted from the background's one. The threshold for the mean of the target's color distribution depended on the standard deviation and increased as the standard deviation became bigger. In experiment 2, the standard deviation of the target's color distribution was shifted. There was the slight dependence of threshold of the standard deviation of the target's distribution on that of the background's distribution. In experiment 3, both of the mean and the standard deviation of the target's color distribution were shifted at the same time. The threshold was not determined by each of the mean and the standard deviation independently. There seemed to be some compensating contribution between them to each other. The threshold could be characterized by Doyle metric or modified Doyle metric.     

Quantification of the effect of control strategies on classical swine fever epidemics

Emergency vaccination during an epidemic of classical swine fever virus (CSFV) has become a serious option because of the ethical problems of strategies with massive culling and the availability of a marker vaccine that reduces virus transmission. Here we present a model of between-herd CSFV transmission, which quantifies the effect of control strategies with and without vaccination. We estimate the model parameters from data of the Dutch CSFV epidemic of 1997/1998. With the model, a set of control strategies is compared, consisting of five control measures in several combinations. Consequently, the following general requirements of successful strategies can be formulated. First, to achieve extinction of a CSFV epidemic, transmission through transport should be prevented and the indirect virus transmission, i.e. all transmission not through animal contacts, should at least be halved, either by vaccination or by culling of the susceptible pig population. Second, to minimize the size and duration of an epidemic, the extinction requirements should be met quickly and indirect virus transmission should be reduced by far more than a half. Although the origin of the model parameters let the requirements in fact be only applicable for the south-eastern part of the Netherlands, it is argued that epidemics in other areas will not need stricter control strategies.     

Probability Density Function of the Red Cell Membrane Permeability Coefficient

The distribution of a random variable is determined by the probability density functions (PDF) of all other random variables with which the variable in question is jointly distributed. If the PDF of the random variable of interest is normal, or skewed normal, then the distributions with which it is jointly distributed determine its mean and standard deviation. In the case described here (where hemolysis time of the red blood cell is a function of the permeability coefficient and geometric variables of the cell) the mean and standard deviation of the permeability coefficient and the known distributions of the geometric variables on which the hemolysis time depends determine a predicted distribution of hemolysis time. An observed distribution of the hemolysis time is obtained spectrophotometrically. By choosing the mean and standard deviation of the permeability coefficient so that the predicted PDF of the hemolysis time matches the observed PDF best by least-squares criterion, the complete distribution of the permeability coefficient is determined.     

Timing of diapause in relation to temporally variable catastrophes

This paper analyses the response of the distribution of diapause switching times in an arthropod population with respect to variation in a catastrophe, which kills nondiapause individuals. For concreteness, the catastrophe will be taken to the onset of winter. The relationship between an individual's switching time and the decision whether to diapause is defined as follows: If she passes through the end of the sensitive period, during which the diapause decision is made, before her switching time, she will complete development and reproduce rather than diapause. If she passes through the sensitive period on or after her switching time, she will diapause. The model follows the evolution of the distribution of switching times for a population over a sequence of years. Random variation in the end of the season is created by sampling from a normal distribution of times at the end of the growing season. The model is for a haploid population in which the distribution of switching times that a female passes to her offspring is normally distributed having her switching time as its mean. This approximates a sexual population with strong positive assortative mating and heritability near 1. This mode of inheritance permits a rapid response to yearly changes in the end of the season as a contrast to earlier models, which incorporated a slow response. Patterns of temporal change in the median switching time are analyzed. The influences of three parameters are considered: the mean and standard deviation of the end of the season, and standard deviation of the offspring distribution. The main conclusion differs from the results of earlier models in that the end of the season must be extremely variable before the median of the distribution of switching times displays conservative behavior, i. e., before it becomes significantly earlier than the median expected when the end of the season is constant and equal to the mean of the normal distribution for the end of the season used in the simulation. Previous models predicted a conservative response even in moderately variable environments.     

Auscultatory indirect measurement of blood pressure in dogs

An indirect method of measuring blood pressure (cuff plus stethoscope) was evaluated in 70 dogs weighing 15 to 30 kg (17.5 +/- 8.8 kg; mean +/- standard deviation). A cuff 12 cm wide was used. The measurements were most audible with the cuff on the upper foreleg of the dog and with the stethoscope placed in the medial epicondylar region just distal to the cuff. The cuff was inflated to greater than systolic pressure and allowed to deflate slowly. In 70 lightly sedated dogs, systolic blood pressures averaged 145 +/- 25 mmHg (mean +/- standard deviation) and diastolic blood pressures averaged 84 +/- 14 mmHg. Indirect measurements were compared to direct measurements (femoral arterial catheter). Systolic pressures obtained by this direct method averaged 138 +/- 29 mmHg (mean +/- standard deviation) and diastolic pressures averaged 84 +/- 17 mmHg. The correlation coefficient for systolic pressure was 0.96 and for diastolic pressure 0.97.     

On being the right size: the impact of population size and stochastic effects on the evolution of drug resistance in hospitals and the community

The evolution of drug resistant bacteria is a severe public health problem, both in hospitals and in the community. Currently, some countries aim at concentrating highly specialized services in large hospitals in order to improve patient outcomes. Emergent resistant strains often originate in health care facilities, but it is unknown to what extent hospital size affects resistance evolution and the resulting spillover of hospital-associated pathogens to the community. We used two published datasets from the US and Ireland to investigate the effects of hospital size and controlled for several confounders such as antimicrobial usage, sampling frequency, mortality, disinfection and length of stay. The proportion of patients acquiring both sensitive and resistant infections in a hospital strongly correlated with hospital size. Moreover, we observe the same pattern for both the percentage of resistant infections and the increase of hospital-acquired infections over time. One interpretation of this pattern is that chance effects in small hospitals impede the spread of drug-resistance. To investigate to what extent the size distribution of hospitals can directly affect the prevalence of antibiotic resistance, we use a stochastic epidemiological model describing the spread of drug resistance in a hospital setting as well as the interaction between one or several hospitals and the community. We show that the level of drug resistance typically increases with population size: In small hospitals chance effects cause large fluctuations in pathogen population size or even extinctions, both of which impede the acquisition and spread of drug resistance. Finally, we show that indirect transmission via environmental reservoirs can reduce the effect of hospital size because the slow turnover in the environment can prevent extinction of resistant strains. This implies that reducing environmental transmission is especially important in small hospitals, because such a reduction not only reduces overall transmission but might also facilitate the extinction of resistant strains. Overall, our study shows that the distribution of hospital sizes is a crucial factor for the spread of drug resistance.     

Logistic distributed activation energy model--part 2: application to cellulose pyrolysis

The pyrolysis behavior of cellulose has been investigated by using thermogravimetric analysis (TGA). The non-isothermal TGA data obtained at different heating rates have been analyzed simultaneously. Pattern Search Method has been proposed for the estimation of the model parameter values. Predicted values from the logistic distributed activation energy model have been compared with the experimental data and the results have indicated that the model describes the kinetic behavior of cellulose pyrolysis very well. The mean value and standard deviation of the logistic activation energy distribution for cellulose pyrolysis are found to be 258.5718 kJ mol(-1) and 2.6601 kJ mol(-1), the reaction order is 1.1101 and the k(0) is 1.6218×10(17) s(-1).     

Behavior of bird cherry-oat aphid and green peach aphid in relation to potato virus Y transmission

Potato virus Y is transmitted to potato in a nonpersistent manner by many aphid species, some of which do not colonize this crop. The behavior of bird cherry-oat aphid, Rhopalosiphum padi (L.) on potato, Solanum tuberosum L., a plant species that is not colonized by this aphid, was described and compared with that of the potato-colonizing green peach aphid, Myzuspersicae (Sulzer). A higher proportion of winged morph of R. padi than M. persicae left the plant, but aphids that stayed in contact with the plant took the same mean time to initiate the first probe and it lasted the same mean time compared with M. persicae. Electronic penetration graph technique was used to study the probing behavior of the aphids during Potato virus Y (family Potyviridae, genus Potyvirus, PVY) transmission tests. Transmission rate decreased from 29 to 8% when the acquisition time increased from 5 min of continuous probing to 1 h with M. persicae, but it remained low (2 and 1%) with R. padi. Most of the difference in transmission rate between acquisition time with M. persicae and between aphid species was related to the change in the time and behavior taking place between the last cell puncture of the acquisition phase to the first cell puncture of the inoculation phase. Results presented here clearly demonstrated the importance of host plant selection and probing behavior in the transmission of nonpersistent plant viruses. They also stress the need to consider the behavior of the aphid in the design of laboratory tests of virus vector efficacy.     

Dynamic-persistence of cooperation in public good games when group size is dynamic

The evolution of cooperation is possible with a simple model of a population of agents that can move between groups. The agents play public good games within their group. The relative fitness of individuals within the whole population affects their number of offspring. Groups of cooperators evolve but over time are invaded by defectors which eventually results in the group's extinction. However, for small levels of migration and mutation, high levels of cooperation evolve at the population level. Thus, evolution of cooperation based on individual fitness without kin selection, indirect or direct reciprocity is possible. We provide an analysis of the parameters that affect cooperation, and describe the dynamics and distribution of population sizes over time.     

Modeling routes of chronic wasting disease transmission: environmental prion persistence promotes deer population decline and extinction

Chronic wasting disease (CWD) is a fatal disease of deer, elk, and moose transmitted through direct, animal-to-animal contact, and indirectly, via environmental contamination. Considerable attention has been paid to modeling direct transmission, but despite the fact that CWD prions can remain infectious in the environment for years, relatively little information exists about the potential effects of indirect transmission on CWD dynamics. In the present study, we use simulation models to demonstrate how indirect transmission and the duration of environmental prion persistence may affect epidemics of CWD and populations of North American deer. Existing data from Colorado, Wyoming, and Wisconsin's CWD epidemics were used to define plausible short-term outcomes and associated parameter spaces. Resulting long-term outcomes range from relatively low disease prevalence and limited host-population decline to host-population collapse and extinction. Our models suggest that disease prevalence and the severity of population decline is driven by the duration that prions remain infectious in the environment. Despite relatively low epidemic growth rates, the basic reproductive number, R(0), may be much larger than expected under the direct-transmission paradigm because the infectious period can vastly exceed the host's life span. High prion persistence is expected to lead to an increasing environmental pool of prions during the early phases (i.e. approximately during the first 50 years) of the epidemic. As a consequence, over this period of time, disease dynamics will become more heavily influenced by indirect transmission, which may explain some of the observed regional differences in age and sex-specific disease patterns. This suggests management interventions, such as culling or vaccination, will become increasingly less effective as CWD epidemics progress.