On a size-structured two-phase population model with infinite states-at-birth

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states.

Optimal latent period in a bacteriophage population model structured by infection-age

We study the lysis timing of a bacteriophage population by means of a continuously infection-age-structured population dynamics model. The features of the model are the infection process of bacteria, the natural death process, and the lysis process which means the replication of bacteriophage viruses inside bacteria and the destruction of them. We consider that the length of the lysis timing (or latent period) is distributed according to a general probability distribution function. We have carried out an optimization procedure and we have found the latent period corresponding to the maximal fitness (i.e. maximal growth rate) of the bacteriophage population.

Oscillations in a molecular structured cell population model

We consider a nonlinear cyclin content structured model of a cell population divided into proliferative and quiescent cells. We show, for particular values of the parameters, existence of solutions that do not depend on the cyclin content. We make numerical simulations for the general case obtaining, for some values of the parameters convergence to the steady state but also oscillations of the population for others.

Stochastic Dynamic Northern Corn Rootworm Population Model, January 2000

A complete life cycle model for northern corn rootworm, Diabrotica barberi Smith and Lawrence, is developed using a published single-season model of adult population dynamics and data from field experiments. Temperature-dependent development and age-dependent advancement determine adult population dynamics and oviposition, while a simple stochastic hatch and density-dependent larval survival model determine adult emergence. Dispersal is not modeled. To evaluate the long-run performance of the model, stochastically generated daily air and soil temperatures are used for 100-year simulations for a variety of corn planting and flowering dates in Ithaca, NY, and Brookings, SD. Once the model is corrected for a bias in oviposition, model predictions for both locations are consistent with anecdotal field data. Extinctions still occur, but these may be consistent with northern corn rootworm metapopulation dynamics.

Optimal latent period in a bacteriophage population model structured by infection-age

We study the lysis timing of a bacteriophage population by means of a continuously infection-age-structured population dynamics model. The features of the model are the infection process of bacteria, the death process, and the lysis process which means the replication of bacteriophage viruses inside bacteria and the destruction of them. The time till lysis (or latent period) is assumed to have an arbitrary distribution. We have carried out an optimization procedure, and we have found that the latent period corresponding to maximal fitness (i.e. maximal growth rate of the bacteriophage population) is of fixed length. We also study the dependence of the optimal latent period on the amount of susceptible bacteria and the number of virions released by a single infection. Finally, the evolutionarily stable strategy of the latent period is also determined as a fixed period taking into account that super-infections are not considered

Complex Transition to Cooperative Behavior in a Structured Population Model

Cooperation plays an important role in the evolution of species and human societies. The understanding of the emergence and persistence of cooperation in those systems is a fascinating and fundamental question. Many mechanisms were extensively studied and proposed as supporting cooperation. The current work addresses the role of migration for the maintenance of cooperation in structured populations. This problem is investigated in an evolutionary perspective through the prisoner's dilemma game paradigm. It is found that migration and structure play an essential role in the evolution of the cooperative behavior. The possible outcomes of the model are extinction of the entire population, dominance of the cooperative strategy and coexistence between cooperators and defectors. The coexistence phase is obtained in the range of large migration rates. It is also verified the existence of a critical level of structuring beyond that cooperation is always likely. In resume, we conclude that the increase in the number of demes as well as in the migration rate favor the fixation of the cooperative behavior.

Evaluating Effects of Everglades Restoration on American Crocodile Populations in South Florida Using a Spatially-Explicit, Stage-Based Population Model

The distribution and abundance of the American crocodile (Crocodylus acutus) in the Florida Everglades is dependent on the timing, amount, and location of freshwater flow. One of the goals of the Comprehensive Everglades Restoration Plan (CERP) is to restore historic freshwater flows to American crocodile habitat throughout the Everglades. To predict the impacts on the crocodile population from planned restoration activities, we created a stage-based spatially explicit crocodile population model that incorporated regional hydrology models and American crocodile research and monitoring data. Growth and survival were influenced by salinity, water depth, and density-dependent interactions. A stage-structured spatial model was used with discrete spatial convolution to direct crocodiles toward attractive sources where conditions were favorable. The model predicted that CERP would have both positive and negative impacts on American crocodile growth, survival, and distribution. Overall, crocodile populations across south Florida were predicted to decrease approximately 3 % with the implementation of CERP compared to future conditions without restoration, but local increases up to 30 % occurred in the Joe Bay area near Taylor Slough, and local decreases up to 30 % occurred in the vicinity of Buttonwood Canal due to changes in salinity and freshwater flows.

Intraocular penetration of penciclovir after oral administration of famciclovir: a population pharmacokinetic model.

OBJECTIVES: We developed a population model that describes the ocular penetration and pharmacokinetics of penciclovir in human aqueous humour and plasma after oral administration of famciclovir. METHODS: Fifty-three patients undergoing cataract surgery received a single oral dose of 500 mg of famciclovir prior to surgery. Concentrations of penciclovir in both plasma and aqueous humour were measured by HPLC with fluorescence detection. Concentrations in plasma and aqueous humour were fitted using a two-compartment model (NONMEM software). Inter-individual and intra-individual variabilities were quantified and the influence of demographics and physiopathological and environmental variables on penciclovir pharmacokinetics was explored. RESULTS: Drug concentrations were fitted using a two-compartment, open model with first-order transfer rates between plasma and aqueous humour compartments. Among tested covariates, creatinine clearance, co-intake of angiotensin-converting enzyme inhibitors and body weight significantly influenced penciclovir pharmacokinetics. Plasma clearance was 22.8 ± 9.1 L/h and clearance from the aqueous humour was 8.2 × 10(-5) L/h. AUCs were 25.4 ± 10.2 and 6.6 ± 1.8 μg · h/mL in plasma and aqueous humour, respectively, yielding a penetration ratio of 0.28 ± 0.06. Simulated concentrations in the aqueous humour after administration of 500 mg of famciclovir three times daily were in the range of values required for 50% growth inhibition of non-resistant strains of the herpes zoster virus family. CONCLUSIONS: Plasma and aqueous penciclovir concentrations showed significant variability that could only be partially explained by renal function, body weight and comedication. Concentrations in the aqueous humour were much lower than in plasma, suggesting that factors in the blood-aqueous humour barrier might prevent its ocular penetration or that redistribution occurs in other ocular compartments.

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

Mechanistic population Models in Biology: Model Derivation and Application

In general, models of ecological systems can be broadly categorized as ’top-down’ or ’bottom-up’ models, based on the hierarchical level that the model processes are formulated on. The structure of a top-down, also known as phenomenological, population model can be interpreted in terms of population characteristics, but it typically lacks an interpretation on a more basic level. In contrast, bottom-up, also known as mechanistic, population models are derived from assumptions and processes on a more basic level, which allows interpretation of the model parameters in terms of individual behavior. Both approaches, phenomenological and mechanistic modelling, can have their advantages and disadvantages in different situations. However, mechanistically derived models might be better at capturing the properties of the system at hand, and thus give more accurate predictions. In particular, when models are used for evolutionary studies, mechanistic models are more appropriate, since natural selection takes place on the individual level, and in mechanistic models the direct connection between model parameters and individual properties has already been established. The purpose of this thesis is twofold. Firstly, a systematical way to derive mechanistic discrete-time population models is presented. The derivation is based on combining explicitly modelled, continuous processes on the individual level within a reproductive period with a discrete-time maturation process between reproductive periods. Secondly, as an example of how evolutionary studies can be carried out in mechanistic models, the evolution of the timing of reproduction is investigated. Thus, these two lines of research, derivation of mechanistic population models and evolutionary studies, are complementary to each other.

Towards a model-based integration of co-registered electroencephalography/functional magnetic resonance imaging data with realistic neural population meshes

Brain activity can be measured with several non-invasive neuroimaging modalities, but each modality has inherent limitations with respect to resolution, contrast and interpretability. It is hoped that multimodal integration will address these limitations by using the complementary features of already available data. However, purely statistical integration can prove problematic owing to the disparate signal sources. As an alternative, we propose here an advanced neural population model implemented on an anatomically sound cortical mesh with freely adjustable connectivity, which features proper signal expression through a realistic head model for the electroencephalogram (EEG), as well as a haemodynamic model for functional magnetic resonance imaging based on blood oxygen level dependent contrast (fMRI BOLD). It hence allows simultaneous and realistic predictions of EEG and fMRI BOLD from the same underlying model of neural activity. As proof of principle, we investigate here the influence on simulated brain activity of strengthening visual connectivity. In the future we plan to fit multimodal data with this neural population model. This promises novel, model-based insights into the brain's activity in sleep, rest and task conditions.

Prediction of residential radon exposure of the whole Swiss population: comparison of model-based predictions with measurement-based predictions

Radon plays an important role for human exposure to natural sources of ionizing radiation. The aim of this article is to compare two approaches to estimate mean radon exposure in the Swiss population: model-based predictions at individual level and measurement-based predictions based on measurements aggregated at municipality level. A nationwide model was used to predict radon levels in each household and for each individual based on the corresponding tectonic unit, building age, building type, soil texture, degree of urbanization, and floor. Measurement-based predictions were carried out within a health impact assessment on residential radon and lung cancer. Mean measured radon levels were corrected for the average floor distribution and weighted with population size of each municipality. Model-based predictions yielded a mean radon exposure of the Swiss population of 84.1 Bq/m(3) . Measurement-based predictions yielded an average exposure of 78 Bq/m(3) . This study demonstrates that the model- and the measurement-based predictions provided similar results. The advantage of the measurement-based approach is its simplicity, which is sufficient for assessing exposure distribution in a population. The model-based approach allows predicting radon levels at specific sites, which is needed in an epidemiological study, and the results do not depend on how the measurement sites have been selected.

Demographic model of the Swiss cattle population for the years 2009-2011 stratified by gender, age and production type

Demographic composition and dynamics of animal and human populations are important determinants for the transmission dynamics of infectious disease and for the effect of infectious disease or environmental disasters on productivity. In many circumstances, demographic data are not available or of poor quality. Since 1999 Switzerland has been recording cattle movements, births, deaths and slaughter in an animal movement database (AMD). The data present in the AMD offers the opportunity for analysing and understanding the dynamic of the Swiss cattle population. A dynamic population model can serve as a building block for future disease transmission models and help policy makers in developing strategies regarding animal health, animal welfare, livestock management and productivity. The Swiss cattle population was therefore modelled using a system of ordinary differential equations. The model was stratified by production type (dairy or beef), age and gender (male and female calves: 0-1 year, heifers and young bulls: 1-2 years, cows and bulls: older than 2 years). The simulation of the Swiss cattle population reflects the observed pattern accurately. Parameters were optimized on the basis of the goodness-of-fit (using the Powell algorithm). The fitted rates were compared with calculated rates from the AMD and differed only marginally. This gives confidence in the fitted rates of parameters that are not directly deductible from the AMD (e.g. the proportion of calves that are moved from the dairy system to fattening plants).

Population pharmacokinetics of perhexiline from very sparse, routine monitoring data

Using NONMEM, the population pharmacokinetics of perhexiline were studied in 88 patients (34 F, 54 M) who were being treated for refractory angina. Their mean +/- SD (range) age was 75 +/- 9.9 years (46-92), and the length of perhexiline treatment was 56 +/- 77 weeks (0.3-416). The sampling time after a dose was 14.1 +/- 21.4 hours (0.5-200), and the perhexiline plasma concentrations were 0.39 +/- 0.32 mg/L (0.03-1.56). A one-compartment model with first-order absorption was fitted to the data using the first-order (FO) approximation. The best model contained 2 subpopulations (obtained via the $MIXTURE subroutine) of 77 subjects (subgroup A) and 11 subjects (subgroup B) that had typical values for clearance (CL/F) of 21.8 L/h and 2.06 L/h, respectively. The volumes of distribution (V/F) were 1470 L and 260 L, respectively, which suggested a reduction in presystemic metabolism in subgroup B. The interindividual variability (CV%) was modeled logarithmically and for CL/F ranged from 69.1% (subgroup A) to 86.3% (subgroup B). The interindividual variability in V/F was 111%. The residual variability unexplained by the population model was 28.2%. These results confirm and extend the existing pharmacokinetic data on perhexiline, especially the bimodal distribution of CL/F manifested via an inherited deficiency in hepatic and extrahepatic CYP2D6 activity.