Structured Population Dynamics Model Research Articles

PASCAR: a multiscale framework to explore the design space of constitutive and inducible CAR T cells.

CAR T cells are engineered to bind and destroy tumor cells by targeting overexpressed surface antigens. However, healthy cells expressing lower abundances of these antigens can also be lysed by CAR T cells. Various CAR T cell designs increase tumor cell elimination, whereas reducing damage to healthy cells. However, these efforts are costly and labor-intensive, constraining systematic exploration of potential hypotheses. We develop a protein abundance structured population dynamic model for CAR T cells (PASCAR), a framework that combines multiscale population dynamic models and multi-objective optimization approaches with data from cytometry and cytotoxicity assays to systematically explore the design space of constitutive and tunable CAR T cells. PASCAR can quantitatively describe in vitro and in vivo results for constitutive and inducible CAR T cells and can successfully predict experiments outside the training data. Our exploration of the CAR design space reveals that optimal CAR affinities in the intermediate range of dissociation constants effectively reduce healthy cell lysis, whereas maintaining high tumor cell-killing rates. Furthermore, our modeling offers guidance for optimizing CAR expressions in synthetic notch CAR T cells. PASCAR can be extended to other CAR immune cells.

A Bayesian stock assessment of the eastern Pacific gray whale using abundance and harvest data from 1967-1996

Abundance and harvest data since 1966/67 were used to assess the eastern Pacific stock of gray whales. A Bayesian statistical method was used to estimate probability distributions for the parameters of both a simple and an age and sex structured population dynamics model, as well as output quantities of interest. Model comparisons using the Bayes Factor provided conclusive evidence that an additional parameter should be used to account for unexplained variation in the abundance time series. Incorporating the additional variance parameter decreased the precision of the estimates of the other parameters. Point estimates of carrying capacity ranged from 24,640-31,840 for the different models, but the posterior distributions from the selected models were very broad and excluded few values. The current depletion level (population size as a fraction of carrying capacity) was estimated to be about 0.75, with a lower 2.5th percentile of 0.36. The probability that the population was still below one-half of its carrying capacity was estimated to be 0.21, with a corresponding probability of 0.28 that the population was still below its maximum sustainable yield level. Quantities from which catch limits could potentially be calculated were estimated, including current replacement yield, maximum sustainable yield and the quantity Q1 (described in Wade and Givens, 1997).

Correction To "Null controllability of a nonlinear age, space and two-sex structured population dynamics model"

Correction To "Null controllability of a nonlinear age, space and two-sex structured population dynamics model"

Null controllability of a nonlinear age, space and two-sex structured population dynamics model

<p style='text-indent:20px;'>In this paper, we study the null controllability of a nonlinear age, space and two-sex structured population dynamics model. This model is such that the nonlinearity and the couplage are at birth level. We consider a population with males and females and we are dealing with two cases of null controllability problems.</p><p style='text-indent:20px;'>The first problem is related to the total extinction, which means that, we estimate a time <inline-formula><tex-math id="M1">\begin{document}$ T $\end{document}</tex-math></inline-formula> to bring the male and female subpopulation density to zero. The second case concerns null controllability of male or female subpopulation. Since the absence of males or females in the population stops births; so, if we have the total extinction of the females at time <inline-formula><tex-math id="M2">\begin{document}$ T, $\end{document}</tex-math></inline-formula> and if <inline-formula><tex-math id="M3">\begin{document}$ A $\end{document}</tex-math></inline-formula> is the life span of the individuals, at time <inline-formula><tex-math id="M4">\begin{document}$ T+A $\end{document}</tex-math></inline-formula> one will get certainly the total extinction of the population. Our method uses first an observability inequality related to the adjoint of an auxiliary system, a null controllability of the linear auxiliary system, and after the Schauder's fixed point theorem.</p>

Modelling the potential consequences of adaptive closure management in a penaeid trawl fishery

Spatial management of fishing effort can be used to avoid catching undesirable size classes for target species, and improve yield-per-recruit for the exploited stock. Adaptive closure management has been proposed as a means to more effectively utilise spatial management, however these management provisions often lack quantitative evaluation which constrains the information available to inform decisions. We demonstrate the use of a spatially and size structured population dynamics model to evaluate the potential impact of spatial management on a multijurisdictional fishery for a highly migratory species (eastern king prawn, Penaeus [Melicertus] plebejus). Under current conditions in the fishery, the overall effect of closures on harvest was estimated to be comparatively minor, regardless of assumptions about how effort or fisher behavior are affected by spatial management. Alternative assumptions about the movement patterns of eastern king prawn had little influence on the impact of closures on overall harvest. However, when effort was increased to historic levels similar to those observed when the closures were implemented, a much greater impact on overall harvest was observed. The approach taken and simulation outcomes are discussed in the context of spatial management for both eastern king prawn, and penaeid fisheries more broadly.

Sharp oscillatory traveling waves of structured population dynamics model with degenerate diffusion

We consider a population dynamics model with degenerate diffusion and time delay. We discover sharp-oscillatory waves with sharp edges and non-decaying oscillations arising from density-dependent dispersal and reproduction with age structure. Degenerate diffusion and bad effect of time delay prevent the use of existing approaches. Here, we develop a new delayed iteration framework to show the existence of these peculiar waves. In particular, the estimate of the admissible wave speed is highly nontrivial. We employ a new phase transform method coupled with the detailed analysis of phase energy. Furthermore, we give a complete characterization of the dynamical behaviors of various kinds of waves. Our results indicate that simple invasion rules can generate complex wave patterns and provide some interesting insights into the ecological dynamics.

Possible adverse impact of contaminants on Atlantic cod population dynamics in coastal ecosystems.

While many in-laboratory ecotoxicological studies have shown the adverse impact of pollutants to the fitness of an individual, direct evidence from the field on the population dynamics of wildlife animals has been lacking. Here, we provide empirical support for a negative effect of pollution on Atlantic cod (Gadus morhua) population dynamics in coastal waters of Norway by combining unique time series of juvenile cod abundance, body size, environmental concentration of toxic contaminants and a spatially structured population dynamics model. The study shows that mercury concentration might have decreased the reproductive potential of cod in the region despite the general decline in the environmental concentration of mercury, cadmium and hexachlorobenzene since the implementation of national environmental laws. However, some cod populations appeared to be more resistant to mercury pollution than others, and the strength and shape of mercury effect on cod reproductive potential was fjord-specific. Additionally, cod growth rate changed at scales smaller than fjords with a gradient related to the exposure to the open ocean and offshore cod. These spatial differences in life-history traits emphasize the importance of local adaptation in shaping the dynamics of local wildlife populations. Finally, this study highlights the possibility to mitigate pollution effects on natural populations by reducing the overall pollution level, but also reveals that pollution reduction alone is not enough to rebuild local cod populations. Cod population recovery probably requires complementary efforts on fishing regulation and habitat restoration.

Competition for light in forest population dynamics: From computer simulator to mathematical model

In this article we build a mathematical model for forest growth and we compare this model with a computer forest simulator named SORTIE. The main ingredient taken into account in both models is the competition for light between trees. The parameters of the mathematical model are estimated by using SORTIE model, when the parameter values of SORTIE model correspond to the ones previously evaluated for the Great Mountain Forest in USA. We see that the best fit of the parameters of the mathematical model is obtained when the competition for light influences only the growth rate of trees. We construct a size structured population dynamics model with one and two species and with spatial structure.

Investigating the effects of time-delays on stochastic stability and designing l1-gain controllers for positive discrete-time Markov jump linear systems with time-delay

This paper is concerned with stochastic stability, l1-gain performance analysis and positivity-preserving l1-gain controller design for a positive discrete-time Markov jump linear system with time-delay. First, necessary and sufficient conditions for stochastic stability of the system are derived by constructing a linear co-positive stochastic Lyapunov functional and establishing a system equation whose state variables consist of the mathematical expectation of the markovianized states and whose coefficient matrices depend on time-delay and the transition probability. It is revealed that stochastic stability of the positive discrete-time Markov jump linear system with time-delay is influenced by the size of time-delay and it is demonstrated by an example that the effect of time-delay on stochastic stability can be either positive or negative. Second, exact computation on an l1-gain index of a stochastically stable positive discrete-time Markov jump linear system with time-delay is presented, and a necessary and sufficient condition for the l1-gain performance is derived in the form of linear programming. Third, an iterative algorithm is proposed to design a positivity-preserving l1-gain controller, and in single-input case, an optimal controller is obtained analytically such that the closed-loop system achieves the minimal l1-gain performance. Then, a modified pest’s structured population dynamic model is developed to illustrate the effectiveness of the designed method.

A juvenile–adult population model: climate change, cannibalism, reproductive synchrony, and strong Allee effects

ABSTRACTWe study a discrete time, structured population dynamic model that is motivated by recent field observations concerning certain life history strategies of colonial-nesting gulls, specifically the glaucous-winged gull (Larus glaucescens). The model focuses on mechanisms hypothesized to play key roles in a population's response to degraded environment resources, namely, increased cannibalism and adjustments in reproductive timing. We explore the dynamic consequences of these mechanics using a juvenile–adult structure model. Mathematically, the model is unusual in that it involves a high co-dimension bifurcation at which, in turn, leads to a dynamic dichotomy between equilibrium states and synchronized oscillatory states. We give diagnostic criteria that determine which dynamic is stable. We also explore strong Allee effects caused by positive feedback mechanisms in the model and the possible consequence that a cannibalistic population can survive when a non-cannibalistic population cannot.

Hopf bifurcation for a spatially and age structured population dynamics model

This paper is devoted to the study of a spatially and age structured population dynamics model. We study the stability and Hopf bifurcation of the positive equilibrium of the model by using a bifurcation theory in the context of integrated semigroups. This problem is a first example for Hopf bifurcation for a spatially and age/size structured population dynamics model. Bifurcation analysis indicates that Hopf bifurcation occurs at a positive age/size dependent steady state of the model. The results are confirmed by some numerical simulations.

Formula omitted]-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: A linear programming approach

This paper is concerned with the l1-gain performance analysis and positive filter design for a positive discrete-time Markov jump linear system (MJLS) by using a linear programming (LP) approach. First, by constructing a linear stochastic Lyapunov function and introducing an “equivalent” deterministic positive discrete-time linear system, necessary and sufficient conditions in the form of LP are derived for stochastic stability and l1-gain performance of the positive discrete-time MJLS. Then a sufficient condition on the existence of the desired positive l1-gain filter is provided. The desired positive l1-gain filter can be designed by solving a standard LP problem. The pest’s structured population dynamic model is employed to illustrate the effectiveness of the proposed method.

Hopf Bifurcation for a Maturity Structured Population Dynamic Model

This article is devoted to investigate some dynamical properties of a structured population dynamic model with random walk on (0,+∞). This model has a nonlinear and nonlocal boundary condition. We reformulate the problem as an abstract non-densely defined Cauchy problem, and use integrated semigroup theory to study such a partial differential equation. Moreover, a Hopf bifurcation theorem is given for this model.

NONLINEAR BOUNDARY CONDITIONS DERIVED BY SINGULAR PERTUBATION IN AGE STRUCTURED POPULATION DYNAMICS MODEL

In this article, we derive Ricker’s [22, 23] type nonlinear boundary condition for an age structured population dynamic model by using a singular perturbation. The question addressed in this paper is the convergence of the singularly perturbed system. We first obtain a finite time convergence for a fixed initial distribution. Then we focus on the convergence uniformly of the singularly perturbed system with respect to the initial distribution in bounded sets.

DENSITY DEPENDENCE AND THE SPREAD OF ANTHELMINTIC RESISTANCE

Variation in the strength of selection pressures acting upon different subpopulations may cause density-dependent regulatory processes to act differentially on particular genotypes and may influence the rate of selection of adaptive traits. Using host-helminth parasite systems as examples, we investigate the impact of different positive and negative density dependence on the potential spread of anthelmintic resistance. Following chemotherapy, the negative density-dependent processes restricting parasite population growth will be relaxed, increasing the genetic contribution of resistant parasites to the next generation. Simple deterministic models of directly transmitted nematodes that merge population dynamics and genetics show that the frequency of drug-resistant alleles may increase faster in species whose population size is down-regulated by density-dependent parasite fecundity than in species with density-dependent establishment or parasite mortality. A genetically structured population dynamics model of an indirectly transmitted nematode is used to highlight how population regulation will influence the resistance allele frequency in different parasite lifestages. Results indicate that surveys aimed at monitoring the evolution of drug resistance should consider carefully which life stage to sample, and the time following treatment samples should be collected. Anthelmintic resistance offers a good opportunity to apply fundamental evolutionary and ecological principles to the management of a potentially crucial public health problem.

Modelling of the age–sex–structured population dynamics with maternal care

We consider an age–sex–structured population dynamics model taking into account spatial diffusion, temporal pairs (for period of mating) and child care. All individuals have pre-reproductive, reproductive, and post-reproductive age intervals. Females of reproductive age are divided into single, fertilized and taking child care classes. Individuals of pre-reproductive age are divided into young (under maternal care) and juvenile groups. Juveniles can live without maternal care, but cannot reproduce. Separable solutions to this model and to the nondispersing population model are studied and numerical results are given.

Larval dynamics and recruitment modelling of the Moroccan Atlantic coast sardine ( Sardina pilchardus)

An age structured population dynamics model of the Moroccan Atlantic coast sardine is presented. The model focuses essentially on the larval phase which is composed of two stages: endogenous and exogenous stages called, respectively, S 1 and S 2. The entrance in stage S 2, here called pre-recruitment, is characterized by yolk resorption and mouth opening. At the beginning of stage S 2, there is a short but critical period when larvae have consumed their vitelline reserves but are not yet able to move enough in quest of food. The recruitment in the juvenile phase occurs when the larva reaches a threshold size related to a certain amount of food it has to ingest during the whole stage S 2. Larval mortality and feeding are density-dependent. A function ω ( t , X ) is introduced to take implicitly into account the impact of environmental and hydrographic conditions variability (upwelling, enrichment, retention, … , etc.) on pre-recruitment.

Wavefronts and global stability in a time-delayed population model with stage structure

We formulate and study a one–dimensional single–species diffusive–delay population model. The time delay is the time taken from birth to maturity. Without diffusion, the delay differential model extends the well–known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes. This delayed model is known to have simple global dynamics similar to that of the logistic equation. Through the use of a sub/supersolution pair method, we show that the diffusive delay model continues to generate simple global dynamics. This has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics. We also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population, connecting the zero solution of that equation with the positive steady state. Our main finding here is that our fronts appear to be all monotone, regardless of the size of the delay. This is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity, with the front developing a prominent hump in some other delay models.