Stochastic Growth Model Research Articles

Mean exit time and escape probability for the stochastic logistic growth model with multiplicative α-stable Lévy noise

In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability and the Fokker–Planck equation for fish population [Formula: see text]. In the Gaussian case, these quantities satisfy local partial differential equations while in the non-Gaussian case, they satisfy nonlocal partial differential equations. Following a discussion of existence, uniqueness and stability, we calculate numerical approximations of the solutions of those equations. For each noise model we then compare the behaviors of the mean time to extinction and the solution of the Fokker–Planck equation as growth rate [Formula: see text], carrying capacity [Formula: see text], intensity of Gaussian noise [Formula: see text], noise intensity [Formula: see text] and stability index [Formula: see text] vary. The MET from the interval [Formula: see text] at the right boundary is finite if [Formula: see text]. For [Formula: see text], the MET from [Formula: see text] at this boundary is infinite. A larger stability index [Formula: see text] is less likely leading to the extinction of the fish population.

A System Biology-Based Approach for Designing Combination Therapy in Cancer Precision Medicine.

In this paper, we have used an agent-based stochastic tumor growth model and presented a mathematical and theoretical perspective to cancer therapy. This perspective can be used to theoretical study of precision medicine and combination therapy in individuals. We have conducted a series of in silico combination therapy experiments. Based on cancer drugs and new findings of cancer biology, we hypothesize relationships between model parameters which in some cases represent individual genome characteristics and cancer drugs, i.e., in our approach, therapy players are delegated by biologically reasonable parameters. In silico experiments showed that combined therapies are more effective when players affect tumor via different mechanisms and have different physical dimensions. This research presents for the first time an algorithm as a theoretical viewpoint for the prediction of effectiveness and classification of therapy sets.

Financial globalization and its consequences for productive government expenditure

This paper employs a stochastic growth model to study the impact of international financial liberalization on the share of productive government expenditure in GDP. Financial liberalization is specified to take the form of reducing the costs of both lending to, and borrowing from, abroad. This is shown to impinge on the economy through (i) its interaction with the volatility of returns to domestic capital, and (ii) the impact on agents’ allocation of their portfolio across domestic and foreign assets, and its effect on domestic activity. Reduced foreign lending costs tend to divert resources from the domestic economy, requiring the government to compensate by increasing the share of domestic output allocated to productive activity. Reducing borrowing costs have the opposite effects. Empirical evidence, using a dataset of 97 countries over the period 1970 to 2015 provides convincing support for these findings and the underlying mechanism.

Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections

This study proposes a general bivariate stochastic differential equation model of population growth which includes random forces governing the dynamics of the bivariate distribution of size variables. The dynamics of the bivariate probability density function of the size variables in a population are described by the mixed-effect parameters Vasicek, Gompertz, Bertalanffy, and the gamma-type bivariate stochastic differential equations (SDEs). The newly derived bivariate probability density function and its marginal univariate, as well as the conditional univariate function, can be applied for the modeling of population attributes such as the mean value, quantiles, and much more. The models presented here are the basis for further developments toward the tree diameter–height and height–diameter relationships for general purpose in forest management. The present study experimentally confirms the effectiveness of using bivariate SDEs to reconstruct diameter–height and height–diameter relationships by using measurements obtained from mountain pine tree (Pinus mugo Turra) species dataset in Lithuania.

Internal trophic pressure, a regulator of plant development? Insights from a stochastic functional-structural plant growth model applied to Coffea trees.

Using internal trophic pressure as a regulating variable to model the complex interaction loops between organogenesis, production of assimilates and partitioning in functional-structural models of plant growth has attracted increasing interest in recent years. However, this approach is hampered by the fact that internal trophic pressure is a non-measurable quantity that can be assessed only through model parametric estimation, for which the methodology is not straightforward, especially when the model is stochastic. A stochastic GreenLab model of plant growth (called 'GL4') is developed with a feedback effect of internal trophic competition, represented by the ratio of biomass supply to demand (Q/D), on organogenesis. A methodology for its parameter estimation is presented and applied to a dataset of 15 two-year-old Coffea canephora trees. Based on the fitting results, variations in Q/D are reconstructed and analysed in relation to the estimated variations in organogenesis parameters. Our stochastic retroactive model was able to simulate realistically the progressive set-up of young plant architecture and the branch pruning effect. Parameter estimation using real data for Coffea trees provided access to the internal trophic dynamics. These dynamics correlated with the organogenesis probabilities during the establishment phase. The model can satisfactorily reproduce the measured data, thus opening up promising avenues for further applying this original procedure to other experimental data. The framework developed can serve as a model-based toolkit to reconstruct the hidden internal trophic dynamics of plant growth.

Human Capital Divergence and the Size Distribution of Cities: Is Gibrat's Law Obsolete?

This paper studies how the changing geographic distribution of skilled workers in the US affects theoretical models that use Gibrat's law to explain the size distribution of cities. In the empirical literature, a divergence hypothesis holds that college share increases faster in cities where college share is larger, and a growth hypothesis maintains that the rate of city population growth is also directly related to initial college share. Examining the divergence hypothesis, the classic test for Gibrat's law is shown to be a test for beta-convergence. Testing shows there has been absolute, not relative, divergence in human capital since the 1970s. However, the combination of even absolute divergence and the growth hypothesis is shown to violate the model condition that population growth is stochastic. Additional testing finds that the relation between initial college share and city growth is concave rather than monotonic.These results imply that stochastic growth models can survive the challenge posed by trends in the distribution of human capital.

Neoclassical stochastic economic growth model: An application to the Bolivian economy

The following project is to consider a neoclassical model. To see the grow in one-sector a continuous-time of Ramsey-type with an utility and production function. Where each component are exposed in exogenous shocks. The corresponding dynamics are represented by stochastic differential equations. Equations are solved explicitly maximizing the average, the utility level that it has by consumption. In particular, Bolivia‟s economy, the period of analysis and the equations that describe the behaviour or long-term trajectory of real PIB, Gross Fixed Capital Formation. The total population is considered as a labor force and the optimal consumption. As a result, we presented the equations that were found through simulations to use mathematical software Mat Lab, making some replicas observed in panel data in Bolivian´s economy. Which represents fluctuations and long-term growth of the economy? To investigate the fluctuations and the economic growing in Bolivia, with the model neoclassic in a large period.

Effects of colored noises on the statistical properties of a population growth model with Allee effect**Research is supported by the National Natural Science Foundation of China (11801224), Natural Science Foundation of Jiangsu Province (BK20180856).

We study a stochastic population growth model with Allee effect, it is driven by correlated multiplicative and additive colored noises. The influences of noises on the statistical properties of the stochastic model are discussed. Applying an approximative Fokker-Planck equation, we first obtain the stationary probability distribution (SPD) of the stochastic model, and then present a more detailed discussion of how the noises determine the behaviors of the SPD, mean, variance and skewness of the population size. The research of the shape of SPD shows that the phenomenological bifurcation may occur when the noise intensity passes through a critical value. We also find that the additive and multiplicative noises have different effects on the moments (mean, variance and skewness) of population density.

The welfare and distributional effects of fiscal volatility: A quantitative evaluation

This study explores the welfare and distributional effects of fiscal volatility using a neoclassical stochastic growth model with incomplete markets. In our model, households face uninsurable idiosyncratic risks in their labor income and discount factor processes, and we allow aggregate uncertainty to arise from both productivity and government purchases shocks. We calibrate our model to key features of the U.S. economy, before eliminating government purchases shocks. We then evaluate the distributional consequences of the elimination of fiscal volatility and find that, in our baseline case, welfare gains increase with private wealth holdings.

TOWARDS A STOCHASTIC TWO-COMPARTMENT MODEL IN TUMOR GROWTH

A stochastic model of tumor growth incorporating several key elements of the growth processes is presented. Generalizing a previous work by the authors, two one-dimensional diffusion processes representing populations of proliferating and quiescent cells are obtained. Their forms turn out by their relation with total tumor population analysed in (1). The proposed model is able to incorporate the effects of the mutual interactions between the two subpopulations. It is also used to simulate the effects of two kinds of time-dependent therapies: non-specific cycle and specific cycle drugs. Moreover, the first-exit-time problem is analyzed to study cancer evolution in the presence of a time-dependent therapy. 1 Introduction and background Tumor is one of the main causes of death in our so- ciety so, in the last twenty years a lot of attempts have been made to describe the tumor kinetic. Cancer cells population consists of a combination of proliferating, quiescent and dead cells that determine tumor growth based on surrounding environmental conditions (cf. (5)). Furthermore, since experimental data show the existence of more or less intense random fluctuations in tumor growth, in a previous work (see (1)) the authors provided a stochastic generalization of the Gompertz law in order to model monoclonal tumor growth. So tumor size is described by means of a one-dimensional diffusion process X(t) and the first exit time problem (FET) for X(t) from a region D has been analysed. In particular, D is restricted by two absorbing boundaries representing healing threshold and the carrying capacity. A first natural generalization consists of including all the essential biological phenomena of a cellular population. To this aim, following Kozusko and Bajzer (cf. (7)), we split tumor population in two subpopulations: proliferating and quiescent cells. In this direction, in (7), the authors proposed a deterministic model to describe tumor dynamics, assuming that the transition rates between proliferating and quiescent populations depend on the total population size. By imposing that the total population is governed by the Gompertz law, Kozusko and Bajzer resolved analytically the model and obtained the dynamics of prolif- erating and quiescent populations as functions of the whole population size. Following this approach, we describe proliferating and quiescent populations via two new diffusion pro- cesses, generally time-non-homogeneous, connected to the process X(t). The FET problem for such processes through suitable boundaries is considered. The followed approach per- mits to analyse the effect of different therapies on tumor cells. In Section 2 we will review the main characteristics of the model proposed in (1) in which the effect of a therapy is seen as a moderation term of the growth rate of the tumor cells. In Section 3 we generalize the deterministic model by Kozusko and Bajzer by obtaining two diffusion processes P(t) and Q(t) representing the populations of proliferating and quies- cent cells, respectively. Finally, in Section 4 the effect of a therapy on X(t) is investigated

Beyond modified mean field: a case for a stochastic grain growth model

ABSTRACTWe address the basic mechanism of grain growth in two and three dimensions in single phase metallic systems. It is argued, a comprehensive grain growth model is best based on a stochastic process described by a Fokker Planck equation. This concept is sufficient to determine almost all features of grain growth in general terms. The existence of the von Neumann law and its counterpart in three dimensions enables us to provide an explicit form of the Fokker Planck equation and thus determine many features of grain growth in great detail. Finally, we illustrate this model by determining the salient features of grain growth in three dimensions in the long time limit, and comparing them with experimental and computational results.

Do Natural Disasters Make Sustainable Growth Impossible?

We consider the prospects for sustainable growth using expected utility models of optimal investment under threat from natural disasters. Adoption of a continuous time, stochastic Ramsey growth model over an infinite time horizon permits the analysis of sustainability under uncertainty regarding adverse events, including both one-time and recurrent disasters. As appropriate to small economies, we consider adaptation to the risk of disaster. Natural disasters reduce capital stocks and disrupt the optimal consumption and felicity paths. While the time path of inter-temporal welfare might consequently shift downward, the path may still be non-decreasing over time, even without adding strong or weak sustainability constraints. Prudent disaster preparedness includes precautionary investment in productive capital, programs of adaptation to disaster risk, and avoiding distortionary policies undermining the prospects of optimality and sustainability.

Path-wise uniqueness, convergence of approximated solutions for a stochastic model of tumor growth with colored noise

Path-wise uniqueness, convergence of approximated solutions for a stochastic model of tumor growth with colored noise

Coexistence in chase-escape

We study a competitive stochastic growth model called chase-escape in which red particles spread to adjacent uncolored sites and blue only to adjacent red sites. Red particles are killed when blue occupies the same site. If blue has rate-1 passage times and red rate-$\lambda$, a phase transition occurs for the probability red escapes to infinity on $\mathbb Z^d$, $d$-ary trees, and the ladder graph $\mathbb Z \times \{0,1\}$. The result on the tree was known, but we provide a new, simpler calculation of the critical value, and observe that it is a lower bound for a variety of graphs. We conclude by showing that red can be stochastically slower than blue, but still escape with positive probability for large enough $d$ on oriented $\mathbb Z^d$ with passage times that resemble Bernoulli bond percolation.

Forecast Disagreement about Long-run Macroeconomic Relationships

Using survey forecast data, we study if professional forecasters utilize long-run co-integration relationships among macroeconomic variables to forecast future as postulated in workhorse stochastic growth models. There exists a significant heterogeneity among forecasters, the majority of whom do not use these long-run relationships and generally make more accurate forecasts (comparing with those who use). Simple parsimonious recursive forecasting models are fitted to the data as one way to approximate the expectation formation process of the forecasters who utilize (or do not utilize) the long-run relationships.

A tractable framework for analyzing a class of nonstationary Markov models

We consider a class of infinite‐horizon dynamic Markov economic models in which the parameters of utility function, production function, and transition equations change over time. In such models, the optimal value and decision functions are time‐inhomogeneous: they depend not only on state but also on time. We propose a quantitative framework, calledextended function path(EFP), for calibrating, solving, simulating, and estimating such nonstationary Markov models. The EFP framework relies on the turnpike theorem which implies that the finite‐horizon solutions asymptotically converge to the infinite‐horizon solutions if the time horizon is sufficiently large. The EFP applications include unbalanced stochastic growth models, the entry into and exit from a monetary union, information news, anticipated policy regime switches, deterministic seasonals, among others. Examples of MATLAB code are provided.

The effect of spatial variation for predicting aphid outbreaks

AbstractIn order to improve forecasting of pest epidemics, it is important to know the spatial scale at which specific forecasts are reliable. To investigate the spatial scale of aphid outbreaks, we have developed a spatio‐temporal stochastic aphid population growth model and fitted the model to empirical spatial time series of aphid population data using a Bayesian hierarchical fitting procedure. Furthermore, detailed spatial data of the initial phases of population growth were investigated in semivariograms. Our results suggest that spatial variation is low in the initial occurrence probability at a spatial scale of 10 km. Consequently, the results support the hypothesis that initial aphid population sizes and outbreaks may be predicted in fields within a 10 km radius. For farmers, this may imply that they can rely their decision of whether to spray against aphids on observations made by other nearby farmers or by the consultancy service.

Machine-Learning and Stochastic Tumor Growth Models for Predicting Outcomes in Patients With Advanced Non-Small-Cell Lung Cancer.

The prediction of clinical outcomes for patients with cancer is central to precision medicine and the design of clinical trials. We developed and validated machine-learning models for three important clinical end points in patients with advanced non-small-cell lung cancer (NSCLC)-objective response (OR), progression-free survival (PFS), and overall survival (OS)-using routinely collected patient and disease variables. We aggregated patient-level data from 17 randomized clinical trials recently submitted to the US Food and Drug Administration evaluating molecularly targeted therapy and immunotherapy in patients with advanced NSCLC. To our knowledge, this is one of the largest studies of NSCLC to consider biomarker and inhibitor therapy as candidate predictive variables. We developed a stochastic tumor growth model to predict tumor response and explored the performance of a range of machine-learning algorithms and survival models. Models were evaluated on out-of-sample data using the standard area under the receiver operating characteristic curve and concordance index (C-index) performance metrics. Our models achieved promising out-of-sample predictive performances of 0.79 area under the receiver operating characteristic curve (95% CI, 0.77 to 0.81), 0.67 C-index (95% CI, 0.66 to 0.69), and 0.73 C-index (95% CI, 0.72 to 0.74) for OR, PFS, and OS, respectively. The calibration plots for PFS and OS suggested good agreement between actual and predicted survival probabilities. In addition, the Kaplan-Meier survival curves showed that the difference in survival between the low- and high-risk groups was significant (log-rank test P < .001) for both PFS and OS. Biomarker status was the strongest predictor of OR, PFS, and OS in patients with advanced NSCLC treated with immune checkpoint inhibitors and targeted therapies. However, single biomarkers have limited predictive value, especially for programmed death-ligand 1 immunotherapy. To advance beyond the results achieved in this study, more comprehensive data on composite multiomic signatures is required.

Threshold behavior in a stochastic algal growth model with stoichiometric constraints and seasonal variation

In this paper, we propose and investigate a stochastic algal growth model with the explicit incorporation of season-dependent light and nutrient availability. We first establish the threshold 〈λ〉ϖ that determines the persistence and extinction of the algae: when 〈λ〉ϖ>0, the algal will persist in mean, while when 〈λ〉ϖ<0, the algae will eventually die out. Then we prove the existence and global attractiveness of a positive stochastic periodic solution when 〈λ〉ϖ>0 by constructing suitable Lyapunov functions. Numerical simulations are carried out to substantiate our analytical results and investigate effective methods to control algal blooms.

A Method to Project Future Impacts From Threats and Conservation on the Probability of Extinction for North American Migratory Monarch (Danaus plexippus) Populations

The United States Fish and Wildlife Service is currently evaluating the monarch butterfly (Danaus plexippus) for listing under the Endangered Species Act and using the Species Status Assessment (SSA) framework to estimate and forecast drivers that impact the species’ risk of extinction. To evaluate eastern and western monarch populations the monarch SSA built on a foundation of published population models and other literature to identify current growth rates and information on threats and conservation efforts. Here we present the resulting methodology, which aimed to explore the magnitude of monarch population responses to the aggregation of multiple drivers under various scenarios. Our methodology differs from previous research by developing a series of functional cause and effect relationships that link monarch population-specific responses to threats or conservation actions. We incorporated these population-specific responses into stochastic geometric growth models for both eastern and western populations to estimate the probability of quasi-extinction in 50 years. Our models were parameterized using previously estimated population-specific trend data (growth rates and environmental variability) and expert elicited estimates of population responses to multiple drivers (i.e., amount of available breeding and overwintering habitat, insecticide use, migration resource availability, and climate change). We explored plausible future scenarios with realistic place-holder data to evaluate how changes in these drivers influenced monarch quasi-extinction risk for each population. In addition, we captured uncertainty in quasi-extinction risk by calculating cumulative quasi-extinction risk over a full range of quasi-extinction threshold values which were sampled from a uniform distribution bounded by expert-elicited estimates. In both populations, our baseline for comparison was the “current” condition defined by population-specific growth rate and environmental stochasticity from previous research. The result of the methodology presented here is a novel and comprehensive tool that incorporates the impact of future stressors into projections of population numbers over time. The approach provides a tractable and updatable tool that includes multiple types of information and the associated uncertainty of drivers, population impacts, and risk of extinction. For monarchs, this tool will be critical for incorporating the best scientific and commercial information available in the upcoming listing decision.