Stochastic models to estimate population dynamics

2020 ◽  
Vol 8 (1) ◽  
pp. 136-152
Author(s):  
Saba Infante ◽  
Luis Sanchez ◽  
Aracelis Hernandez
Keyword(s):  
Stochastic Models ◽  
Growth Dynamics ◽  
Real Data ◽  
Sampling Errors ◽  
High Dimensions ◽  
Deterministic Models ◽  
Dynamics Of Population ◽  
The Republic ◽  
Chemical Conditions ◽  
Control Work

The growth dynamics that a population follows is mainly due to births, deaths or migrations, each of thesephenomena is affected by other factors such as public health, birth control, work sources, economy, safety and conditions of quality of life in neighboring countries, among many others. In this paper is proposed two statistical models based on a system of stochastic differential equations (SDE) that model the dynamics of population growth, and three computational algorithms that allow the generation of probability distribution samples in high dimensions, in models that have non-linear structures and that are useful for making inferences. The algorithms allow to estimate simultaneously states solutions and parameters in SDE models. The interpretation of the parameters is important because they are related to the variables of growth, mortality, migration, physical-chemical conditions of the environment, among other factors. The algorithms are illustrated using real data from a sector of the population of the Republic of Ecuador, and are compared with the results obtained with the models used by theWorld Bank for the same data, which shows that stochastic models Proposals based on an SDE more adequately and reliably adjust the dynamics of demographic randomness, sampling errors and environmental randomness in comparison with the deterministic models used by the World Bank. It is observed that the population grows year by year and seems to have a definite tendency; that is, a clearly growing behavior is seen. To measure the relative success of the algorithms, the relative error was estimated, obtaining small percentage errors.

scholarly journals Spatial pattern and genetic diversity estimates are linked in stochastic models of population differentiation

2000 ◽  
Vol 23 (3) ◽  
pp. 541-544 ◽  
Author(s):  
José Alexandre Felizola Diniz-Filho ◽  
Mariana Pires de Campos Telles
Keyword(s):  
Genetic Diversity ◽  
Spatial Pattern ◽  
Stochastic Models ◽  
Population Differentiation ◽  
Real Data ◽  
Population Heterogeneity ◽  
Data Set ◽  
Mantel’S Test ◽  
The Relationship ◽  
Diversity Estimates

In the present study, we used both simulations and real data set analyses to show that, under stochastic processes of population differentiation, the concepts of spatial heterogeneity and spatial pattern overlap. In these processes, the proportion of variation among and within a population (measured by G ST and 1 - G ST, respectively) is correlated with the slope and intercept of a Mantel's test relating genetic and geographic distances. Beyond the conceptual interest, the inspection of the relationship between population heterogeneity and spatial pattern can be used to test departures from stochasticity in the study of population differentiation.

scholarly journals The dynamics of population by settlements in the Guba-Khachmaz economic-geographical region

2020 ◽  
Vol 3 ◽  
pp. 143-151
Author(s):  
Tural Bayramov ◽  
Keyword(s):  
Population Growth ◽  
Rural Population ◽  
Growth Dynamics ◽  
Living Standards ◽  
Geographical Region ◽  
Employment Rate ◽  
Social Survey ◽  
Rural And Urban ◽  
The Social ◽  
Dynamics Of Population

The article shows and analyzes the population growth dynamics in the Guba-Khachmaz economic-geographical region, the economic region’s urban and rural population. Its share of the population of Azerbaijan for the years 1990-2015 are shown in the tables and also analyzed. The population for rural and urban sectors and the indicators of rate are shown in the map for 2016-2017 years. Also, as a result of the social survey conducted in the region, the living standards of the population as well as the employment rate in the settlements were studied, and ways to mitigate problems were identified.

scholarly journals Estimating the distribution of time to extinction of infectious diseases in mean-field approaches

2020 ◽  
Author(s):  
Maryam Aliee ◽  
Kat S. Rock ◽  
Matt J. Keeling
Keyword(s):  
Infectious Diseases ◽  
Stochastic Models ◽  
Mean Field ◽  
Practical Method ◽  
Deterministic Models ◽  
Recovery Processes ◽  
Time To Extinction ◽  
And Control ◽  
Field Approaches ◽  
Birth Death

AbstractA key challenge for many infectious diseases is to predict the time to extinction under specific interventions. In general this question requires the use of stochastic models which recognise the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when parameter uncertainty also needs to be incorporated. Deterministic models are often used for prediction as they are more tractable, however their inability to precisely reach zero infections makes forecasting extinction times problematic. Here, we study the extinction problem in deterministic models with the help of an effective “birth-death” description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth-death framework. We show these predictions agree very well with the results of stochastic models by analysing the simplified SIS dynamics as well as studying an example of more complex and realistic dynamics accounting for the infection and control of African sleeping sickness (Trypanosoma brucei gambiense).

Optimization models for managing limited resources in logistics

2021 ◽  
Author(s):  
Aleksandr Mischenko ◽  
Anastasiya Ivanova
Keyword(s):  
Stochastic Models ◽  
Optimization Models ◽  
Limited Resources ◽  
Model Parameters ◽  
Systems Modeling ◽  
Deterministic Models ◽  
Logistics Systems ◽  
Industrial Enterprises ◽  
The Stability ◽  
Senior Students

In the proposed monograph, optimization models for managing limited resources in logical systems are considered. Such systems are primarily used by industrial enterprises, transport companies and trade organizations, including those that carry out wholesale activities. As a rule, the efficiency of these objects largely depends on how rational use of limited resources such as: consumer camera business, labor, vehicles, etc. In this paper, various approaches to managing such resources are considered both for deterministic models and for the situation when a number of model parameters are not specified exactly, that is, for stochastic models. In this case, it is proposed to evaluate the stability of models to the occurrence of various types of risk events, both by the structure of the solution and by the functionality. It is addressed to senior students, postgraduates and masters studying in the specialty "Management" and "Logistics", as well as specialists in the field of logistics systems modeling.

scholarly journals Translating environmental xenobiotic fate models across scales

1997 ◽  
Vol 1 (4) ◽  
pp. 895-904 ◽  
Author(s):  
O. Richter ◽  
B. Diekkrüger
Keyword(s):  
Stochastic Models ◽  
Process Models ◽  
Spatial Process ◽  
Soil Parameters ◽  
Deterministic Models ◽  
Deterministic Process ◽  
Statistical Variation ◽  
Scale Models ◽  
Classical Models ◽  
Environmental Xenobiotic

Abstract. The classical models developed for degradation and transport of xenobiotics have been derived with the assumption of homogeneous environments. Unfortunately, deterministic models function well in the laboratory under homogeneous conditions but such homogeneous conditions often do not prevail in the field. A possible solution is the incorporation of the statistical variation of soil parameters into deterministic process models. This demands the development of stochastic models of spatial variability. To this end, spatial soil parameter fields are conceived as the realisation of a random spatial process. Extrapolation of local fine scale models to large heterogeneous fields is achieved by coupling deterministic process models with random spatial field models.

The dynamics of neutral mutation

1978 ◽  
Vol 203 (1150) ◽  
pp. 91-91
Keyword(s):  
Stochastic Models ◽  
Diffusion Approximations ◽  
Neutral Systems ◽  
Effective Population ◽  
Gene Frequencies ◽  
Deterministic Models ◽  
New Approach ◽  
Large Populations ◽  
Quantitative Results ◽  
Infinite Alleles Model

A variety of mathematical models have been proposed, over the years since the pioneering work of Fisher and Wright, for the evolution of gene frequencies in large populations under the pressure of selection and mutation. It is broadly true to say that deterministic models are adequate, at least to a first approximation, when selective differences are large compared with the reciprocal of the effective population size. When selection is weaker than this, genetic drift is sufficiently obtrusive to make stochastic models essential. Such models are typically much more difficult to analyse than deterministic ones, and detailed studies have usually been confined to the very special situation of statistical equilibrium. But of course no biological system is really in equilibrium for very long, and moreover the relaxation of nearly neutral systems is usually slow; hence the need for dynamical stochastic models and for their analysis outside a state of equilibrium. The usual way of attacking this problem is by diffusion approximations, and the theory of such processes is surveyed. Questions of existence, uniqueness and adequacy of approximation are well understood, but much less is known about methods of deriving explicit quantitative results or qualitative insight. A new approach is suggested which is particularly useful for studying a locus at which many different alleles are possible. It leads, for example, to a dynamical picture (in terms of a diffusing Poisson process) for the neutral infinite-alleles model of Kimura & Crow.

scholarly journals Revisiting the reduction of stochastic models of genetic feedback loops with fast promoter switching

2019 ◽  
Author(s):  
J. Holehouse ◽  
R. Grima
Keyword(s):  
Transcriptional Regulation ◽  
Master Equation ◽  
Gene Regulatory Networks ◽  
Stochastic Models ◽  
Regulatory Networks ◽  
Burst Size ◽  
Protein Translation ◽  
Feedback Loops ◽  
Deterministic Models ◽  
Gene Regulatory

AbstractPropensity functions of the Hill-type are commonly used to model transcriptional regulation in stochastic models of gene expression. This leads to an effective reduced master equation for the mRNA and protein dynamics only. Based on deterministic considerations, it is often stated or tacitly assumed that such models are valid in the limit of rapid promoter switching. Here, starting from the chemical master equation describing promoter-protein interactions, mRNA transcription, protein translation and decay, we prove that in the limit of fast promoter switching, the distribution of protein numbers is different than that given by standard stochastic models with Hill-type propensities. We show the differences are pronounced whenever the protein-DNA binding rate is much larger than the unbinding rate, a special case of fast promoter switching. Furthermore we show using both theory and simulations that use of the standard stochastic models leads to drastically incorrect predictions for the switching properties of positive feedback loops and that these differences decrease with increasing mean protein burst size. Our results confirm that commonly used stochastic models of gene regulatory networks are only accurate in a subset of the parameter space consistent with rapid promoter switching.Statement of SignificanceA large number of models of gene regulatory networks in the literature assume that since promoter switching is fast then transcriptional regulation can be effectively modeled using Hill functions. While this approach can be rigorously justified for deterministic models, it is presently unclear if it is also the case for stochastic models. In this article we prove that this is not the case, i.e. stochastic models of gene regulatory systems, namely those with feedback loops, describing transcriptional regulation using Hill functions are only valid in a subset of parameter conditions consistent with fast promoter switching. We identify parameter regimes where these models are correct and where their predictions cannot be trusted.

scholarly journals Stochastic models of the growth dynamics of some dendritic cells

2018 ◽  
Author(s):  
Khairia El-Said El-Nadi Khairia
Keyword(s):  
Dendritic Cells ◽  
Stochastic Models ◽  
Growth Dynamics ◽  
Advanced Stage ◽  
Mathematical Methods ◽  
Stochastic Dynamical Systems ◽  
Subject Classifications ◽  
Different Types ◽  
Aggressive Tumor ◽  
The Ideal

AbstractDifferent models of tumor growth are considered. Some mathematical methods are developed to analyze the dynamics of mutations enabling cells in cancer patients to metas-tize. The mathematical models consist of some stochastic dynamical systems describing tumor cells and immune effectors. It is also considered a method to find the ideal outcome of some treatments. Some different types of dendritic cells are considered. The obtained results will help to find some suitable treatments,which can be successful in returning an aggressive tumor to its passive,non-immune evading state. The principle goal of this paper is to find ways to treat the cancer tumors before they can reach an advanced stage devel-opmen.AMS Subject Classifications92B05, 37C45.

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