STUDY OF STOCHASTIC SYSTEMS FOR EPIDEMIC DISEASE MODELS

As we know there are two kind of systems in modeling epidemic disease, deterministic systems and stochastic systems. This two systems relate to deterministic and stochastic epidemic disease models, respectively. Almost we use deterministic model for big population size and stochastic model for small population size. To use stochastic models for epidemic disease models, can obtain good results with less error. Study and solving of full stochastic models has not been yet investigated so more. In this article we use the homotopy analysis method to solve the full stochastic susceptible-infective epidemic disease model in disease-free equilibrium point.

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Evolutionary genetics of small populations

10.1093/oso/9780198783398.003.0002 ◽

2017 ◽

Author(s):

Richard Frankham ◽

Jonathan D. Ballou ◽

Katherine Ralls ◽

Mark D. B. Eldridge ◽

Michele R. Dudash ◽

...

Keyword(s):

Genetic Diversity ◽

Population Size ◽

Evolutionary Genetics ◽

Small Population ◽

Small Populations ◽

Effective Population ◽

Genetic Management ◽

Evolutionary Genetic ◽

Loss Of Genetic Diversity ◽

Number Of Individuals

Genetic management of fragmented populations involves the application of evolutionary genetic theory and knowledge to alleviate problems due to inbreeding and loss of genetic diversity in small population fragments. Populations evolve through the effects of mutation, natural selection, chance (genetic drift) and gene flow (migration). Large outbreeding, sexually reproducing populations typically contain substantial genetic diversity, while small populations typically contain reduced levels. Genetic impacts of small population size on inbreeding, loss of genetic diversity and population differentiation are determined by the genetically effective population size, which is usually much smaller than the number of individuals.

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Genetic and Nongenetic Bases for the L-Shaped Distribution of Quantitative Trait Loci Effects

Genetics ◽

10.1093/genetics/157.4.1773 ◽

2001 ◽

Vol 157 (4) ◽

pp. 1773-1787 ◽

Cited By ~ 8

Author(s):

Bruno Bost ◽

Dominique de Vienne ◽

Frédéric Hospital ◽

Laurence Moreau ◽

Christine Dillmann

Keyword(s):

Linkage Disequilibrium ◽

Quantitative Trait Loci ◽

Population Size ◽

Quantitative Trait ◽

Metabolic Flux ◽

Genetic Model ◽

Small Population ◽

Additive Genetic Model ◽

Metabolic Mechanism ◽

Qtl Effects

Abstract The L-Shaped distribution of estimated QTL effects (R2) has long been reported. We recently showed that a metabolic mechanism could account for this phenomenon. But other nonexclusive genetic or nongenetic causes may contribute to generate such a distribution. Using analysis and simulations of an additive genetic model, we show that linkage disequilibrium between QTL, low heritability, and small population size may also be involved, regardless of the gene effect distribution. In addition, a comparison of the additive and metabolic genetic models revealed that estimates of the QTL effects for traits proportional to metabolic flux are far less robust than for additive traits. However, in both models the highest R2's repeatedly correspond to the same set of QTL.

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Population Density or Populations Size. Which Factor Determines Urban Traffic Congestion?

Sustainability ◽

10.3390/su13084280 ◽

2021 ◽

Vol 13 (8) ◽

pp. 4280

Author(s):

Yu Sang Chang ◽

Sung Jun Jo ◽

Yoo-Taek Lee ◽

Yoonji Lee

Keyword(s):

Population Density ◽

Population Size ◽

Traffic Congestion ◽

Critical Role ◽

Small Population ◽

High Density ◽

Urban Traffic ◽

Contradictory Result ◽

Low Density

A large number of articles have documented that as population density of cities increases, car use declines and public transit use rises. These articles had a significant impact of promoting high-density compact urban development to mitigate traffic congestion. Another approach followed by other researchers used the urban scaling model to indicate that traffic congestion increases as population size of cities increases, thus generating a possible contradictory result. Therefore, this study examines the role of both density and population size on traffic congestion in 164 global cities by the use of Stochastic Impacts by Regression on Population, Affluence and Technology model. We divide 164 cities into the two subgroups of 66 low density cities and 98 high density cities for analysis. The findings from the subgroups analysis indicated a clear-cut difference on the critical role of density in low-density cities and the exclusive role of population size in high-density cities. Furthermore, using threshold regression model, 164 cities are divided into the two regions of large and small population cities to determine population scale advantage of traffic congestion. Our findings highlight the importance of including analysis of subgroups based on density and/or population size in future studies of traffic congestion.

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Stability and Hopf bifurcation for an epidemic disease model with time delay

2017 29th Chinese Control And Decision Conference (CCDC) ◽

10.1109/ccdc.2017.7979167 ◽

2017 ◽

Author(s):

Yuguang Wang ◽

Yanan Li ◽

Wenshuai Wang

Keyword(s):

Hopf Bifurcation ◽

Time Delay ◽

Disease Model ◽

Epidemic Disease

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Modeling Noisy Time Series: Physiological Tremor

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127498001157 ◽

1998 ◽

Vol 08 (07) ◽

pp. 1505-1516 ◽

Cited By ~ 51

Author(s):

J. Timmer

Keyword(s):

Time Series ◽

Stochastic Systems ◽

State Space Model ◽

Physiological Tremor ◽

Space Model ◽

Deterministic Systems ◽

Estimated Parameters ◽

Noisy Time Series ◽

Observational Noise ◽

Small Amplitude Oscillation

Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the outstretched hand of healthy subjects, we compare the results for a linear model that explicitly includes additional observational noise to one that ignores this noise. We discuss problems and possible solutions for nonlinear deterministic as well as nonlinear stochastic processes. Especially we discuss the state space model applicable for modeling noisy stochastic systems and Bock's algorithm capable for modeling noisy deterministic systems.

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Eumops floridanus (Chiroptera: Molossidae)

Mammalian Species ◽

10.1093/mspecies/seab012 ◽

2021 ◽

Vol 53 (1009) ◽

pp. 125-133

Author(s):

Jessica M Vannatta ◽

Jeffery A Gore ◽

Verity L Mathis ◽

Brian D Carver

Keyword(s):

United States ◽

Population Size ◽

The United States ◽

Small Population ◽

Species Level ◽

Small Population Size ◽

Restricted Distribution ◽

Dead Trees ◽

Fish And Wildlife Service

Abstract Eumops floridanus (Allen, 1932) is a molossid commonly called the Florida bonneted bat or the Florida mastiff bat. Eumops floridanus is the largest species of bat in Florida and is one of 16 species in the genus Eumops. With one of the smallest distributions of any bat in the United States, it is endemic to southern peninsular Florida where it roosts in cavities of live and dead trees and man-made structures. Eumops floridanus was formerly classified as a subspecies of E. glaucinus but has been elevated to species level based on morphology. Due primarily to its restricted distribution, small population size, and the continued loss of habitat, E. floridanus is federally listed as “Endangered” (EN) by the United States Fish and Wildlife Service.

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Clipperton Atoll as a model to study small marine populations: Endemism and the genomic consequences of small population size

PLoS ONE ◽

10.1371/journal.pone.0198901 ◽

2018 ◽

Vol 13 (6) ◽

pp. e0198901 ◽

Cited By ~ 4

Author(s):

Nicole L. Crane ◽

Juliette Tariel ◽

Jennifer E. Caselle ◽

Alan M. Friedlander ◽

D. Ross Robertson ◽

...

Keyword(s):

Population Size ◽

Small Population ◽

Small Population Size

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Comparing stochastic systems using regenerative simulation with common random numbers

Advances in Applied Probability ◽

10.1017/s0001867800033048 ◽

1979 ◽

Vol 11 (04) ◽

pp. 804-819 ◽

Cited By ~ 3

Author(s):

Philip Heidelberger ◽

Donald L. Iglehart

Keyword(s):

Stochastic Models ◽

Stochastic System ◽

Variance Reduction ◽

Stochastic Systems ◽

Sufficient Conditions ◽

Random Numbers ◽

Numerical Examples ◽

Common Random Numbers ◽

Regenerative Simulation ◽

Alternative Designs

Suppose two alternative designs for a stochastic system are to be compared. These two systems can be simulated independently or dependently. This paper presents a method for comparing two regenerative stochastic processes in a dependent fashion using common random numbers. A set of sufficient conditions is given that guarantees that the dependent simulations will produce a variance reduction over independent simulations. Numerical examples for a variety of simple stochastic models are included which illustrate the variance reduction achieved.

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