scholarly journals Demographic Dynamics in Multitype Populations with Migrations

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 246
Author(s):  
Manuel Molina-Fernández ◽  
Manuel Mota-Medina
Keyword(s):  
Mathematical Modeling ◽  
Population Dynamics ◽  
Branching Process ◽  
Probability Model ◽  
Biological Systems ◽  
Research Work ◽  
General Setting ◽  
Process Theory ◽  
Multitype Branching Process ◽  
Demographic Dynamics

This research work deals with mathematical modeling in complex biological systems in which several types of individuals coexist in various populations. Migratory phenomena among the populations are allowed. We propose a class of mathematical models to describe the demographic dynamics of these type of complex systems. The probability model is defined through a sequence of random matrices in which rows and columns represent the various populations and the several types of individuals, respectively. We prove that this stochastic sequence can be studied under the general setting provided by the multitype branching process theory. Probabilistic properties and limiting results are then established. As application, we present an illustrative example about the population dynamics of biological systems formed by long-lived raptor colonies.

scholarly journals Modeling the ecology of parasitic plasmids

2021 ◽  
Author(s):  
Jaime G. Lopez ◽  
Mohamed S. Donia ◽  
Ned S. Wingreen
Keyword(s):  
Mathematical Modeling ◽  
Population Dynamics ◽  
Tragedy Of The Commons ◽  
Fitness Costs ◽  
Metapopulation Model ◽  
The Commons ◽  
Modern Biotechnology ◽  
Natural Ecology ◽  
Unique Plasmid ◽  
Competing Populations

AbstractPlasmids are autonomous genetic elements that can be exchanged between microorganisms via horizontal gene transfer (HGT). Despite the central role they play in antibiotic resistance and modern biotechnology, our understanding of plasmids’ natural ecology is limited. Recent experiments have shown that plasmids can spread even when they are a burden to the cell, suggesting that natural plasmids may exist as parasites. Here, we use mathematical modeling to explore the ecology of such parasitic plasmids. We first develop models of single plasmids and find that a plasmid’s population dynamics and optimal infection strategy are strongly determined by the plasmid’s HGT mechanism. We then analyze models of co-infecting plasmids and show that parasitic plasmids are prone to a “tragedy of the commons” in which runaway plasmid invasion severely reduces host fitness. We propose that this tragedy of the commons is averted by selection between competing populations and demonstrate this effect in a metapopulation model. We derive predicted distributions of unique plasmid types in genomes—comparison to the distribution of plasmids in a collection of 17,725 genomes supports a model of parasitic plasmids with positive plasmid–plasmid interactions that ameliorate plasmid fitness costs or promote the invasion of new plasmids.

Branching processes and functional differential equations determining steady-size distributions in cell populations

1995 ◽  
Vol 32 (01) ◽  
pp. 1-10
Author(s):  
Ziad Taib
Keyword(s):  
Differential Equation ◽  
Branching Process ◽  
Branching Processes ◽  
Functional Differential Equations ◽  
Cell Populations ◽  
Size Distributions ◽  
Multitype Branching Process ◽  
Functional Differential ◽  
Intuitive Interpretation ◽  
Infinite Sum

The functional differential equation y′(x) = ay(λx) + by(x) arises in many different situations. The purpose of this note is to show how it arises in some multitype branching process cell population models. We also show how its solution can be given an intuitive interpretation as the probability density function of an infinite sum of independent but not identically distributed random variables.

scholarly journals Galton–Watson and branching process representations of the normalized Perron–Frobenius eigenvector

2019 ◽  
Vol 23 ◽  
pp. 797-802
Author(s):  
Raphaël Cerf ◽  
Joseba Dalmau
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Branching Process ◽  
Invariant Probability Measure ◽  
Classical Formula ◽  
Multitype Branching Process ◽  
Primitive Matrix ◽  
Watson Process

Let A be a primitive matrix and let λ be its Perron–Frobenius eigenvalue. We give formulas expressing the associated normalized Perron–Frobenius eigenvector as a simple functional of a multitype Galton–Watson process whose mean matrix is A, as well as of a multitype branching process with mean matrix e(A−I)t. These formulas are generalizations of the classical formula for the invariant probability measure of a Markov chain.

Predictive Modeling as guide for Health Informatics Deployment

2017 ◽  
pp. 128-162
Author(s):  
Fabrizio L. Ricci ◽  
Oscar Tamburis
Keyword(s):  
Mathematical Modeling ◽  
Predictive Modeling ◽  
Health Informatics ◽  
Research Work ◽  
Clinical Information ◽  
Healthcare Sector ◽  
Adoption Process ◽  
Design Features ◽  
Care Processes ◽  
Ex Ante

The present research work shows the main steps conducted towards the exploitation of the LUMIR project, aiming at realizing an EHR framework in the Italian Region of Basilicata (also known as Lucania). It relates to a structure of network–enabled services capable of integrating the ICT solutions used by the operators of the Healthcare System of Basilicata Region. The adoption process of the LuMiR system was meant to address the issues connected to the design features as well as to the EHR diffusion and the acceptance aspects. The mathematical modeling approach introduced aimed at making possible to get to a measure “ex–ante” of both adequacy and significance of the adoption process itself. The final intent is to work out a scalable and exportable model of advanced management of clinical information, towards a stronger cooperation among the provider organizations and a better governance of care processes, as crucial element within the more general path of modernization of the healthcare sector.

Population Dynamics: Mathematical Modeling and Reality

BIOPHYSICS ◽  
2019 ◽  
Vol 64 (6) ◽  
pp. 956-977
Author(s):  
A. B. Medvinsky ◽  
B. V. Adamovich ◽  
A. V. Rusakov ◽  
D. A. Tikhonov ◽  
N. I. Nurieva ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Population Dynamics
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