scholarly journals On mutations in the branching model for multitype populations

2018 ◽  
Vol 50 (2) ◽  
pp. 543-564 ◽  
Author(s):  
Loïc Chaumont ◽  
Thi Ngoc Anh Nguyen
Keyword(s):  
Infectious Diseases ◽  
Asymptotic Behaviour ◽  
Continuous Time ◽  
Mutation Rates ◽  
Genetic Evolution ◽  
Connected Component ◽  
Branching Model ◽  
Limiting Behaviour ◽  
Number Of Individuals

AbstractThe forest of mutations associated to a multitype branching forest is obtained by merging together all vertices in each of its clusters and by preserving connections between them. (Here, by cluster, we mean a maximal connected component of the forest in which all vertices have the same type.) We first show that the forest of mutations of any multitype branching forest is itself a branching forest. Then we give its progeny distribution and we describe some of its crucial properties in terms of the initial progeny distribution. We also obtain the limiting behaviour of the number of mutations both when the total number of individuals tends to ∞ and when the number of roots tends to ∞. The continuous-time case is then investigated by considering multitype branching forests with edge lengths. When mutations are nonreversible, we give a representation of their emergence times which allows us to describe the asymptotic behaviour of the latter, under certain conditions on the mutation rates. These results have potential relevance for emergence of mutations in population cells, particularly for genetic evolution of cancer or development of infectious diseases.

Initial and final behaviour of failure rate functions for mixtures and systems

2003 ◽  
Vol 40 (03) ◽  
pp. 721-740 ◽  
Author(s):  
Henry W. Block ◽  
Yulin Li ◽  
Thomas H. Savits
Keyword(s):  
Asymptotic Behaviour ◽  
Failure Rate ◽  
Rate Function ◽  
Coherent Systems ◽  
Failure Rate Function ◽  
Rate Functions ◽  
Limiting Behaviour

In this paper we consider the initial and asymptotic behaviour of the failure rate function resulting from mixtures of subpopulations and formation of coherent systems. In particular, it is shown that the failure rate of a mixture has the same limiting behaviour as the failure rate of the strongest subpopulation. A similar result holds for systems except the role of strongest subpopulation is replaced by strongest min path set.

scholarly journals Probiotics and Paraprobiotics in Viral Infection: Clinical Application and Effects on the Innate and Acquired Immune Systems

2018 ◽  
Vol 24 (6) ◽  
pp. 710-717 ◽  
Author(s):  
Osamu Kanauchi ◽  
Akira Andoh ◽  
Sazaly AbuBakar ◽  
Naoki Yamamoto
Keyword(s):  
Infectious Diseases ◽  
Viral Infection ◽  
Human Ecology ◽  
Commensal Bacteria ◽  
Mutation Rates ◽  
Viral Diseases ◽  
Interferon Production ◽  
Unique Mechanism ◽  
Stimulation Of

Recently, the risk of viral infection has dramatically increased owing to changes in human ecology such as global warming and an increased geographical movement of people and goods. However, the efficacy of vaccines and remedies for infectious diseases is limited by the high mutation rates of viruses, especially, RNA viruses. Here, we comprehensively review the effectiveness of several probiotics and paraprobiotics (sterilized probiotics) for the prevention or treatment of virally-induced infectious diseases. We discuss the unique roles of these agents in modulating the cross-talk between commensal bacteria and the mucosal immune system. In addition, we provide an overview of the unique mechanism by which viruses are eliminated through the stimulation of type 1 interferon production by probiotics and paraprobiotics via the activation of dendritic cells. Although further detailed research is necessary in the future, probiotics and/or paraprobiotics are expected to be among the rational adjunctive options for the treatment of various viral diseases.

Integer-valued branching processes with immigration

1983 ◽  
Vol 15 (04) ◽  
pp. 713-725 ◽  
Author(s):  
F. W. Steutel ◽  
W. Vervaat ◽  
S. J. Wolfe
Keyword(s):  
Difference Equation ◽  
Continuous Time ◽  
Queueing Theory ◽  
Branching Processes ◽  
Random Variables ◽  
Discrete State ◽  
Limiting Behaviour ◽  
Supercritical Branching Processes

The notion of self-decomposability for -valued random variables as introduced by Steutel and van Harn [10] and its generalization by van Harn, Steutel and Vervaat [5], are used to study the limiting behaviour of continuous-time Markov branching processes with immigration. This behaviour provides analogues to the behaviour of sequences of random variables obeying a certain difference equation as studied by Vervaat [12] and their continuous-time counterpart considered by Wolfe [13]. An application in queueing theory is indicated. Furthermore, discrete-state analogues are given for results on stability in the processes studied by Wolfe, and for results on self-decomposability in supercritical branching processes by Yamazato [14].

Markovian manpower models in continuous time

1977 ◽  
Vol 14 (02) ◽  
pp. 249-259 ◽  
Author(s):  
Alexander Mehlmann
Keyword(s):  
Markov Processes ◽  
Continuous Time ◽  
Asymptotic Form ◽  
New Approach ◽  
Limiting Behaviour

The problem of determining the asymptotic form of the stock vector n (t) in a continuous time Markovian manpower model is solved for asymptotically exponential recruitment functions {R(t)}. A new approach to the limiting behaviour of some manpower systems with given total sizes {N(t)} is then given by means of time-inhomogeneous Markov processes.

A branching model by population size dependence

1975 ◽  
Vol 7 (03) ◽  
pp. 495-510
Author(s):  
Carla Lipow
Keyword(s):  
Limit Theorem ◽  
Population Size ◽  
Generating Function ◽  
Continuous Time ◽  
Branching Process ◽  
Size Dependence ◽  
Stationary Measure ◽  
Markov Branching Process ◽  
Branching Model

A continuous-time Markov branching process is modified to allow some dependence of offspring generating function on population size. The model involves a given population size M, below which the offspring generating function is supercritical and above which it is subcritical. Immigration is allowed when the population size is 0. The process has a stationary measure, and an expression for its generating function is found. A limit theorem for the stationary measure as M tends to ∞ is then obtained.

scholarly journals An Overview of the Progress Made on the Coronavirus Vaccine

2020 ◽  
Vol 185 ◽  
pp. 03042
Author(s):  
Yu Fang
Keyword(s):  
United States ◽  
Infectious Diseases ◽  
Incidence Rate ◽  
Scientific Reasoning ◽  
Vaccine Development ◽  
The United States ◽  
Ideal Solution ◽  
Vaccine Candidates ◽  
Number Of Individuals

The Coronavirus Disease-2019 (COVID-19) pandemic has led to a critical economic crash around the globe, affecting billions of people worldwide. Without a cure, the number of cases continues to increase exponentially. Countries, including the United States, Brazil, and India, currently lead in the number of cases with numbers soaring in the millions. Immunization is crucial to preventing the spread of infectious diseases and can help a large number of individuals quickly while keeping current cases under control. Following the publication of the genome sequence of SARS-CoV-2, vaccine development has been accelerated at an unprecedented rate. 115 vaccine candidates are currently under study with the hope of finding an ideal solution and mitigating the Coronavirus incidence rate. With some vaccine candidates having more potential than others, this review focuses on the characterization of different vaccine options. The analysis of probable vaccines, including mRNA vaccines and adenovirus vaccines, is conducted, and the scientific reasoning behind the vaccines is also discussed. In this review, the latest strategy vaccine is introduced and the effective vaccines are analysed.

Strict supercritical generation-dependent Crump–Mode–Jagers branching processes

1978 ◽  
Vol 10 (04) ◽  
pp. 744-763 ◽  
Author(s):  
L. Edler
Keyword(s):  
Generating Functions ◽  
Positive Real Number ◽  
Branching Processes ◽  
Positive Real ◽  
Quadratic Mean ◽  
Malthusian Parameter ◽  
Renewal Equations ◽  
Branching Model ◽  
Age Dependent ◽  
Number Of Individuals

The general age-dependent branching model of Crump, Mode and Jagers will be generalized towards generation-dependent varying lifespan and reproduction distributions. A system of integral and renewal equations is established for the generating functions and the first two moments of Zi (t) (the number of individuals alive at time t), if the population was initiated at time 0 by one ancestor of age 0 from generation i. Convergence in quadratic mean of Zi (t)/EZi (t) as t tends to infinity is obtained if the generation-dependent reproduction functions converge to a supercritical one. In particular, if this convergence is slow enough t γ exp (αt) is the asymptotic behavior of EZi (t) for t tending to infinity, where γ is a positive real number and α the Malthusian parameter of growth of the limiting reproduction function.

scholarly journals Collective Dynamics of Swarms with a New Attraction/Repulsion Function

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Hong Shi ◽  
Guangming Xie
Keyword(s):  
Euclidean Space ◽  
Numerical Simulations ◽  
Continuous Time ◽  
Dimensional Euclidean Space ◽  
Continuous Time Model ◽  
Time Model ◽  
Collective Dynamics ◽  
Number Of Individuals ◽  
Swarm Size

We specify an “individual-based” continuous-time model for swarm aggregation in -dimensional Euclidean space. We show that the swarm is completely stable, and the center of the swarm is stationary. Numerical simulations indicate that the individuals will form a stable and cohesive swarm, and under the attraction/repulsion function, the bound of the swarm size will increase as the number of individuals increases.

Limit theorems for the total size of a spatial epidemic

1997 ◽  
Vol 34 (3) ◽  
pp. 698-710 ◽  
Author(s):  
Håkan Andersson ◽  
Boualem Djehiche
Keyword(s):  
Asymptotic Behaviour ◽  
Epidemic Model ◽  
Limit Theorems ◽  
Total Size ◽  
Spatial Epidemic Model ◽  
Spatial Epidemic ◽  
Number Of Individuals ◽  
General Stochastic

We study the long-term behaviour of a sequence of multitype general stochastic epidemics, converging in probability to a deterministic spatial epidemic model, proposed by D. G. Kendall. More precisely, we use branching and deterministic approximations in order to study the asymptotic behaviour of the total size of the epidemics as the number of types and the number of individuals of each type both grow to infinity.

Sign in / Sign up

Export Citation Format

Share Document