BibSonomyburst/user/ebo/stochasticBibSonomy RSS feed for /user/ebo/stochastic2012-02-16T10:46:34+01:00http://www.bibsonomy.org/bibtex/24a799026e607dbc68b8f86d5e89ac3c9/eboebo2009-08-05T19:10:59+02:00evolution immunity imported influenza stochastic winmong <span class="authorEditorList"><a href="/author/Minayev"> Minayev</a>, and <a href="/author/Ferguson">N Ferguson</a> </span><em>Journal of the Royal Society Interface</em> (<em>January 2009</em>)Wed Aug 05 19:10:59 CEST 2009Journal of the Royal Society InterfaceJanIncorporating demographic stochasticity into multi-strain epidemic models: application to influenza A2009evolution immunity imported influenza stochastic winmong We develop mathematical models of the transmission and evolution of multi-strain pathogens that incorporate strain extinction and the stochastic generation of new strains via mutation. The dynamics resulting from these models is then examined with the applied aim of understanding the mechanisms underpinning the evolution and dynamics of rapidly mutating pathogens, such as human influenza viruses. Our approach, while analytically relatively simple, gives results that are qualitatively similar to those obtained from much more complex individually based simulation models. We examine strain dynamics as a function of cross-immunity and key transmission parameters, and show that introducing strain extinction and modelling mutation as a stochastic process significantly changes the model dynamics, leading to lower strain diversity, reduced infection prevalence and shorter strain lifetimes. Finally, we incorporate transient strain-transcending immunity in the model and demonstrate that it reduces strain diversity further, giving patterns of sequential strain replacement similar to that seen in human influenza A viruses.Incorporating demographic stochasticity into multi...[J R Soc Interface. 2009] - PubMed Resulthttp://www.bibsonomy.org/bibtex/2d90bcd22e8c01e07a69873eb971b1a68/eboebo2009-07-20T22:39:12+02:00imported stochastic <span class="authorEditorList"><a href="/author/Moschopoulos">Panagis Moschopoulos</a>, and <a href="/author/Shpak">Max Shpak</a> </span>(<em>2009</em>)<em>cite arxiv:0901.1066 . </em>Mon Jul 20 22:39:12 CEST 2009cite arxiv:0901.1066 Taxon Size Distribution in a Time Homogeneous Birth and Death Process2009imported stochastic The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade) themselves follow a random birth process, deriving the distribution of lineage sizes involves averaging the solutions to a birth and death process over the distribution of time intervals separating the origin of the lineages. In this paper, we show that the resulting distributions can be represented by hypergeometric functions of the second kind. We also provide approximations of these distributions up to the second order, and compare these results to the asymptotic distributions and numerical approximations used in previous studies. For two limiting cases, one with a relatively high rate of lineage origin, one with a low rate, the cumulative probability densities and percentiles are compared to show that the approximations are robust over a wide rane of parameters. It is proposed that the probability density distributions of lineage size may have a number of relevant applications to biological problems such as the coalescence of genetic lineages and in predicting the number of species in living and extinct higher taxa, as these systems are special instances of the underlying process analyzed in this paper. [0901.1066] Taxon Size Distribution in a Time Homogeneous Birth and Death Processhttp://www.bibsonomy.org/bibtex/2affdb48572e7bc346cce1a1c600c2b68/eboebo2009-07-10T19:23:40+02:00branching imported stochastic <span class="authorEditorList"><a href="/author/Athreya">Krishna Balasundaram Athreya</a> </span><em>Annals of Mathematical Statistics</em> (<em>1968</em>)Fri Jul 10 19:23:40 CEST 2009Annals of Mathematical Statistics347--357Some results on multitype continuous time {M}arkov branching processes391968branching imported stochastic MR: Publications results for "MR Number=(221600)"http://www.bibsonomy.org/bibtex/2768b177a9276e81345f0e7124e0e2919/eboebo2009-07-10T02:17:19+02:00epi imported stochastic <span class="authorEditorList"><a href="/author/Kendall">D.G. Kendall</a> </span> (<em>1956</em>)Fri Jul 10 02:17:19 CEST 2009Proc. 3rd Berkeley Symp. Math. Statist. Prob149--165{Deterministic and stochastic epidemics in closed populations}41956epi imported stochastic http://www.bibsonomy.org/bibtex/22e1ed1de4ab36e19ccea06c8634111d6/eboebo2009-07-09T00:05:35+02:00branching imported stochastic <span class="authorEditorList"><a href="/author/Yakovlev">Andrei Y. Yakovlev</a>, and <a href="/author/Yanev">Nikolay M. Yanev</a> </span>(<em>2009</em>)<em>cite arxiv:0902.4773 Comment: Published in at http://dx.doi.org/10.1214/08-AAP539 the Annals of Applied Probability http://www.imstat.org/aap/ by the I<span class="info">...<div>cite arxiv:0902.4773 Comment: Published in at http://dx.doi.org/10.1214/08-AAP539 the Annals of Applied Probability http://www.imstat.org/aap/ by the Institute of Mathematical Statistics http://www.imstat.org</div></span> . </em>Thu Jul 09 00:05:35 CEST 2009cite arxiv:0902.4773 Comment: Published in at http://dx.doi.org/10.1214/08-AAP539 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)Relative frequencies in multitype branching processes2009branching imported stochastic This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time of observation is fixed. The result is valid for any branching process with a finite number of types; the only assumption required is that of independent individual evolutions. The problem under consideration is motivated by applications in the area of cell biology. Specifically, the reported limiting results are of advantage in cell kinetics studies where the relative frequencies but not the absolute cell counts are accessible to measurement. Relevant statistical applications are discussed in the context of asymptotic maximum likelihood inference for multitype branching processes. [0902.4773] Relative frequencies in multitype branching processeshttp://www.bibsonomy.org/bibtex/28be83f74960d3cdf9fdfb37b660f269b/eboebo2009-07-08T23:39:42+02:00branching imported stochastic <span class="authorEditorList"><a href="/author/Mode">Charles Mode</a> </span><em>Bulletin of Mathematical Biology</em> <em>31(3):575--589</em> (<em>September 1969</em>)Wed Jul 08 23:39:42 CEST 2009Bulletin of Mathematical Biology#sep#3575--589Applications of generalized multi-type age-dependent branching processes in population genetics311969branching imported stochastic Without Abstract ER -SpringerLink - Journal Articlehttp://www.bibsonomy.org/bibtex/25188727be38bd3bc0cca61f86acfaa88/eboebo2009-07-03T04:33:39+02:00branching imported stochastic <span class="authorEditorList"><a href="/author/Nerman">Olle Nerman</a> </span><em>Probability Theory and Related Fields</em> <em>57(3):365--395</em> (<em>September 1981</em>)Fri Jul 03 04:33:39 CEST 2009Probability Theory and Related Fields#sep#3365--395On the convergence of supercritical general (C-M-J) branching processes571981branching imported stochastic Convergence in probability of Malthus normed supercritical general branching processes (i.e. Crump-Mode-Jagers branching processes) counted with a general characteristic are established, provided the latter satisfies mild regularity conditions. If the Laplace transform of the reproduction point process evaluated in the Malthusian parameter has a finite ‘x log x-moment’ convergence in probability of the empirical age distribution and more generally of the ratio of two differently counted versions of the process also follow. ER -SpringerLink - Journal Articlehttp://www.bibsonomy.org/bibtex/27a5dc6b7374c8394bc7653e64b8e790a/eboebo2009-07-03T02:50:54+02:00epi stochastic <span class="authorEditorList"><a href="/author/Ball">Frank Ball</a>, and <a href="/author/Donnelly">Peter Donnelly</a> </span><em>Stochastic Processes and their Applications</em> <em>55(1):1 - 21</em> (<em>1995</em>)Fri Jul 03 02:50:54 CEST 2009Stochastic Processes and their Applications11 - 21Strong approximations for epidemic models551995epi stochastic This paper is concerned with the approximation of early stages of epidemic processes by branching processes. A general model for an epidemic in a closed, homogeneously mixing population is presented. A construction of a sequence of such epidemics, indexed by the initial number of susceptibles N, from the limiting branching process is described. Strong convergence of the epidemic processes to the branching process is shown when the latter goes extinct. When the branching process does not go extinct, necessary and sufficient conditions on the sequence (tN) for strong convergence over the time interval [0, tN] are provided. Convergence of a wide variety of functionals of the epidemic process to corresponding functionals of the branching process is shown, and bounds are provided on the total variation distance for given N. The theory is illustrated by reference to the general stochastic epidemic. Generalisations to, for example, multipopulation epidemics are described briefly.ScienceDirect - Stochastic Processes and their Applications : Strong approximations for epidemic models