Pandemic spread in communities via random graphs by Minzer, Dor, Oz, Yaron, Safra, Muli, Wainstain, Lior

“…<jats:title>Abstract</jats:title> <jats:p>Working in the multi-type Galton–Watson branching-process framework we analyse the spread of a pandemic via a general multi-type random contact graph. …”
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Using real-time modelling to inform the 2017 Ebola outbreak response in DR Congo by Thompson, R, Hart, W, Keita, M, Fall, I, Gueye, A, Chamla, D, Mossoko, M, Ahuka-Mundeke, S, Nsio-Mbeta, J, Jombart, T, Polonsky, J

“…Eight cases occurred before 15 May 2017, when the Ebola Response Team (ERT; co-ordinated by the World Health Organisation and DRC Ministry of Health) was deployed to reduce transmission. We used a branching process model to estimate that, pre-ERT arrival, the reproduction number was R=1.49 (95% credible interval (0.67, 2.81)). …”

Estimating the measles effective reproduction number in Australia from routine notification data by May Chiew, Heather F Gidding, Aditi Dey, James Wood, Nicolee Martin, Stephanie Davis, Peter McIntyre

“…The other methods estimated R by fitting a subcritical branching process that modelled the spread of an infection with a given R to the observed distributions of outbreak sizes (method 2) and generations of spread (method 3). …”
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Inference of R(0) and transmission heterogeneity from the size distribution of stuttering chains. by Seth Blumberg, James O Lloyd-Smith

“…Previous researchers have used chain size distributions to infer [Formula: see text], but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, [Formula: see text]) has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both [Formula: see text] and the dispersion parameter that characterizes heterogeneity. …”
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Intrinsic randomness in epidemic modelling beyond statistical uncertainty by Matthew J. Penn, Daniel J. Laydon, Joseph Penn, Charles Whittaker, Christian Morgenstern, Oliver Ratmann, Swapnil Mishra, Mikko S. Pakkanen, Christl A. Donnelly, Samir Bhatt

“…Here, we characterise both epistemic and aleatoric uncertainty using a time-varying general branching process. Our framework explicitly decomposes aleatoric variance into mechanistic components, quantifying the contribution to uncertainty produced by each factor in the epidemic process, and how these contributions vary over time. …”
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Estimating local outbreak risks and the effects of non-pharmaceutical interventions in age-structured populations: SARS-CoV-2 as a case study by Lovell-Read, F, Shen, S, Thompson, R

“…Here, using SARS-CoV-2 as a case study, we develop a branching process model for assessing the risk that an infectious case arriving in a new location will initiate a local outbreak, accounting for the age distribution of the host population. …”

Estimating local outbreak risks and the effects of non-pharmaceutical interventions in age-structured populations: SARS-CoV-2 as a case study by Lovell-Read, FA, Shen, S, Thompson, RN

“…Here, using SARS-CoV-2 as a case study, we develop a branching process model for assessing the risk that an infectious case arriving in a new location will initiate a local outbreak, accounting for the age distribution of the host population. …”

Plexin A3 and turnout regulate motor axonal branch morphogenesis in zebrafish. by Rajiv Sainath, Michael Granato

“…This precisely timed and spatially restricted branching process is disrupted in turnout mutants we identified in a forward genetic screen. …”
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Synthesis of Soluble High Molar Mass Poly(Phenylene Methylene)-Based Polymers by Marco F. D’Elia, Yingying Yu, Melvin Renggli, Madeleine A. Ehweiner, Carina Vidovic, Nadia C. Mösch-Zanetti, Markus Niederberger, Walter Caseri

“…Interestingly, thermal and optical characterization established that the branching process does not affect the thermoplastic behavior and the fluorescence of the material, thus opening up PPM-based compounds with high molar mass for applications.…”
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The choice of tree prior and molecular clock does not substantially affect phylogenetic inferences of diversification rates by Brice A.J. Sarver, Matthew W. Pennell, Joseph W. Brown, Sara Keeble, Kayla M. Hardwick, Jack Sullivan, Luke J. Harmon

“…In Bayesian phylogenetics, estimating a phylogeny requires specifying priors on parameters characterizing the branching process and rates of substitution among lineages, in addition to others. …”
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Stochastic modeling of biological sequence evolution by Xu, Keyuan

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Semidefinite relaxation based branch-and-bound method for nonconvex quadratic programming by Hu, Sha, S.M. Massachusetts Institute of Technology

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The risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions by Sachak-Patwa, R, Byrne, HM, Dyson, L, Thompson, RN

“…<br> <strong>Methods</strong> Using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases arriving in low prevalence settings initiate a local outbreak. …”

How absolute is zero? An evaluation of historical and current definitions of malaria elimination. by Cohen, J, Moonen, B, Snow, R, Smith, D

“…The review has been supported by analysis of the underlying mathematical concepts on which these definitions are based through simple branching process models that describe the proliferation of malaria cases following importation. …”

Modeling scenarios for mitigating outbreaks in congregate settings. by Seth Blumberg, Phoebe Lu, Ada T Kwan, Christopher M Hoover, James O Lloyd-Smith, David Sears, Stefano M Bertozzi, Lee Worden

“…Introduction of disease into the resident population from the community is modeled as a stochastic point process coupled to a branching process, while spread between residents is modeled via a deterministic compartmental model that accounts for depletion of susceptible individuals. …”
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Finding Rumor Sources on Random Trees by Shah, Devavrat, Zaman, Tauhid R

“…The key result is an interesting connection between a continuous time branching process and the effectiveness of rumor centrality. …”
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Finding Rumor Sources on Random Graphs by Shah, Devavrat, Zaman, Tauhid

“…The key result is an interesting connection between a multi-type continuous time branching process (an equivalent representation of a generalized Polya's urn, cf. [1]) and the effectiveness of rumor centrality. …”
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Self-organised criticality in random graph processes by Yeo, D

“…</p> <p> We prove a convergence result for the proportion of vertices of each type which survive until time <em>t</em>, and describe the local limit in terms of a multitype branching process whose parameters are critical and given by the solution to an unusual differential equation driven by Perron--Frobenius eigenvectors. …”

Estimating COVID-19 outbreak risk through air travel by Daon, Y, Thompson, RN, Obolski, U

“…We use a probabilistic, branching-process-based approach that considers the volume of air travelers between airports and the reproduction number at each location, accounting for local population density.…”

Using contact data to model the impact of contact tracing and physical distancing to control the SARS-CoV-2 outbreak in Kenya by Wagner, M, Kombe, I, Kiti, MC, Aziza, R, Barasa, E, Nokes, J

“…<br><strong>Methods:</strong> We extend a previously developed branching process model for contact tracing to include realistic contact data from Kenya. …”