263 research outputs found
Potential-Density Basis Sets for Galactic Disks
A class of complete potential-density basis sets in cylindrical (R,phi,z)
coordinates is presented. This class is suitable for stability studies of
galactic disks in three dimensions and includes basis sets tailored for disks
with vertical density profiles that are exponential (exp(-|z|/\zn)), Gaussian
(exp(-(z/\zn)^2) or locally isothermal (sech^2(z/\zn)). The basis sets are
non-discrete and non-biorthogonal; however, the extra numerical computations
required (compared with discrete biorthogonal sets) are explained and
constitute a small overhead. The method of construction (and proof of
completeness) is simple and can be used to construct basis sets for other
density distributions that are best described in circular or elliptic
cylindrical coordinates. When combined with a basis set designed for spheroidal
systems, the basis sets presented here can be used to study the stability of
realistic disks embedded in massive halos.Comment: Accepted for publication in The Astrophysical Journal, 13 pages,
plain TeX, uses mtexsis.tex, no figure
Equation-free modeling of evolving diseases: Coarse-grained computations with individual-based models
We demonstrate how direct simulation of stochastic, individual-based models
can be combined with continuum numerical analysis techniques to study the
dynamics of evolving diseases. % Sidestepping the necessity of obtaining
explicit population-level models, the approach analyzes the (unavailable in
closed form) `coarse' macroscopic equations, estimating the necessary
quantities through appropriately initialized, short `bursts' of
individual-based dynamic simulation. % We illustrate this approach by analyzing
a stochastic and discrete model for the evolution of disease agents caused by
point mutations within individual hosts. % Building up from classical SIR and
SIRS models, our example uses a one-dimensional lattice for variant space, and
assumes a finite number of individuals. % Macroscopic computational tasks
enabled through this approach include stationary state computation, coarse
projective integration, parametric continuation and stability analysis.Comment: 16 pages, 8 figure
THE OPTIMAL N-BODY METHOD FOR STABILITY STUDIES OF GALAXIES
The stability of a galaxy model is most easily assessed through N-body
simulation. Particle-mesh codes have been widely used for this purpose, since
they enable the largest numbers of particles to be employed. We show that the
functional expansion technique, originally proposed by Clutton-Brock for other
simulation problems, is in fact superior for stability work. For simulations of
linear evolution it is not much slower than grid methods using the same number
of particles, and reproduces analytical results with much greater accuracy.
This success rests on its ability to represent global modes with a modest
number of basis functions; grid methods may be more effective for other
applications, however. Our conclusions are based on implementations of
functional expansion and grid algorithms for disk galaxies.Comment: Accepted for publication in The Astrophysical Journal, to appear
October 1, 1995; 16 pages including 4 figures, self-unpacking uuencoded
gzipped postscript, also available by email from [email protected]
Age-specific mortality during the 1918 influenza pandemic: unravelling the mystery of high young adult mortality.
The worldwide spread of a novel influenza A (H1N1) virus in 2009 showed that influenza remains a significant health threat, even for individuals in the prime of life. This paper focuses on the unusually high young adult mortality observed during the Spanish flu pandemic of 1918. Using historical records from Canada and the U.S., we report a peak of mortality at the exact age of 28 during the pandemic and argue that this increased mortality resulted from an early life exposure to influenza during the previous Russian flu pandemic of 1889-90. We posit that in specific instances, development of immunological memory to an influenza virus strain in early life may lead to a dysregulated immune response to antigenically novel strains encountered in later life, thereby increasing the risk of death. Exposure during critical periods of development could also create holes in the T cell repertoire and impair fetal maturation in general, thereby increasing mortality from infectious diseases later in life. Knowledge of the age-pattern of susceptibility to mortality from influenza could improve crisis management during future influenza pandemics
Generation of potential/surface density pairs in flat disks Power law distributions
We report a simple method to generate potential/surface density pairs in flat
axially symmetric finite size disks. Potential/surface density pairs consist of
a ``homogeneous'' pair (a closed form expression) corresponding to a uniform
disk, and a ``residual'' pair. This residual component is converted into an
infinite series of integrals over the radial extent of the disk. For a certain
class of surface density distributions (like power laws of the radius), this
series is fully analytical. The extraction of the homogeneous pair is
equivalent to a convergence acceleration technique, in a matematical sense. In
the case of power law distributions, the convergence rate of the residual
series is shown to be cubic inside the source. As a consequence, very accurate
potential values are obtained by low order truncation of the series. At zero
order, relative errors on potential values do not exceed a few percent
typically, and scale with the order N of truncation as 1/N**3. This method is
superior to the classical multipole expansion whose very slow convergence is
often critical for most practical applications.Comment: Accepted for publication in Astronomy & Astrophysics 7 pages, 8
figures, F90-code available at
http://www.obs.u-bordeaux1.fr/radio/JMHure/intro2applawd.htm
Evaluating undercounts in epidemics: response to Maruotti et al. 2022
Maruotti et al. 2022 used a mark-recapture approach to estimate bounds on the
true number of monkeypox infections in various countries. These approaches are
fundamentally flawed; it is impossible to estimate undercounting based solely
on a single stream of reported cases. Simulations based on a Richards curve for
cumulative incidence show that, for reasonable epidemic parameters, the
proposed methods estimate bounds on the ascertainment ratio of roughly independently of the true ascertainment ratio. These methods
should not be used
Dynamical epidemic suppression using stochastic prediction and control
We consider the effects of noise on a model of epidemic outbreaks, where the
outbreaks appear. randomly. Using a constructive transition approach that
predicts large outbreaks, prior to their occurrence, we derive an adaptive
control. scheme that prevents large outbreaks from occurring. The theory
inapplicable to a wide range of stochastic processes with underlying
deterministic structure.Comment: 14 pages, 6 figure
Bifurcations and chaotic dynamics in a tumour-immune-virus system
Despite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunity-dependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.Publisher PDFPeer reviewe
Pandemic Paradox: Early Life H2N2 Pandemic Influenza Infection Enhanced Susceptibility to Death during the 2009 H1N1 Pandemic.
Recent outbreaks of H5, H7, and H9 influenza A viruses in humans have served as a vivid reminder of the potentially devastating effects that a novel pandemic could exert on the modern world. Those who have survived infections with influenza viruses in the past have been protected from subsequent antigenically similar pandemics through adaptive immunity. For example, during the 2009 H1N1 "swine flu" pandemic, those exposed to H1N1 viruses that circulated between 1918 and the 1940s were at a decreased risk for mortality as a result of their previous immunity. It is also generally thought that past exposures to antigenically dissimilar strains of influenza virus may also be beneficial due to cross-reactive cellular immunity. However, cohorts born during prior heterosubtypic pandemics have previously experienced elevated risk of death relative to surrounding cohorts of the same population. Indeed, individuals born during the 1890 H3Nx pandemic experienced the highest levels of excess mortality during the 1918 "Spanish flu." Applying Serfling models to monthly mortality and influenza circulation data between October 1997 and July 2014 in the United States and Mexico, we show corresponding peaks in excess mortality during the 2009 H1N1 "swine flu" pandemic and during the resurgent 2013-2014 H1N1 outbreak for those born at the time of the 1957 H2N2 "Asian flu" pandemic. We suggest that the phenomenon observed in 1918 is not unique and points to exposure to pandemic influenza early in life as a risk factor for mortality during subsequent heterosubtypic pandemics.IMPORTANCE The relatively low mortality experienced by older individuals during the 2009 H1N1 influenza virus pandemic has been well documented. However, reported situations in which previous influenza virus exposures have enhanced susceptibility are rare and poorly understood. One such instance occurred in 1918-when those born during the heterosubtypic 1890 H3Nx influenza virus pandemic experienced the highest levels of excess mortality. Here, we demonstrate that this phenomenon was not unique to the 1918 H1N1 pandemic but that it also occurred during the contemporary 2009 H1N1 pandemic and 2013-2014 H1N1-dominated season for those born during the heterosubtypic 1957 H2N2 "Asian flu" pandemic. These data highlight the heretofore underappreciated phenomenon that, in certain instances, prior exposure to pandemic influenza virus strains can enhance susceptibility during subsequent pandemics. These results have important implications for pandemic risk assessment and should inform laboratory studies aimed at uncovering the mechanism responsible for this effect
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Determinants of Influenza Mortality Trends: Age-Period-Cohort Analysis of Influenza Mortality in the United States, 1959-2016.
This study examines the roles of age, period, and cohort in influenza mortality trends over the years 1959-2016 in the United States. First, we use Lexis surfaces based on Serfling models to highlight influenza mortality patterns as well as to identify lingering effects of early-life exposure to specific influenza virus subtypes (e.g., H1N1, H3N2). Second, we use age-period-cohort (APC) methods to explore APC linear trends and identify changes in the slope of these trends (contrasts). Our analyses reveal a series of breakpoints where the magnitude and direction of birth cohort trends significantly change, mostly corresponding to years in which important antigenic drifts or shifts took place (i.e., 1947, 1957, 1968, and 1978). Whereas child, youth, and adult influenza mortality appear to be influenced by a combination of cohort- and period-specific factors, reflecting the interaction between the antigenic experience of the population and the evolution of the influenza virus itself, mortality patterns of the elderly appear to be molded by broader cohort factors. The latter would reflect the processes of physiological capital improvement in successive birth cohorts through secular changes in early-life conditions. Antigenic imprinting, cohort morbidity phenotype, and other mechanisms that can generate the observed cohort effects, including the baby boom, are discussed
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