scholarly journals Fractional SIR Epidemiological Models

2020 ◽  
Author(s):  
Amirhossein Taghvaei ◽  
Tryphon T. Georgiou ◽  
Larry Norton ◽  
Allen Tannenbaum
Keyword(s):  
Transmission Rate ◽  
Strong Mixing ◽  
Epidemiological Models ◽  
Fractional Powers ◽  
Product Model ◽  
Standard Assumption ◽  
Data Set ◽  
Disease Propagation ◽  
Standard Product ◽  
Early Phases

AbstractThe purpose of this work is to make a case for epidemiological models with fractional exponent in the contribution of sub-populations to the transmission rate. More specifically, we question the standard assumption in the literature on epidemiological models, where the transmission rate dictating propagation of infections is taken to be proportional to the product between the infected and susceptible sub-populations; a model that relies on strong mixing between the two groups and widespread contact between members of the groups. We content, that contact between infected and susceptible individuals, especially during the early phases of an epidemic, takes place over a (possibly diffused) boundary between the respective sub-populations. As a result, the rate of transmission depends on the product of fractional powers instead. The intuition relies on the fact that infection grows in geographically concentrated cells, in contrast to the standard product model that relies on complete mixing of the susceptible to infected sub-populations. We validate the hypothesis of fractional exponents i) by numerical simulation for disease propagation in graphs imposing a local structure to allowed disease transmissions and ii) by fitting the model to a COVID-19 data set provided by John Hopkins University (JHUCSSE) for the period Jan-31-20 to Mar-24-20, for the countries of Italy, Germany, Iran, and France.

scholarly journals Fractional SIR epidemiological models

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Amirhossein Taghvaei ◽  
Tryphon T. Georgiou ◽  
Larry Norton ◽  
Allen Tannenbaum
Keyword(s):  
Incidence Rate ◽  
Local Structure ◽  
Strong Mixing ◽  
Epidemiological Models ◽  
Fractional Powers ◽  
Product Model ◽  
Standard Assumption ◽  
Disease Propagation ◽  
Standard Product ◽  
Early Phases

AbstractThe purpose of this work is to make a case for epidemiological models with fractional exponent in the contribution of sub-populations to the incidence rate. More specifically, we question the standard assumption in the literature on epidemiological models, where the incidence rate dictating propagation of infections is taken to be proportional to the product between the infected and susceptible sub-populations; a model that relies on strong mixing between the two groups and widespread contact between members of the groups. We contend, that contact between infected and susceptible individuals, especially during the early phases of an epidemic, takes place over a (possibly diffused) boundary between the respective sub-populations. As a result, the rate of transmission depends on the product of fractional powers instead. The intuition relies on the fact that infection grows in geographically concentrated cells, in contrast to the standard product model that relies on complete mixing of the susceptible to infected sub-populations. We validate the hypothesis of fractional exponents (1) by numerical simulation for disease propagation in graphs imposing a local structure to allowed disease transmissions and (2) by fitting the model to the JHU CSSE COVID-19 Data for the period Jan-22-20 to April-30-20, for the countries of Italy, Germany, France, and Spain.

Subtractive MLM and Prosodically Defective Morphemes

2017 ◽  
Author(s):  
Eva Zimmermann
Keyword(s):  
Prosodic Structure ◽  
Standard Assumption ◽  
Data Set ◽  
Representative Data

It is shown how the theory of PDM accounts for instances of subtractive MLM—the empirical phenomenon that is notoriously challenging for the claim that morphology is additive. Two general mechanisms inside PDM can predict subtractive MLM: usurpation of moras and the defective integration of morphemic prosodic nodes. Usurpation can arise if a segment underlyingly lacks a mora and ‘usurps’ it from a neighbouring segment that is hence deprived of it. In the second scenario, a prosodic node that is underlyingly not integrated into the higher/lower prosodic structure is affixed to a base and remains defectively integrated in the output. Given the standard assumption that only elements properly integrated under the highest prosodic node of the prosodic hierarchy are visible for the phonetics, this affix node and everything it dominates remain phonetically uninterpreted. It is shown how all attested types of subtractive MLM in the representative data set fall out from these two basic mechanisms.

scholarly journals A computationally tractable birth-death model that combines phylogenetic and epidemiological data

2020 ◽  
Author(s):  
Alexander E. Zarebski ◽  
Louis du Plessis ◽  
Kris V. Parag ◽  
Oliver G. Pybus
Keyword(s):  
Transmission Rate ◽  
Epidemiological Data ◽  
Heterogeneous Data ◽  
Pathogen Transmission ◽  
Data Sources ◽  
Primary Data ◽  
Analytic Approximation ◽  
Data Set ◽  
Combining Data ◽  
Birth Death

Inferring the dynamics of pathogen transmission during an outbreak is an important problem in both infectious disease epidemiology and phylodynamics. In mathematical epidemiology, estimates are often informed by time-series of infected cases while in phylodynamics genetic sequences sampled through time are the primary data source. Each data type provides different, and potentially complementary, insights into transmission. However inference methods are typically highly specialised and field-specific. Recent studies have recognised the benefits of combining data sources, which include improved estimates of the transmission rate and number of infected individuals. However, the methods they employ are either computationally prohibitive or require intensive simulation, limiting their real-time utility. We present a novel birth-death phylogenetic model, called TimTam which can be informed by both phylogenetic and epidemiological data. Moreover, we derive a tractable analytic approximation of the TimTam likelihood, the computational complexity of which is linear in the size of the data set. Using the TimTam we show how key parameters of transmission dynamics and the number of unreported infections can be estimated accurately using these heterogeneous data sources. The approximate likelihood facilitates inference on large data sets, an important consideration as such data become increasingly common due to improving sequencing capability.

scholarly journals The Spectral Energy Distribution of the Earliest Phases of Massive Star Formation

2015 ◽  
Vol 12 (S316) ◽  
pp. 151-152
Author(s):  
Randolf Klein ◽  
Jennifer Cooper ◽  
Leslie Looney ◽  
Thomas Henning ◽  
Sukanya Chakrabarti ◽  
...  
Keyword(s):  
Star Formation ◽  
Energy Distribution ◽  
Massive Star ◽  
Spectral Energy Distribution ◽  
Spectral Energy ◽  
Status Report ◽  
Massive Star Formation ◽  
Data Set ◽  
Good Spatial Resolution ◽  
Early Phases

AbstractWe have selected cold and massive (M > 100M⊙) cores as candidates for early phases of star formation from millimeter continuum surveys without associations at short wavelengths. We compared the millimeter continuum peak positions with IR and radio catalogs and excluded cores that had sources associated with the cores’ peaks. We compiled a list of 173 cores in over 117 regions that are candidates for very early phases of Massive Star Formation (MSF). Now with the Spitzer and Herschel archives, these cores can be characterized further. We are compiling this data set to construct the complete spectral energy distribution (SED) in the mid- and far-infrared with good spatial resolution and broad spectral coverage. This allow us to disentangle the complex regions and model the SED of the deeply embedded protostars/clusters. We present a status report of our efforts: a preview of the IR properties of all cores and their embedded source inferred from a grey body fit to the compiled SEDs.

scholarly journals Analysis of Ode Models for Malaria Propagation

2020 ◽  
Vol 17 (1) ◽  
pp. 31-39
Author(s):  
Fanni Dorner ◽  
Rahele Mosleh
Keyword(s):  
Existence And Uniqueness ◽  
Numerical Models ◽  
Equilibrium Points ◽  
Epidemiological Models ◽  
Qualitative Properties ◽  
Data Set ◽  
Ode Models ◽  
Population Dynamics Models ◽  
Dynamics Models ◽  
Uniqueness Of Equilibrium

AbstractEpidemiological models play an important role in the study of diseases. These models belong to population dynamics models and can be characterized with differential equations. In this paper we focus our attention on two epidemic models for malaria spreading, namely Ross-, and extended Ross model. As both the continous and the corresponding numerical models should preserve the basic qualitative properties of the phenomenon, we paid special attention to its examination, and proved their invariance with reference to the data set. Moreover, existence and uniqueness of equilibrium points for both models of malaria are considered. We demonstrate the theoritical results with numerical simulations.

scholarly journals Why are most COVID-19 infection curves linear?

2020 ◽  
Author(s):  
Stefan Thurner ◽  
Peter Klimek ◽  
Rudolf Hanel
Keyword(s):  
Linear Growth ◽  
Transmission Rate ◽  
Herd Immunity ◽  
Fine Tuning ◽  
Infection Prevalence ◽  
Epidemiological Models ◽  
Contact Networks ◽  
Empirical Estimates ◽  
The Us ◽  
New Phase

Many countries have passed their first COVID-19 epidemic peak. Traditional epidemiological models describe this as a result of non-pharmaceutical interventions that pushed the growth rate below the recovery rate. In this new phase of the pandemic many countries show an almost linear growth of confirmed cases for extended time-periods. This new containment regime is hard to explain by traditional models where infection numbers either grow explosively until herd immunity is reached, or the epidemic is completely suppressed (zero new cases). Here we offer an explanation of this puzzling observation based on the structure of contact networks. We show that for any given transmission rate there exists a critical number of social contacts, Dc, below which linear growth and low infection prevalence must occur. Above Dc traditional epidemiological dynamics takes place, as e.g. in SIR-type models. When calibrating our corresponding model to empirical estimates of the transmission rate and the number of days being contagious, we find Dc ~ 7.2. Assuming realistic contact networks with a degree of about 5, and assuming that lockdown measures would reduce that to household-size (about 2.5), we reproduce actual infection curves with a remarkable precision, without fitting or fine-tuning of parameters. In particular we compare the US and Austria, as examples for one country that initially did not impose measures and one that responded with a severe lockdown early on. Our findings question the applicability of standard compartmental models to describe the COVID-19 containment phase. The probability to observe linear growth in these is practically zero.

Performance Comparison of Various Algorithms During Software Fault Prediction

2021 ◽  
Vol 13 (2) ◽  
pp. 70-94
Author(s):  
Munish Khanna ◽  
Abhishek Toofani ◽  
Siddharth Bansal ◽  
Mohammad Asif
Keyword(s):  
Roc Analysis ◽  
Performance Comparison ◽  
Fault Prediction ◽  
Data Set ◽  
Software Fault Prediction ◽  
The Public ◽  
Machine Learning Model ◽  
Software Fault ◽  
Early Phases ◽  
Volume Size

Producing software of high quality is challenging in view of the large volume, size, and complexity of the developed software. Checking the software for faults in the early phases helps to bring down testing resources. This empirical study explores the performance of different machine learning model, fuzzy logic algorithms against the problem of predicting software fault proneness. The work experiments on the public domain KC1 NASA data set. Performance of different methods of fault prediction is evaluated using parameters such as receiver characteristics (ROC) analysis and RMS (root mean squared), etc. Comparison is made among different algorithms/models using such results which are presented in this paper.

scholarly journals Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nitu Kumari ◽  
Sumit Kumar ◽  
Sandeep Sharma ◽  
Fateh Singh ◽  
Rana Parshad
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Real Data ◽  
Time Frame ◽  
Complete Analysis ◽  
Data Set ◽  
Definition Of ◽  
The Basic Reproduction Number

<p style='text-indent:20px;'>Since the start of COVID-19 pandemic, the definition of normal life has changed drastically. The number of cases of this pandemic is rising everyday across the globe. In this study, we propose a compartmental model, which considers the isolation factor of Coronavirus infected individuals. The model consists of five compartments: susceptible (S), exposed (E), Infected (I), Isolated (L) and recovered (R). We have estimated the parameters of the model system and the expression of the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ R_0 $\end{document}</tex-math></inline-formula> using real data set. The exact value of the basic reproduction number is computed for India, Brazil and Peru. The local and global stability analysis of disease-free equilibrium and endemic equilibrium points is carried out. The forecasting of the pandemic is done using real data. It has been observed that to understand the pandemic the time frame has to be divided into small intervals as the parameters of the pandemic are changing with time. Within a time frame of approximately four months (i.e. from July to October 2020), the transmission rate of India has been reduced by approximately 84%. Whereas the transmission rate in Brazil and Peru has increased by 79% and 45% respectively. The sensitivity of various parameters involved in the model has been analyzed. We have presented a complete analysis to check the existence of backward bifurcation.</p>

scholarly journals Inhomogeneous Transmission and Asynchronic Mixing in the Spread of COVID-19 Epidemics

2021 ◽  
Vol 9 ◽  
Author(s):  
Carlos I. Mendoza
Keyword(s):  
Reproduction Number ◽  
Transmission Rate ◽  
Real Data ◽  
Epidemiological Models ◽  
Subexponential Growth ◽  
The Public ◽  
Transmission Rates ◽  
Proposed Model ◽  
Containment Measures ◽  
Mitigation Policies

The ongoing epidemic of COVID-19 first found in China has reinforced the need to develop epidemiological models capable of describing the progression of the disease to be of use in the formulation of mitigation policies. Here, this problem is addressed using a metapopulation approach to consider the inhomogeneous transmission of the spread arising from a variety of reasons, like the distribution of local epidemic onset times or of the transmission rates. We show that these contributions can be incorporated into a susceptible-infected-recovered framework through a time-dependent transmission rate. Thus, the reproduction number decreases with time despite the population dynamics remaining uniform and the depletion of susceptible individuals is small. The obtained results are consistent with the early subexponential growth observed in the cumulated number of confirmed cases even in the absence of containment measures. We validate our model by describing the evolution of COVID-19 using real data from different countries, with an emphasis in the case of Mexico, and show that it also correctly describes the longtime dynamics of the spread. The proposed model yet simple is successful at describing the onset and progression of the outbreak, and considerably improves the accuracy of predictions over traditional compartmental models. The insights given here may prove to be useful to forecast the extent of the public health risks of the epidemics, thus improving public policy-making aimed at reducing such risks.

scholarly journals Upwelling conditions in the Early Miocene Central Paratethys Sea

2010 ◽  
Vol 61 (2) ◽  
pp. 129-145 ◽  
Author(s):  
Patrick Grunert ◽  
Ali Soliman ◽  
Mathias Harzhauser ◽  
Stefan Müllegger ◽  
Werner Piller ◽  
...  
Keyword(s):  
Stable Isotope ◽  
Driving Forces ◽  
Foreland Basin ◽  
Early Miocene ◽  
Strong Mixing ◽  
Bulk Sediment ◽  
Data Set ◽  
Central Paratethys ◽  
High Productivity ◽  
North Alpine Foreland Basin

Upwelling conditions in the Early Miocene Central Paratethys SeaEvidence for regional upwelling conditions in the Central Paratethys Sea is presented for mid-Burdigalian (early Ottnangian) times. The oceanographic phenomenon is detected in clay-diatomite successions along the steep escarpment of the Bohemian Massif in the eastern North Alpine Foreland Basin. Interpretations are based on a multiproxy data-set including published sedimentological and paleontological data, newly performed stable isotope measurements (δ18O, δ13C) of foraminifers and bulk sediment samples, and analyses of dinoflagellate cyst assemblages. The revealed stable isotope values of planktonic foraminifers point to upwelling: low δ13C values indicate strong mixing of surface waters with rising nutrient-rich waters, high δ18O values reflect cool sea surface temperatures (SST). Temperature calculations give SSTs ranging from 10-14 °C. Cool SSTs and high productivity are additionally supported by bulk sediment analyses. Assemblages of dinoflagellate cysts indicate a distal-shelf environment with nutrient-rich waters. Westerly winds and tidal currents are discussed as potential driving forces behind the local upwelling event. As mid-Burdigalian geography favoured strong current patterns in the Central Paratethys as documented in the sedimentary record from the Rhône Basin to Hungary upwelling might have been a more common phenomenon in this epicontinental sea than currently known.

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