scholarly journals Modeling Growth, Containment and Decay of the COVID-19 Epidemic in Italy

2020 ◽  
Vol 8 ◽  
Author(s):  
Francesco Capuano
Keyword(s):  
Exponential Growth ◽  
Compartment Model ◽  
Growth Behavior ◽  
Time Dependent ◽  
Model Parameters ◽  
Susceptible Population ◽  
Dependent Rate ◽  
Slow Decay ◽  
Cumulative Curve ◽  
Modeling Growth

A careful inspection of the cumulative curve of confirmed COVID-19 infections in Italy and in other hard-hit countries reveals three distinct phases: i) an initial exponential growth (unconstrained phase), ii) an algebraic, power-law growth (containment phase), and iii) a relatively slow decay. We propose a parsimonious compartment model based on a time-dependent rate of depletion of the susceptible population that captures all such phases for a plausible range of model parameters. The results suggest an intimate interplay between the growth behavior, the timing and implementation of containment strategies, and the subsequent saturation of the outbreak.

scholarly journals Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China

Science ◽  
2020 ◽  
Vol 368 (6492) ◽  
pp. 742-746 ◽  
Author(s):  
Benjamin F. Maier ◽  
Dirk Brockmann
Keyword(s):  
Exponential Growth ◽  
Early Phase ◽  
Mainland China ◽  
Direct Consequence ◽  
Growth Behavior ◽  
Behavioral Changes ◽  
Susceptible Population ◽  
Subexponential Growth ◽  
Recent Outbreak ◽  
Parsimonious Model

The recent outbreak of coronavirus disease 2019 (COVID-19) in mainland China was characterized by a distinctive subexponential increase of confirmed cases during the early phase of the epidemic, contrasting with an initial exponential growth expected for an unconstrained outbreak. We show that this effect can be explained as a direct consequence of containment policies that effectively deplete the susceptible population. To this end, we introduce a parsimonious model that captures both quarantine of symptomatic infected individuals, as well as population-wide isolation practices in response to containment policies or behavioral changes, and show that the model captures the observed growth behavior accurately. The insights provided here may aid the careful implementation of containment strategies for ongoing secondary outbreaks of COVID-19 or similar future outbreaks of other emergent infectious diseases.

scholarly journals Nonlinear Compartment Models with Time-Dependent Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1657
Author(s):  
Jochen Merker ◽  
Benjamin Kunsch ◽  
Gregor Schuldt
Keyword(s):  
Stable Equilibrium ◽  
Compartment Model ◽  
Basins Of Attraction ◽  
Dynamical Behaviour ◽  
Time Dependent ◽  
Compartment Models ◽  
Autonomous Case ◽  
Hyperbolic Equilibrium ◽  
Interior Points ◽  
Two Parameter

A nonlinear compartment model generates a semi-process on a simplex and may have an arbitrarily complex dynamical behaviour in the interior of the simplex. Nonetheless, in applications nonlinear compartment models often have a unique asymptotically stable equilibrium attracting all interior points. Further, the convergence to this equilibrium is often wave-like and related to slow dynamics near a second hyperbolic equilibrium on the boundary. We discuss a generic two-parameter bifurcation of this equilibrium at a corner of the simplex, which leads to such dynamics, and explain the wave-like convergence as an artifact of a non-smooth nearby system in C0-topology, where the second equilibrium on the boundary attracts an open interior set of the simplex. As such nearby idealized systems have two disjoint basins of attraction, they are able to show rate-induced tipping in the non-autonomous case of time-dependent parameters, and induce phenomena in the original systems like, e.g., avoiding a wave by quickly varying parameters. Thus, this article reports a quite unexpected path, how rate-induced tipping can occur in nonlinear compartment models.

scholarly journals Unraveling the time-dependent relevance of input model uncertainties for a lumped hydrologic model of a pre-alpine karst system

2021 ◽  
Author(s):  
Daniel Bittner ◽  
Beatrice Richieri ◽  
Gabriele Chiogna
Keyword(s):  
Groundwater Recharge ◽  
Temporal Variations ◽  
Hydrologic Model ◽  
Time Dependent ◽  
Model Parameters ◽  
Lumped Parameter ◽  
Hydrodynamic Processes ◽  
Input Model ◽  
Karst Model ◽  
Input Uncertainties

AbstractUncertainties in hydrologic model outputs can arise for many reasons such as structural, parametric and input uncertainty. Identification of the sources of uncertainties and the quantification of their impacts on model results are important to appropriately reproduce hydrodynamic processes in karst aquifers and to support decision-making. The present study investigates the time-dependent relevance of model input uncertainties, defined as the conceptual uncertainties affecting the representation and parameterization of processes relevant for groundwater recharge, i.e. interception, evapotranspiration and snow dynamic, on the lumped karst model LuKARS. A total of nine different models are applied, three to compute interception (DVWK, Gash and Liu), three to compute evapotranspiration (Thornthwaite, Hamon and Oudin) and three to compute snow processes (Martinec, Girons Lopez and Magnusson). All the input model combinations are tested for the case study of the Kerschbaum spring in Austria. The model parameters are kept constant for all combinations. While parametric uncertainties computed for the same model in previous studies do not show pronounced temporal variations, the results of the present work show that input uncertainties are seasonally varying. Moreover, the input uncertainties of evapotranspiration and snowmelt are higher than the interception uncertainties. The results show that the importance of a specific process for groundwater recharge can be estimated from the respective input uncertainties. These findings have practical implications as they can guide researchers to obtain relevant field data to improve the representation of different processes in lumped parameter models and to support model calibration.

Contributions of Time Dependent and Cyclic Crack Growth to the Crack Growth Behavior of Non Strain-Crystallizing Elastomers

2002 ◽  
Vol 75 (4) ◽  
pp. 643-656 ◽  
Author(s):  
J. J. C. Busfield ◽  
K. Tsunoda ◽  
C. K. L. Davies ◽  
A. G. Thomas
Keyword(s):  
Crack Growth ◽  
Growth Behavior ◽  
Time Dependent ◽  
Crack Growth Behavior ◽  
Wide Range ◽  
Dependent Component ◽  
Tearing Energy ◽  
Quasi Crystals ◽  
Crack Growth Rates ◽  
Time Dependent Crack Growth

Abstract Engineering components are observed to fail more rapidly under cyclic loading than under static loading. This reflects features of the underlying crack growth behavior. This behavior is characterized by the relation between the tearing energy, T, and the crack growth per cycle, dc/dn. The increment of crack growth during each cycle is shown here to result from the sum of time dependent and cyclic crack growth components. The time dependent component represents the crack growth behavior that would be present in a conventional constant T crack growth test. Under repeated stressing additional crack growth, termed the cyclic crack growth component, occurs. For a non-crystallizing elastomer, significant effects of frequency have been found on the cyclic crack growth behavior, reflecting the presence of this cyclic element of crack growth. The cyclic crack growth behavior over a wide range of frequencies was investigated for unfilled and swollen SBR materials. The time dependent crack growth component was calculated from constant T crack growth tests and the cyclic contribution derived from comparison with the observed cyclic growth. It is shown that decreasing the frequency or increasing the maximum tearing energy during a cycle results in the cyclic crack growth behavior being dominated by time dependent crack growth. Conversely at high frequency and at low tearing energy, cyclic crack growth is dominated by the cyclic crack growth component. A large effect of frequency on cyclic crack growth behavior was observed for highly swollen SBR. The cyclic crack growth behavior was dominated by the time dependent crack growth component over the entire range of tearing energy and/or crack growth rate. The origin of the cyclic component may be the formation/melting of quasi crystals at the crack tip, which is absent at fast crack growth rates in the unswollen SBR and is absent at all rates in the swollen SBR.

Complex kinetic systems with time-dependent rate coefficients

1989 ◽  
Vol 44 (3) ◽  
pp. 185-191 ◽  
Author(s):  
J.C. Andre ◽  
F. Baros ◽  
J.M.G. Martinho
Keyword(s):  
Time Dependent ◽  
Rate Coefficients ◽  
Dependent Rate

CONSTANT ELASTICITY OF VARIANCE OPTION PRICING MODEL WITH TIME-DEPENDENT PARAMETERS

2000 ◽  
Vol 03 (04) ◽  
pp. 661-674 ◽  
Author(s):  
C. F. LO ◽  
P. H. YUEN ◽  
C. H. HUI
Keyword(s):  
Option Pricing ◽  
Algebraic Approach ◽  
Time Dependent ◽  
Model Parameters ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Pricing Options ◽  
Term Structures ◽  
Option Values

This paper provides a method for pricing options in the constant elasticity of variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for the option values incorporating time-dependent model parameters are obtained in various CEV processes with different elasticity factors. The numerical results indicate that option values are sensitive to volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. Furthermore, the Lie-algebraic approach is very simple and can be easily extended to other option pricing models with well-defined algebraic structures.

scholarly journals Kinetic Analysis of 2-[11C]Thymidine PET Imaging Studies of Malignant Brain Tumors: Compartmental Model Investigation and Mathematical Analysis

2002 ◽  
Vol 1 (3) ◽  
pp. 153535002002021
Author(s):  
Joanne M. Wells ◽  
David A. Mankoff ◽  
Mark Muzi ◽  
Finbarr O'Sullivan ◽  
Janet F. Eary ◽  
...  
Keyword(s):  
Brain Tumor ◽  
Brain Tumors ◽  
Cellular Proliferation ◽  
Compartment Model ◽  
Response To Therapy ◽  
Model Parameters ◽  
Normal Brain ◽  
Identifiability Analysis ◽  
Pet Tracer ◽  
Thymidine Transport

2-[11C]Thymidine (TdR), a PET tracer for cellular proliferation, may be advantageous for monitoring brain tumor progression and response to therapy. We previously described and validated a five-compartment model for thymidine incorporation into DNA in somatic tissues, but the effect of the blood–brain barrier on the transport of TdR and its metabolites necessitated further validation before it could be applied to brain tumors. Methods: We investigated the behavior of the model under conditions experienced in the normal brain and brain tumors, performed sensitivity and identifiability analysis to determine the ability of the model to estimate the model parameters, and conducted simulations to determine whether it can distinguish between thymidine transport and retention. Results: Sensitivity and identifiability analysis suggested that the non-CO2 metabolite parameters could be fixed without significantly affecting thymidine parameter estimation. Simulations showed that K1t and KTdR could be estimated accurately ( r = .97 and .98 for estimated vs. true parameters) with standard errors < 15%. The model was able to separate increased transport from increased retention associated with tumor proliferation. Conclusion: Our model adequately describes normal brain and brain tumor kinetics for thymidine and its metabolites, and it can provide an estimate of the rate of cellular proliferation in brain tumors.

Sign in / Sign up

Export Citation Format

Share Document