scholarly journals Flow, Wind, and Stochastic Connectivity Modeling Infectious Diseases

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
C. Udriste ◽  
I. Tevy ◽  
A. S. Rasheed
Keyword(s):  
Infectious Diseases ◽  
Differential Inclusion ◽  
Stochastic Equations ◽  
Evolutionary Models ◽  
Geodesic Motion ◽  
Disease Evolution ◽  
First Order ◽  
Ode System ◽  
Stochastic Sir ◽  
Geometric Dynamics

We study in this paper the trends of the evolution of different infections using a SIR flow (first-order ODE system), completed by a differential inclusion, a geodesic motion in a gyroscopic field of forces, and a stochastic SIR perturbation of the flow (Itô ODE system). We are interested in mathematical analysis, bringing new results on studied evolutionary models: infection flow together with a differential inclusion, bounds of evolution, dual description of disease evolution, log-optimal and rapid path, epidemic wind (geometric dynamics), stochastic equations of evolution, and stochastic connectivity. We hope that the paper will be a guideline for strategizing optimal sociopolitical countermeasures to mitigate infectious diseases.

scholarly journals Global mapping of infectious disease

2013 ◽  
Vol 368 (1614) ◽  
pp. 20120250 ◽  
Author(s):  
Simon I. Hay ◽  
Katherine E. Battle ◽  
David M. Pigott ◽  
David L. Smith ◽  
Catherine L. Moyes ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Disease Outbreaks ◽  
Data Sources ◽  
Global Burden ◽  
Rapid Improvement ◽  
Disease Evolution ◽  
Infectious Disease Outbreaks ◽  
Disease Occurrence ◽  
Global Mapping

The primary aim of this review was to evaluate the state of knowledge of the geographical distribution of all infectious diseases of clinical significance to humans. A systematic review was conducted to enumerate cartographic progress, with respect to the data available for mapping and the methods currently applied. The results helped define the minimum information requirements for mapping infectious disease occurrence, and a quantitative framework for assessing the mapping opportunities for all infectious diseases. This revealed that of 355 infectious diseases identified, 174 (49%) have a strong rationale for mapping and of these only 7 (4%) had been comprehensively mapped. A variety of ambitions, such as the quantification of the global burden of infectious disease, international biosurveillance, assessing the likelihood of infectious disease outbreaks and exploring the propensity for infectious disease evolution and emergence, are limited by these omissions. An overview of the factors hindering progress in disease cartography is provided. It is argued that rapid improvement in the landscape of infectious diseases mapping can be made by embracing non-conventional data sources, automation of geo-positioning and mapping procedures enabled by machine learning and information technology, respectively, in addition to harnessing labour of the volunteer ‘cognitive surplus’ through crowdsourcing.

scholarly journals The Deterministic Circuit Model for Noise Influence on the Averaged Transient Responses of Large-scale Nonlinear ICs Analyzed with Itô's Stochastic Differential Equations

VLSI Design ◽  
2001 ◽  
Vol 13 (1-4) ◽  
pp. 257-264
Author(s):  
Magnus Willander ◽  
Yevgeny Mamontov ◽  
Jonathan Vincent
Keyword(s):  
Differential Equation ◽  
Integrated Circuits ◽  
Stochastic Resonance ◽  
Large Scale ◽  
Noise Source ◽  
Computing Time ◽  
Second Order ◽  
Order Model ◽  
First Order ◽  
Ode System

The second-order nonrandom ordinary differential equation (ODE) system derived as the noise-source-aware model for expectations of solutions of Itô's stochastic differential equation (ISDE) system is discussed in connection with large-scale integrated circuits (ICs). The work explains the reason why the new model consistently allows for the noise-induced phenomena in the expectations, namely, stochastic resonance, stochastic linearization, stochastic self-oscillations and stochastic chaos. The case of stochastic resonance is considered as an example. In spite of the fact that the above second-order model is more complex than the nonrandom first-order IC ODE system for the expectations commonly used in engineering, an efficient practical technique for its implementation is proposed. The corresponding predicted computing time is only in 2.5 times greater than in the case of the first-order model which does not include any noise-source influence upon the expectations of the modelled IC responses.

scholarly journals MOTION OF A VECTOR PARTICLE IN A CURVED SPACETIME. II: FIRST-ORDER CORRECTION TO A GEODESIC IN A SCHWARZSCHILD BACKGROUND

2005 ◽  
Vol 20 (36) ◽  
pp. 2785-2798 ◽  
Author(s):  
ZAFAR TURAKULOV ◽  
MARGARITA SAFONOVA
Keyword(s):  
Order Correction ◽  
Vector Particle ◽  
Geodesic Motion ◽  
Curved Spacetime ◽  
First Order ◽  
First Order Correction ◽  
Schwarzschild Background

The influence of spin on a photon's motion in a Schwarzschild and FRW spacetimes is studied. The first-order correction to the geodesic motion is found. It is shown that unlike the worldlines of spinless particles, the photons worldlines do not lie in a plane.

scholarly journals Selected aspects of infectious disease evolution in the modern world

2020 ◽  
Vol 27 (4) ◽  
pp. 18-26
Author(s):  
V. V. Maleyev
Keyword(s):  
Infectious Diseases ◽  
Global Climate ◽  
Human Microbiome ◽  
Modern World ◽  
High Morbidity ◽  
Drug Interference ◽  
Disease Evolution ◽  
Main Components ◽  
Transmission Pathways ◽  
The Impact

The article presents current views on the evolution of infectious processes and the role of infectious diseases in global healthcare. The reversion of the main components of epidemic processes leads to an atypical course of many infectious diseases and to the emergence of new transmission pathways. Urbanisation, global climate change, agroindustrial boost, migration waves and other factors provoked a cross-border expansion of many wild focal infections across countries and continents. The high morbidity and mortality of infectious diseases are determined by novel and “resurrecting” infections. The possibility of appearing both epidemic and pandemic outbreaks of emergent infections is as relevant as ever.In this context, the impact of modern scientific achievements on environmental microbiotic associations and human microbiome, as well as safety of medical technologies, is of paramount importance.Despite current progress in the drug therapy of infectious diseases, a serious emerging challenge is amplified antimicrobial resistance and drug interference.

scholarly journals MOTION OF A VECTOR PARTICLE IN A CURVED SPACETIME III: DEVELOPMENT OF TECHNIQUES OF CALCULATIONS

2006 ◽  
Vol 21 (26) ◽  
pp. 1981-1990 ◽  
Author(s):  
Z. YA. TURAKULOV ◽  
A. T. MUMINOV
Keyword(s):  
Differential Equation ◽  
World Line ◽  
Linear Ordinary Differential Equation ◽  
Order Correction ◽  
Vector Particle ◽  
System Of Equations ◽  
Geodesic Motion ◽  
First Order ◽  
First Order Correction ◽  
The Green Function

The studies of influence of spin on a photon's motion in a Schwarzschild spacetime is continued. In the previous paper13the first-order correction to the geodesic motion is found for the first half of the photon world line. The system of equations for the first-order correction to the geodesic motion is reduced to a non-uniform linear ordinary differential equation. The equation obtained is solved by the standard method of integration of the Green function.

scholarly journals On solving non-homogeneous partial differential equations with right-hand side defined on the grid

2021 ◽  
Vol 31 (3) ◽  
pp. 443-457
Author(s):  
L.I. Rubina ◽  
O.N. Ul'yanov
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Grid Point ◽  
Original Equation ◽  
Partial Differential ◽  
First Order ◽  
Ode System ◽  
Right Hand ◽  
The Right

An algorithm is proposed for obtaining solutions of partial differential equations with right-hand side defined on the grid $\{ x_{1}^{\mu}, x_{2}^{\mu}, \ldots, x_{n}^{\mu}\},\ (\mu=1,2,\ldots,N)\colon f_{\mu}=f(x_{1}^{\mu}, x_{2}^{\mu}, \ldots, x_{n}^{\mu}).$ Here $n$ is the number of independent variables in the original partial differential equation, $N$ is the number of rows in the grid for the right-hand side, $f=f( x_{1}, x_{2}, \ldots, x_{n})$ is the right-hand of the original equation. The algorithm implements a reduction of the original equation to a system of ordinary differential equations (ODE system) with initial conditions at each grid point and includes the following sequence of actions. We seek a solution to the original equation, depending on one independent variable. The original equation is associated with a certain system of relations containing arbitrary functions and including the partial differential equation of the first order. For an equation of the first order, an extended system of equations of characteristics is written. Adding to it the remaining relations containing arbitrary functions, and demanding that these relations be the first integrals of the extended system of equations of characteristics, we arrive at the desired ODE system, completing the reduction. The proposed algorithm allows at each grid point to find a solution of the original partial differential equation that satisfies the given initial and boundary conditions. The algorithm is used to obtain solutions of the Poisson equation and the equation of unsteady axisymmetric filtering at the points of the grid on which the right-hand sides of the corresponding equations are given.

scholarly journals Threshold Dynamics of a Stochastic SIR Model with Vertical Transmission and Vaccination

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Anqi Miao ◽  
Jian Zhang ◽  
Tongqian Zhang ◽  
B. G. Sampath Aruna Pradeep
Keyword(s):  
Infectious Diseases ◽  
Vertical Transmission ◽  
Sir Model ◽  
Threshold Dynamics ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
Epidemic Diseases

A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control.

scholarly journals An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations

2006 ◽  
Vol 2006 ◽  
pp. 1-21 ◽  
Author(s):  
Valeri Obukhovskii ◽  
Pietro Zecca ◽  
Victor Zvyagin
Keyword(s):  
Differential Equation ◽  
Differential Inclusion ◽  
Mixed System ◽  
Fredholm Operators ◽  
Multivalued Maps ◽  
Coincidence Points ◽  
Implicit Differential Equation ◽  
First Order ◽  
Coincidence Index ◽  
Zero Index

We suggest the construction of an oriented coincidence index for nonlinear Fredholm operators of zero index and approximable multivalued maps of compact and condensing type. We describe the main properties of this characteristic, including applications to coincidence points. An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a differential inclusion, is given.

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