scholarly journals Covid-19: Why Herd Immunity was not Approached Anywhere? Ultrametric Diffusion Modeling of Virus Spread in Hierarchically Clustered Population

2021 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Herd Immunity ◽  
Disease Spread ◽  
The Novel ◽  
Virus Spread ◽  
Ultrametric Spaces ◽  
The Social ◽  
Standard Models ◽  
Models Of Disease ◽  
Basic Features ◽  
Novel Model

In spite of numerous predictions, the natural herd immunity for covid-19 visru had not been approahed anywhere in the world. Thus, the traditional mathematical models of disease spread demonstrated their inability to describe adequately the covid-19 pandemic. In author's works, the novel model of the disease spread was developed. This model reflects the basic features of the covid-19 pandemic: a) the social clustering character of virus spread, b) . Social clustering is mathematically modelled with ultrametric spaces having the treelike geometry encoding hierarchy of the regulation constraints. The virus spread is described by ultrametric diffusion or random walk on the hierarchic energy landscape. In contrast to the standard models which are characterized by the exponential decrease of the probability to become infected - at the stage of approaching of the herd immunity, the ultrametric model is characterized by the power law. Moreover, the model gives the possibility to quantify the influence of restriction measures up to the lockdown. Our main result is that the play with restrictions, including lockdowns, is counterproductive and leads to the essential slowdown of approaching the herd immunity or even makes this impossible.

scholarly journals Utrametric diffusion equation on energy landscape to model disease spread in hierarchic socially clustered population

2021 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Diffusion Equation ◽  
Mathematical Models ◽  
Statistical Physics ◽  
Herd Immunity ◽  
Number Fields ◽  
Disease Spread ◽  
Ultrametric Spaces ◽  
Social Barriers ◽  
Hierarchic Structure ◽  
Medical Specialities

We present a new mathematical model of disease spread reflecting some specialities of the covid-19 epidemic by elevating the role of hierarchic social clustering of population. The model can be used to explain slower approaching herd immunity, e.g., in Sweden, than it was predicted by a variety of other mathematical models and was expected by epidemiologists; see graphs Fig. \ref{fig:minipage1},\ref{fig:minipage2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider trees with the constant number $p>1$ of branches leaving each vertex. Such trees are endowed with an algebraic structure, these are $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe a virus spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, a virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. We consider {\it linearly increasing barriers.} A virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model; in particular, by notion of the probability to be infected (at time $t$ in a social cluster $C).$ We present socio-medical specialities of the covid-19 epidemic supporting our model.

scholarly journals Utrametric diffusion model for spread of covid-19 in socially clustered population: Can herd immunity be approached in Sweden?

2020 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Mathematical Models ◽  
Statistical Physics ◽  
Herd Immunity ◽  
Number Fields ◽  
Disease Spread ◽  
Ultrametric Spaces ◽  
Medical Specialties ◽  
Social Barriers ◽  
Hierarchic Structure ◽  
Diffusional Model

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. 2. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with p-branches leaving each vertex. Such trees are endowed with algebraic structure, the p-adic number fields. We apply theory of the p-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling dynamics on energy landscapes. To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider linearly increasing barriers. This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

scholarly journals P-adic (treelike) Diffusion Model for COVID-19 Epidemic

2020 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Mathematical Models ◽  
Statistical Physics ◽  
Herd Immunity ◽  
Number Fields ◽  
Disease Spread ◽  
Ultrametric Spaces ◽  
Medical Specialties ◽  
Social Barriers ◽  
Hierarchic Structure ◽  
Diffusional Model

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. \ref{GROWTH2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with $p$-branches leaving each vertex. Such trees are endowed with algebraic structure, the $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider {\it linearly increasing barriers.} This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

scholarly journals Ultrametric Model for COVID-19 Dynamics: An Attempt to Explain Slow Approaching Herd Immunity in Sweden

2020 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Random Walk ◽  
Spin Glasses ◽  
Herd Immunity ◽  
Human Society ◽  
Ultrametric Spaces ◽  
Social Barriers ◽  
Infection Dynamics ◽  
Hierarchic Structure ◽  
Standard Models ◽  
Social Clusters

We present a model of infection dynamics that might explain slower approaching the herd immunity during the covid-19 epidemy in Sweden than it was predicted by a variety of other models; see graphs Fig. \ref{GROWTH2}. The new model takes into account the hierarchic structure of social clusters in the human society. We apply the well developed theory of random walk on the energy landscapes represented mathematically with ultrametric spaces. This theory was created for applications to spin glasses and protein dynamics. To move from one social cluster (valley) to another, the virus should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider linearly increasing (with respect to hierarchy's levels) barriers. This structure of barriers matches with a rather soft regulations imposed in Sweden in March 2020. In this model, the infection spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This model's feature matches with the real situation during the covid-19 epidemy, with its cluster spreading structure. Clusters need not be determined solely geographically, they are based on a number of hierarchically ordered social coordinates. The model differs crucially from the standard models of spread of disease, such as the SIR-model. Our model describes such a specialty of spread of covid-19 virus as the presence of ``super-infectors'' who by performing a kind of random walk on a hierarchic landscape of social clusters spreads infection. In future, this model will be completed by adding the SIR-type counterpart. But, the latter is not a specialty of covid-19 spreading.

COVID-19

2021 ◽  
Vol 13 (1) ◽  
pp. 57-68
Author(s):  
Sonal Kanungo ◽  
Dolly Sharma ◽  
Alankrita Aggarwal
Keyword(s):  
Mortality Rate ◽  
Older Persons ◽  
Blood Clotting ◽  
Disease Spread ◽  
The Novel ◽  
Infected Person ◽  
Virus Spread ◽  
Wuhan City ◽  
Respiratory Problems ◽  
The World

The novel corona or COVID-19 disease spread from Wuhan city of China. The virus spread rapidly around the different countries, and now there are 6,040,609 confirmed cases across the globe. People inflected with virus are suffering from respiratory problems, blood clotting, etc. It is evident to be more dangerous for older persons and those who are already facing other serious illnesses. The virus spreads mainly through droplets of saliva or discharge from the nose of infected person when he coughs or sneezes. The purpose of this review is to focus on social and economic impact of COVID-19 in India and how the world will change because of this pandemic and what will be the ‘new normal' with and after this pandemic. This deadly virus has put the globe on alert because of its the high mortality rate and expansion of new number of cases rapidly. Until now, four lockdown phases had helped India to prevent the spike in the curve of new cases, but currently the authors are witnessing steeper rise in new corona cases every day.

scholarly journals An Ultrametric Random Walk Model for Disease Spread Taking into Account Social Clustering of the Population

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 931 ◽  
Author(s):  
Andrei Khrennikov ◽  
Klaudia Oleschko
Keyword(s):  
Random Walk ◽  
Spin Glasses ◽  
Statistical Physics ◽  
Herd Immunity ◽  
Social Hierarchy ◽  
Disease Spread ◽  
Ultrametric Spaces ◽  
Social Barriers ◽  
Preventative Measures ◽  
One Step

We present a mathematical model of disease (say a virus) spread that takes into account the hierarchic structure of social clusters in a population. It describes the dependence of epidemic’s dynamics on the strength of barriers between clusters. These barriers are established by authorities as preventative measures; partially they are based on existing socio-economic conditions. We applied the theory of random walk on the energy landscapes represented by ultrametric spaces (having tree-like geometry). This is a part of statistical physics with applications to spin glasses and protein dynamics. To move from one social cluster (valley) to another, a virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy levels composing this barrier. Infection spreads rather easily inside a social cluster (say a working collective), but jumps to other clusters are constrained by social barriers. The model implies the power law, 1−t−a, for approaching herd immunity, where the parameter a is proportional to inverse of one-step barrier Δ. We consider linearly increasing barriers (with respect to hierarchy), i.e., the m-step barrier Δm=mΔ. We also introduce a quantity characterizing the process of infection distribution from one level of social hierarchy to the nearest lower levels, spreading entropy E. The parameter a is proportional to E.

Analytical Study of Violence Theme in Victoria Schwab’s This Savage Song

2019 ◽  
Keyword(s):  
Analytical Study ◽  
Research Paper ◽  
The Novel ◽  
Vicious Cycle ◽  
Aggressive Approach ◽  
Research Article ◽  
The People ◽  
The Social ◽  
Different Dimensions ◽  
The Right

This research article focuses on the theme of violence and its representation by the characters of the novel “This Savage Song” by Victoria Schwab. How violence is transmitted through genes to next generations and to what extent socio- psycho factors are involved in it, has also been discussed. Similarly, in what manner violent events and deeds by the parents affect the psychology of children and how it inculcates aggressive behaviour in their minds has been studied. What role is played by the parents in grooming the personality of children and ultimately their decisions to choose the right or wrong way has been argued. In the light of the theory of Judith Harris, this research paper highlights all the phenomena involved: How the social hierarchy controls the behaviour. In addition, the aggressive approach of the people in their lives has been analyzed in the light of the study of second theorist Thomas W Blume. As the novel is a unique representation of supernatural characters, the monsters, which are the products of some cruel deeds, this research paper brings out different dimensions of human sufferings with respect to these supernatural beings. Moreover, the researcher also discusses that, in what manner the curse of violence creates an inevitable vicious cycle of cruel monsters that makes the life of the characters turbulent and miserable.

Aravind Adiga’s The White Tiger: A Socio –Political Study of Poverty and Injustice

IJOHMN ◽  
2016 ◽  
Vol 2 (6) ◽  
pp. 11-19
Author(s):  
RASHMI Ahlawat
Keyword(s):  
Indian Society ◽  
Poor People ◽  
The Novel ◽  
The Social ◽  
White Tiger

Aravind Adiga’s Man Booker Prize winning debut novel The White Tiger is sharp, fascinating, attacks poverty and injustice. The White Tiger is a ground breaking Indian novel. Aravind Adiga speaks of suppression and exploitation of various sections of Indian society. Mainly a story of Balram, a young boy’s journey from  rags to riches, Darkness to Light transforming from a village teashop boy into a Bangalore entrepreneur. This paper deals with poverty and injustice. The paper analyses Balram’s capability to overcome the adversities and cruel realities. The pathetic condition of poor people try to make both ends meet. The novel mirrors the lives of  poor in a realistic mode. The White Tiger is a story about a man’s journey for freedom. The protagonist   Balram in this novel is a victim of injustice, inequality and poverty. He worked hard inspite   of his low caste and overcame the social hindrance and become a successful entrepreneur. Through this novel Adiga portrays realistic and painful image of modern India. The novel exposes the anxieties of the oppressed.

KONSEP DIRI “ I “ DAN “ME” TOKOH HIROKO DALAM NOVEL NAMAKU HIROKO KARYA NH.DINI

2012 ◽  
Vol 5 (2) ◽  
pp. 109
Author(s):  
Besin Gaspar
Keyword(s):  
Point Of View ◽  
The Other ◽  
Self Concept ◽  
The Novel ◽  
Main Character ◽  
Fictional Character ◽  
Social Customs ◽  
The Social ◽  
The Village ◽  
The City

This research deals with the development of  self concept of Hiroko as the main character in Namaku Hiroko by Nh. Dini and tries to identify how Hiroko is portrayed in the story, how she interacts with other characters and whether she is portrayed as a character dominated by ”I” element or  ”Me”  element seen  from sociological and cultural point of view. As a qualitative research in nature, the source of data in this research is the novel Namaku Hiroko (1967) and the data ara analyzed and presented deductively. The result of this analysis shows that in the novel, Hiroko as a fictional character is  portrayed as a girl whose personality  develops and changes drastically from ”Me”  to ”I”. When she was still in the village  l iving with her parents, she was portrayed as a obedient girl who was loyal to the parents, polite and acted in accordance with the social customs. In short, her personality was dominated by ”Me”  self concept. On the other hand, when she moved to the city (Kyoto), she was portrayed as a wild girl  no longer controlled by the social customs. She was  firm and determined totake decisions of  her won  for her future without considering what other people would say about her. She did not want to be treated as object. To put it in another way, her personality is more dominated by the ”I” self concept.

Coronavirus: Towards controlling of the pandemic - Indian scenario

2020 ◽  
Vol 11 (SPL1) ◽  
pp. 462-468
Author(s):  
Latika kothari ◽  
Sanskruti Wadatkar ◽  
Roshni Taori ◽  
Pavan Bajaj ◽  
Diksha Agrawal
Keyword(s):  
Control Measures ◽  
The Novel ◽  
Medical Treatments ◽  
Health Crisis ◽  
The Public ◽  
Infection Control Measures ◽  
The Social ◽  
Asking Questions ◽  
The Government ◽  
Novel Coronavirus

Coronavirus disease 2019 (COVID-19) is a communicable infection caused by the novel coronavirus resulting in severe acute respiratory syndrome coronavirus 2 (SARS-CoV). It was recognized to be a health crisis for the general population of international concern on 30th January 2020 and conceded as a pandemic on 11th March 2020. India is taking various measures to fight this invisible enemy by adopting different strategies and policies. To stop the COVID-19 from spreading, the Home Affairs Ministry and the health ministry, of India, has issued the nCoV 19 guidelines on travel. Screening for COVID-19 by asking questions about any symptoms, recent travel history, and exposure. India has been trying to get testing kits available. The government of India has enforced various laws like the social distancing, Janata curfew, strict lockdowns, screening door to door to control the spread of novel coronavirus. In this pandemic, innovative medical treatments are being explored, and a proper vaccine is being hunted to deal with the situation. Infection control measures are necessary to prevent the virus from further spreading and to help control the current situation. Thus, this review illustrates and explains the criteria provided by the government of India to the awareness of the public to prevent the spread of COVID-19.

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