\r\n\tThe book on Ventricular Tachycardia is expected to assist clinicians to navigate within the forest of new information on cardiac arrhythmias and especially ventricular tachycardia. The advances made in cardiac mapping brought new and substantial information on the effect of antiarrhythmic drugs, catheter ablation and ICDs. Clinicians deserve relevant information on the proven therapies and those more scrupulous should find out about the newest experimental and promising therapies.
\r\n\r\n\tThe authors are expected to cover the Anatomy of the left and right ventricles, the Mechanisms of ventricular tachycardia: Reentry, Automaticity and Triggered activity, and the general evaluation of patients with VT: ECG, Holter EKG, stress test, echocardiography and MRI. The book should also include information on invasive methods of arrhythmia testing: coronarography and electrophysiological testing.
\r\n\r\n\tFurthermore, the book will deal with treatment and prevention of VT: antiarrhythmic drugs like betablockers, amiodarone, sotalol and class IC, implantable defibrillators and catheter ablation. The editor would appreciate if authors also decided to cover special topics such asVT as a side effect of chemotherapy and Brugada Syndrome.
",isbn:null,printIsbn:null,pdfIsbn:null,doi:null,price:0,priceEur:null,priceUsd:null,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"f968d9a2e5d4e8d6c0a6339c5d18b7f6",bookSignature:"Dr. Gabriel Cismaru",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8675.jpg",keywords:"Ventricular Tachycardia, ECG, Holter, Stress Test, Echocardiography, Amiodarone, Sotalol, Lidocaine, Propafenone, Catheter, Mapping",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 16th 2018",dateEndSecondStepPublish:"November 6th 2018",dateEndThirdStepPublish:"January 5th 2019",dateEndFourthStepPublish:"March 26th 2019",dateEndFifthStepPublish:"May 25th 2019",remainingDaysToSecondStep:"2 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"191888",title:"Dr.",name:"Gabriel",middleName:null,surname:"Cismaru",slug:"gabriel-cismaru",fullName:"Gabriel Cismaru",profilePictureURL:"https://mts.intechopen.com/storage/users/191888/images/system/191888.jpeg",biography:"Dr. Cismaru Gabriel is an Assistant Professor at the University of Medicine and Pharmacy Cluj-Napoca, certified in Cardiology. He earned his MD degree from the same university in 2005 and received his Ph.D. in medicine in 2016. After completing his certification in cardiology, Dr. Cismaru began his electrophysiology fellowship at the Institut Lorrain du Coeur et des Vaisseaux Louis Mathieu, Nancy, France. In 2011, he started working at the Electrophysiology Laboratory of the Rehabilitation Hospital, Cluj-Napoca. He is a well-versed operator and performs pacemaker, CRT, and ICD implantations both in children and adults. He is also trained for catheter ablation of both supraventricular and ventricular arrhythmias. Dr. Cismaru has authored or co-authored peer-reviewed articles and book chapters in the field of cardiac pacing, defibrillation, electrophysiological study and catheter ablation.",institutionString:"Iuliu Hațieganu University of Medicine and Pharmacy",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"6",totalChapterViews:"0",totalEditedBooks:"2",institution:{name:"Iuliu Hațieganu University of Medicine and Pharmacy",institutionURL:null,country:{name:"Romania"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"983",title:"Cardiac Electrophysiology",slug:"cardiac-electrophysiology"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"270935",firstName:"Rozmari",lastName:"Marijan",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/270935/images/7974_n.png",email:"rozmari@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"5970",title:"Bedside Procedures",subtitle:null,isOpenForSubmission:!1,hash:"ba56d3036ac823a7155f40e4a02c030d",slug:"bedside-procedures",bookSignature:"Gabriel Cismaru",coverURL:"https://cdn.intechopen.com/books/images_new/5970.jpg",editedByType:"Edited by",editors:[{id:"191888",title:"Dr.",name:"Gabriel",surname:"Cismaru",slug:"gabriel-cismaru",fullName:"Gabriel Cismaru"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9064",title:"Epidemiology and Treatment of Atrial Fibrillation",subtitle:null,isOpenForSubmission:!1,hash:"1cd6bf2b3181eb82446347fbe478a2bc",slug:"epidemiology-and-treatment-of-atrial-fibrillation",bookSignature:"Gabriel Cismaru and Keith Andrew Chan",coverURL:"https://cdn.intechopen.com/books/images_new/9064.jpg",editedByType:"Edited by",editors:[{id:"191888",title:"Dr.",name:"Gabriel",surname:"Cismaru",slug:"gabriel-cismaru",fullName:"Gabriel Cismaru"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"358",title:"Advances in Electrocardiograms",subtitle:"Methods and Analysis",isOpenForSubmission:!1,hash:"a61fed85204779463e6e483483601fdf",slug:"advances-in-electrocardiograms-methods-and-analysis",bookSignature:"Richard M. 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Because of their electronic structure, they are the promising materials for the construction of nanoscale devices (quantum wires, nonlinear electronic elements, transistors, molecular memory devices, or electron field emitters) and the inventions in the material science.
\nThe planar geometry of the molecular surface is disrupted by the disclinations in the molecular structure that are most often presented by the pentagons and the heptagons in the hexagonal lattice. This change of the geometry is manifested by the positive or the negative curvature, respectively, that can be enlarged by the supply of higher number of the defects. In this way, by the supply of 1–5 pentagonal defects, we get conical structures with different values of the vortex angle (Figure 2).
\nOne more defect can be added and a nanotube is created. This nanostructure can be considered closed as well as opened, i.e., without the cap that contains the pentagonal defects. The second case is more common (Figure 3, left part). The number of the defects can be increased up to 12, and in this way, a completely closed, spherical nanostructure arises (fullerene—Figure 3, middle part).
\nHexagonal carbon plain lattice.
Conical nanostructures with different numbers of pentagonal defects in the tip.
Different kinds of graphene nanostructures: nanotube (left), fullerene (middle), wormhole (right).
Analogical manipulations with the graphene lattice can be made by the supply of the heptagonal defects (Figure 4). For the case of 12 heptagonal defects, if they are placed appropriately, the wormhole structure is created (Figure 3, right part).
\nHexagonal lattice disclinated by one heptagonal defect.
A lot of other variants of the graphitic nanostructures can be created using different combinations of the pentagonal and the heptagonal defects. Some of them are presented in Figure 5.
\nLess common forms of the graphene nanostructures: triple-walled nanotube (left), pillared graphene (middle), nanotoroid (right).
We investigate the electronic properties of several kinds of the carbon nanostructures. After the explanation of the computational methods, we demonstrate how to utilize these methods for the purpose of the investigation of graphene and some simple forms of the nanostructures—different kinds of nanoribbons and their modifications. Then, we will concentrate on the calculation of the properties of more complicated forms—the graphitic nanocone [1–3] and the graphitic wormhole [4–6]. In the first case, we consider the influence of the additional effects like the spin-orbit coupling (SOC) and the boundary effects coming from the finite size and from the extreme curvature of the surface geometry in the tip. In the second case, we investigate the effects that arise in the place of the wormhole bridge. Here, two additional effects appear: first, the SOC arising in the connecting nanotube and second, the increase of the electron mass due to relativistic effects coming from the extreme curvature of the surface geometry. As a result, the chiral massive electrons should be observed.
\nThe electronic structure can be characterized by the density of states (DOS)—the number of the electronic states per the unit interval of energies. This quantity can be used as the measure of the density of the electrons and generally we can say that the higher value of DOS, the higher conductivity. With the help of DOS, the electric field can be calculated as well. Besides DOS, one more quantity is defined—the local density of states (LDOS). It is DOS related to the unit area of the molecular surface or to the unit area of the surface in the space of the wave vector
Two methods are used for the calculation of LDOS. The first one is used for the periodical structures with the planar geometry (plain graphene, nanotubes, nanoribbons, etc.), the second one is used for the structures that are aperiodical or that have the curved geometry (fullerene, nanocone, wormhole, nanotoroid, etc.). We outline here the base of these methods. Both the methods start on solving the Schrödinger equation for the electron bounded on the molecular surface
\nHere,
\nFor the periodical structures, the external potential in Eq. (3) is zero, and the carbon lattice can be divided into several sublattices, each containing equivalent atomic sites. We can denote the sites corresponding to the different sublattices as
In the case of graphene, the wave function, which solves Eq. (2), can be expressed as in references [7, 8]
\nwhere the components
where
By the substitution of the solution in Eq. (5) into the Schrödinger equation (Eq. (2)), multiplying it by
Unit cells for different periodical structures: graphene (left), different kinds of nanoribbons (right). The graphene structure is considered to be infinite in 2D, the nanoribbons are considered to have final width and the second size is infinite as well.
If we suppose that the functions
The eigenvalues of the matrix in this equation are the energy eigenvalues, and they create the electronic spectrum. For this purpose, first, we need to determine the values of the matrix elements
where
where
The corresponding graphs of electronic spectrum and DOS are given in Figure 7. We see that for zero energy, the density of states has zero value. This property is typical for the semimetallic nanostructures. For the metallic nanostructures, a peak appears for zero energy. In the first case, a gap is present around zero in the electronic spectrum. Its width can be influenced by the additional defects in the hexagonal structure or by the chemical admixtures and in this way, a material with the predefined properties can be synthesized. In the second case, the gap around zero energy is absent.
\nThe electronic spectrum for
In a similar way, but with a more complicated structure of the wave function in Eq. (4) and for a larger size of the matrix in Eq. (8), the electronic spectrum and DOS can be found for other nanostructures like the nanoribbons in the right side of Figure 6 [9].
\nThe results we see in Figure 8. In the left part, the shape of the segment of the concrete nanoribbon is present. The plot of the electronic spectrum and DOS are given in the middle and in the right part, respectively. The direction of the wave vector
The upper part corresponds to the nanoribbon with zigzag edges [10] and with 12 atomic sites in the unit cell (see Figure 6). That is why the size of the appropriate matrix in Eq. (8) would be 12 × 12 and its spectrum contains 12 eigenvalues. This corresponds to 12 lines in the graph of the electronic spectrum. The graph of DOS shows a zero energy peak that signalizes the metallicity of this kind of nanostructure. It is a typical property for the zigzag nanoribbons unlike the armchair nanoribbons [10].
\nElectronic spectrum and DOS of different kinds of nanoribbons.
The middle and the bottom part correspond to some modifications of the previous form—the nanoribbon with the reconstructed edges. This causes the enlargement of the unit cell (Figure 6) and, consequently, a more complicated structure of the electronic spectrum. The metallic properties depend on the concrete kind of the modification: for the nanostructure in the middle part, the zero energy peak in DOS is preserved, whereas it disappears for the nanostructure in the bottom part. Furthermore, in the first case, the electronic spectrum gets a more complicated structure—the number of the Dirac points, where the lines are crossing, is doubled. This feature remains and strengthens for the larger width: in Figure 9, the form of the electronic spectrum is depicted for the same kind of the nanostructure and its width is three times larger.
\nFor the curved structures, the nontrivial geometry is described by the external potential
For the purpose of the calculations, we express the wave function that solves Eq. (2) in the case of zero external potential in the form of the so-called “Luttinger–Kohn base” [11]:
\nwhere
Electronic spectrum for extra wide nanoribbon with reconstructed edges.
This wave function will be substituted into Eq. (3). In reference [12], a sequence of steps is described whose result is the transformation of this equation to a two-dimensional (2D) Dirac-like equation for the massless fermion. In the practical calculations, a suitable choice of the coordinates is useful. In our case, we will suppose the rotational symmetry. Then, we perform the transformation of the coordinates:
The meaning of the particular terms is the following:
Here,
It remains to explain the sense of the gauge fields
where
The rotational symmetry enables to find the solution of Eq. (15) with the help of the substitution
\nfrom which we get the system
\nHere,
\nFrom the solution, LDOS is defined as the square of the absolute value of the wave function. In this case, we get it as the sum of squares of the absolute values of its
The graphitic nanocone is a nanostructure that can be created from the plain graphene by the insertion of the pentagonal defects into the hexagonal structure. The number of these defects can vary from one to five. In this way, the conical tip arises and its smoothness and the vortex angle are given by the number of the defects and their placement. Then, the real geometry of the graphitic nanocone and the pure conical geometry are different (Figure 10, left part). The value of the vortex angle
where
The electronic structure of the graphitic nanocone with purely conical geometry and without any additional effects was investigated in reference [15]. There, the solution of Eq. (15) for this case is derived. Here, using the gauge field theory approach, we introduce the results of the calculations in different approximations: the nanocone with purely conical geometry influenced by the SOC [1] and the same case with the additional effect of the Coulomb interaction coming from the charge placed into the conical tip [3]. The reason is following: it is one of the possibilities how to simulate the real geometry in the conical tip.
\nIn the case of the purely conical structure, this form is assigned to the Hamiltonian in the Schrödinger equation (Eq. (2)) [15]:
\nIn this equation,
SOC is incorporated using the substitutions [1]
\nLeft: the deviation of the geometry of the graphitic nanocone from the geometry of the real nanocone. Right: The notation of the variables in the nanocone.
where
It includes the strength of SOC through the parameters
Now, the equation
\nwill be solved for the calculation of LDOS. Similarly as in Eq. (19), we can do the following factorization due to the rotational symmetry:
\nIt changes the equation into the form
\nNext parameters appearing in this equation are
\nIn reference [1], a numerical method is introduced in detail that helps to find the solution of this system. Using a modified version of Eq. (22) (we sum up the squares of absolute values of four components instead of two components), we calculate LDOS from this solution. For different numbers of the defects in the conical tip, we see the resulting LDOS in Figure 11. It involves the modes
From these results follows that there could be a strong localization of the electrons in the tip, especially near zero energy in the case of three defects. Now, we will be interested, if this behavior remains the same after the inclusion of some boundary effects that should simulate the real geometry of the nanostructure. Furthermore, we would like to ensure in this way the quadratical integrability of the solution.
\nThree-dimensional graphs of LDOS of the graphitic nanocone influenced by SOC. Here, LDOS corresponds to the sum of the solutions corresponding to
The influence of the charge considered in the conical tip is expressed in the Hamiltonian by the presence of the diagonal term
In this way, the parallel influence of both the Coulomb interaction and SOC is considered [3]. To solve the resulting equation, we use the analogy of the numerical method used in [1]—this analogy is presented in reference [3]. From the calculated results, LDOS is calculated using Eq. (22) again.
\nThe graphs of LDOS based on the found solution are sketched in Figure 12 for the same modes and numbers of the defects as in Figure 11, i.e.,
Graphs of LDOS of the graphitic nanocone influenced by the Coulomb interaction (including the influence of SOC) for different distances
Now, we would like to verify the possible quadratic integrability of the solution found for the case of the additional effect coming from the charge simulation. In Figure 13, we see the dependence of LDOS on
Behavior of
The wormhole is understood as a form that arises when two graphene sheets are connected together with the help of the connecting nanotube. This can be achieved by the supply of the heptagonal defects on both sides of the given nanotube. The number of the defects can vary from 1 to 12. The composition of the graphitic wormhole is depicted in Figure 14: it consists of the connecting nanotube and two (perturbed or unperturbed) graphene sheets. The places of the connections are called the wormhole bridges. Because of the physical limitations, the radius of the nanotube must be much larger than its length (this fact is ignored in Figure 14 for the better illustration of the composition). The limit case of 12 defects is described in references [4, 17], in the other cases, we speak about the so-called “perturbed wormhole” Here, using the formalism of the subsection II B, we derive the electronic structure for both cases, and we will find out the form of the zero modes on the wormhole bridge. Furthermore, we investigate the influence of the additional effects that could appear here due to extreme curvature in the place of the wormhole bridge—the relativistic mass acquisition of the present electrons. This effect together with the effect of SOC that appears in the carbon nanotubes [16] could lead to the appearance of the zero modes of the chiral massive electrons in the place of the wormhole bridge. This could serve as a useful instrument for the detection of the wormhole structures in the graphene bilayer during the process of the synthesis of the corresponding material.
\nThe composition of the graphitic wormhole.
We will solve Eq. (15) in the subsection II B. In this case, the metric tensor has the form
\nHere,
The values of the components of
The only exception is when the chiral vector is (6
Knowledge of the spin connection is also needed—the values of the components have the form
\nAll these expressions we substitute into Eq. (15). The resulting equation is
\nLocal density of states on the bridge of the graphitic wormhole for different values of
Here, each sign ± corresponds to a different Dirac point (the corner of the reciprocal unit lattice). We get these four possibilities: for
and for
In the first case, the solution is
\nHere,
For the presented possibilities, we investigate the zero modes—solutions of the Dirac equation for the zero energy. For this purpose, we consider zero values of the component
Comparison of the properties of the wormhole and the plain graphene: (a) local density of states, (b) zero modes.
and for
If
The second possibility for this value of
Both solutions are strictly normalizable only for
There are no strictly normalizable solutions for the value
On the base of these results, one could expect a strong localization of LDOS near Fermi energy on the wormhole bridge. It is demonstrated in Figure 16a, where LDOS of the plain graphene is supplied for the comparison. It could be experimentally observed. In Figure 16b, we see the comparison of the zero modes of these two structures at different distances from the wormhole bridge.
\nIn the continuum gauge field theory, zero mass of the fermions in the Dirac equation is considered (in other words, it is very small in comparison with energy). On the other hand, the extreme curvature of the investigated structure leads to such values of the Fermi velocity that cause the appearance of the relativistic effects. The changes of the Fermi velocity due to curvature and other effects were demonstrated in references [13, 19]. As a result, the mass of the fermions becomes considerable, similarly as in the bilayer graphene [20, 21]. This effect is strengthened by the effective mass acquisition during the motion along the tube axis that happens due to the extreme size difference between the graphene sheets and the wormhole radius. This change of the space topology of graphene from 2D to 1D is similar to the string theory compactification. It means that we can image the wormhole connecting nanotube as the 1D object.
\nSo we need to incorporate a mass term into the Dirac equation (Eq. (15)). To solve this problem, we go through the system of the corresponding equations (Eq. (20)) and transform it into the following differential equation of the second order:
\nTo simplify the calculations, the cylindrical geometry is supposed: the radius vector of the point at the surface changes as
\nwhere
which is solved by [22]
\nHere,
\nIn references [23, 24], in a very similar form the dispersion relation is given for the massive 1D Dirac equation:
\nwhere
in this case, the mass
Another possibility to identify the wormhole structure comes from the fact that the massive particles could create strain solitons and topological defects on the bridge of the bilayer graphene that should propagate throughout the graphene sheet. These are almost macroscopic effects and should be caught by the experimentalists [26].
\nComparison of LDOS for different masses of fermions at different distances from the wormhole bridge.
Now we will investigate how the electronic structure changes if the number of the heptagonal defects on the wormhole bridge is lowered—in this way, the perturbed wormhole is created.
\nIn Figure 18, the possible forms of this structure are depicted. Due to symmetry preservation, only the even numbers of the defects, i.e., 2, 4, 6, 8, or 10, are considered.
\nThe metric of the sheets can be draught by the radius vector
\nwhere △ is a positive real parameter; its value is derived from the number of the defects of the wormhole. In the case of
The nonzero components of the gauge fields are
\nDifferent forms of the perturbed wormhole: (a) Two defects, (b) Four defects, (c) Six defects, (d) Eight defects, (e) Ten defects.
where (
where
\nIn the case of more than two defects, the value of Δ is not negligible, and we can get only the numerical approximation of LDOS. The derivation of the value of the parameter Δ follows from Figure 19 (right part). From this figure it follows that in the middle part, the upper branch of the graphene sheet converges to the line
Left: LDOS on the bridge of the graphitic perturbed wormhole. Right: Derivation of the Δ parameter.
from which follows
\nso
\nIn Figure 20, we see the comparison of LDOS for different kinds of the perturbed wormhole. From the plots it follows that the intensity is rising with the increasing number of the defects, and it is closer and closer approaching the results in Figure 15, where the case of 12 defects is shown.
\nComparison of
Zero modes of the perturbed wormhole for different numbers of the defects.
In Figure 21, LDOS of zero modes is shown for a varying distance from the wormhole bridge in the units of the radius
Of course, the massive fermions could also appear in the case of the perturbed wormhole. We will not perform a detailed derivation of the electronic structure for the case of this eventuality, and we only note that the corrections to LDOS would be an analogy of the corrections shown in Figure 17.
\nWe performed the calculations of the electronic structure for the graphitic nanocone and the graphene wormhole. In the first case, our aim was to find the quadratically integrable solution that includes the boundary effects and considers the real geometry. This goal was partially achieved, but we need to verify the properties of the found solution close to the tip. The precision of the calculations could be improved by the better choice of the corresponding geometry, by the consideration of the discretion of the energetic spectrum coming from the finite size of the nanostructure, and by the inclusion of next effects coming from the overlap of the neighboring atomic orbitals close to the tip [2]. The localization of the electrons shown in Figures 11 and 12, especially in the case of three defects, makes the graphitic nanocone a possible candidate for the construction of the scanning probe in atomic force microscopy.
\nIn the second case of the graphene wormhole, we presented the mathematical motivation for our prediction of the effects that should appear close to the wormhole bridge. Our predictions will be verified with the help of the geometric optimizations and ab initio calculations. On this base, the most suitable candidates for the experiments will be chosen.
\nNovel Coronavirus, assigned as 2019-nCoV, emerged in Wuhan, China, toward the end of 2019. As of January 24, 2020, as many as 830 cases had been analyzed in nine nations: China, Thailand, Japan, South Korea, Singapore, Vietnam, Taiwan, Nepal, and the United States [1, 2, 3]. Twenty-six fatalities happened, chiefly in patients who had genuine basic sickness. Albeit numerous subtleties of the rise of this infection.
In 2019, the Centers for Disease Control and Prevention (CDC) started monitoring the outbreak of a new coronavirus, SARS-CoV-2, which causes the respiratory illness now known as COVID-19. Authorities first identified the virus in Wuhan, China. More than 74,000 people have contracted the virus in China. Health authorities have identified many other people with COVID-19 around the world, including many in the United States. On January 31, 2020, the virus passed from one person to another in the U.S. The World Health Organization (WHO) have declared a public health emergency relating to COVID-19. Since then, this strain has been diagnosed in several U.S. residents. The CDC have advised that it is likely to spread to more people. COVID-19 has started causing disruption in at least 25 other countries.
All the adjoining nations of India have revealed positive COVID-19 cases. To secure against the lethal infection, the Indian government have taken fundamental and severe measures, including setting up wellbeing check posts between the public lines to test whether individuals entering the nation have the infection. Various nations have presented salvage endeavors and reconnaissance measures for residents wishing to get back from China. The exercise gained from the SARS episode was first that the absence of lucidity and data about SARS debilitated China’s worldwide standing and hampered its financial development. The episode of SARS in China was disastrous and has prompted changes in medical care and clinical frameworks. Contrasted and China, the capacity of India to counter a pandemic is by all accounts a lot of lower. A new report announced that influenced relatives had not visit the Wuhan market in China, proposing that SARS-CoV-2 may spread without showing side effects. Analysts accept that this wonder is typical for some infections. India, with a populace of more than 1.34 billion—the second biggest populace on the planet—will experience issues treating serious COVID-19 cases on the grounds that the nation has just 49,000 ventilators, which is a negligible sum. On the off chance that the quantity of COVID-19 cases increments in the country, it would be a fiasco for India.
As the characteristics of a potential vaccine become better known, mathematical models can be used to explore alternative scenarios about effectively distributing a vaccine in order to limit transmission and protect the most vulnerable population groups.
Coughing and sneezing without covering the mouth can disperse droplets into the air. Touching or shaking hands with a person who has the virus can pass the virus between individuals. Making contact with a surface or object that has the virus and then touching the nose, eyes, or mouth.
The National Institutes of Health (NIH) suggest that several groups of people have the highest risk of developing complications due to COVID-19. These groups include:
Young children
People aged 65 years or older
Pregnant women.
Coronaviruses will contaminate most individuals at a few time amid their lifetime. Coronaviruses can change viably, which makes them so infectious. To anticipate transmission, individuals ought to remain at domestic and rest whereas side effects are dynamic. They ought to moreover maintain a strategic distance from near contact with other individuals. They should also avoid close contact with other people. Covering the mouth and nose with a tissue or handkerchief while coughing or sneezing.
SIR model is first introduced by W.O. Kermach and A.G Mckendrick in 1927. SIR model is a best model of an infectious disease. This model divided the population into the three groups. The groups name is.
S (t) is the Susceptible people at the time.
I (t) is the infected people at the time.
R(t) is the recovered people at the time.
This model is constructing the ordinary differential equations in this model time t is the independent variable and S, I, R is the dependent variables. These groups have taken the number of people on every day. Yet, the data is transitions with time, as human being act from one group to another group. Illustration, human being in group
where
If
We find the trajectories
Initial conditions
(If)
It is impossible for the disease to infect all the susceptible person.
In this research work we have discussed about the COVID 19 disease. also know about how many people got sick in India due to pandemic disease COVID19. In this article, we have given a mathematical model to COVID 19 with the help of SIR model [4, 5, 6]. We have taken data of how many people had become ill in India by COVID 19 on 20 January 2021 and using this data , we have created a mathematical model of COVID 19 with the help of SIR model. We have created three differential equations by taking the original data and solving those equations by the Homotopy Perturbation method (HPM ).We got out the numerical solutions and made a table, and with the help of that table, we tried to tell what is the position of COVID 19 in India by making the graphs. There are a lot of methods which solves the differential equations [7, 8, 9], but we have used the HPM method. This method solves the biggest and most difficult equations very easily and with less of calculations.We will solve the Differential Equations of COVID 19, which is made with the help of SIR model. In these equations, we took the data of 20 January 2021 COVID 19 people of India who were caught by COVID 19 epidemics.
Total confirmed cases on 20 January 2021 in India is 10611728.
Death 152907
Recovered is 102656163
Active cases are 189245
Susceptible persons are 189347782
So, we take the
where
Now we will solve these equations with the help of HPM method.
By the homotopy method we get,
Putting value
Both side comparing the coefficient of p we get
So, by the HPM we get the solution:
We have the table
S.NO. | DATE | S | I | R |
---|---|---|---|---|
1 | 20/01/2021 | 18.9347782 | 1.0611728 | |
2 | 21 /01/2021 | 18.7339566 | 1.0662266 | 1.1175747 |
3 | 22/01/2021 | 18.533135 | 1.06128040 | 1.1933424 |
4 | 23/01/2021 | 18.3323134 | 1.06633424 | 1.2691101 |
5 | 24/01/2021 | 18.1314918 | 1.0613880 | 1.3448778 |
6 | 25/01/2021 | 17.9306702 | 1.0664418 | 1.4206455 |
7 | 26/01/2021 | 17.7298486 | 1.0684956 | 1.4964132 |
8 | 27/01/2021 | 17.529027 | 1.0705494 | 1.5721809 |
9 | 28/01/2021 | 17.3282054 | 1.0716032 | 1.6479486 |
10 | 29/01/2021 | 17.1273838 | 1.0726657 | 1.7237163 |
11 | 30/01/2021 | 16.9265622 | 1.0747108 | 1.799484 |
12 | 31/01/2021 | 16.7257406 | 1.0767646 | 1.8752517 |
From the above table we can predict that infected cases of corona on 31 January which is almost same as actual cases on 31 January. The current COVID-19 pandemic is unprecedented, but the global response draws on the lessons learned from other disease outbreaks over the past several decades.
World scientists on COVID-19 then met at the World Health Organization’s Geneva headquarters on 11–12 February 2020 to assess the current level of knowledge about the new virus, agree on critical research questions that need to be answered urgently, and to find ways to work together to accelerate and fund priority research to curtail this outbreak and prepare for those in the future see Figures 1–3 for reference.
SIR chart depicting no of people susceptible, infected and recovered.
SIR chart depicting no of people susceptible.
SIR chart depicting no of people infected.
In this chapter, we have taken data of people affected by coronavirus in India till 20 January (1). Then we converted this data into three differential equations with the help of SIR model. We solved the equation made from SIR model with HPM. From the result of solving, we estimated the people who got infected with corona virus in the coming 5 days. We converted the result from HPM into a table and graph and from the result we saw that in the coming days, corona cases are increasing and recovering but the corona positive rate is very high, and the rate of recovery is very short. We saw that the information about Corona-positive cases being given by the Government of India was also that the rate of positive is increasing very fast, but the rate of recovery is very low. From all these, we can now say that by solving with HPM we get the result very close to the actual result. We have predicted cases of corona till Jan 31 using SIR model, risk factors for the coronavirus disease. The risk is especially high if two or three of the Cs come together.
IntechOpen implements a robust policy to minimize and deal with instances of fraud or misconduct. As part of our general commitment to transparency and openness, and in order to maintain high scientific standards, we have a well-defined editorial policy regarding Retractions and Corrections.
",metaTitle:"Retraction and Correction Policy",metaDescription:"Retraction and Correction Policy",metaKeywords:null,canonicalURL:"/page/retraction-and-correction-policy",contentRaw:'[{"type":"htmlEditorComponent","content":"IntechOpen’s Retraction and Correction Policy has been developed in accordance with the Committee on Publication Ethics (COPE) publication guidelines relating to scientific misconduct and research ethics:
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\\n\\nA Correction will be issued by the Academic Editor when:
\\n\\n3.1. ERRATUM
\\n\\nAn Erratum will be issued by the Academic Editor when it is determined that a mistake in a Chapter originates from the production process handled by the publisher.
\\n\\nA published Erratum will adhere to the Retraction Notice publishing guidelines outlined above.
\\n\\n3.2. CORRIGENDUM
\\n\\nA Corrigendum will be issued by the Academic Editor when it is determined that a mistake in a Chapter is a result of an Author’s miscalculation or oversight. A published Corrigendum will adhere to the Retraction Notice publishing guidelines outlined above.
\\n\\n4. FINAL REMARKS
\\n\\nIntechOpen wishes to emphasize that the final decision on whether a Retraction, Statement of Concern, or a Correction will be issued rests with the Academic Editor. The publisher is obliged to act upon any reports of scientific misconduct in its publications and to make a reasonable effort to facilitate any subsequent investigation of such claims.
\\n\\nIn the case of Retraction or removal of the Work, the publisher will be under no obligation to refund the APC.
\\n\\nThe general principles set out above apply to Retractions and Corrections issued in all IntechOpen publications.
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\\n\\nPolicy last updated: 2017-09-11
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\n\n1. RETRACTIONS
\n\nA Retraction of a Chapter will be issued by the Academic Editor, either following an Author’s request to do so or when there is a 3rd party report of scientific misconduct. Upon receipt of a report by a 3rd party, the Academic Editor will investigate any allegations of scientific misconduct, working in cooperation with the Author(s) and their institution(s).
\n\nA formal Retraction will be issued when there is clear and conclusive evidence of any of the following:
\n\nPublishing of a Retraction Notice will adhere to the following guidelines:
\n\n1.2. REMOVALS AND CANCELLATIONS
\n\n2. STATEMENTS OF CONCERN
\n\nA Statement of Concern detailing alleged misconduct will be issued by the Academic Editor or publisher following a 3rd party report of scientific misconduct when:
\n\nIntechOpen believes that the number of occasions on which a Statement of Concern is issued will be very few in number. In all cases when such a decision has been taken by the Academic Editor the decision will be reviewed by another editor to whom the author can make representations.
\n\n3. CORRECTIONS
\n\nA Correction will be issued by the Academic Editor when:
\n\n3.1. ERRATUM
\n\nAn Erratum will be issued by the Academic Editor when it is determined that a mistake in a Chapter originates from the production process handled by the publisher.
\n\nA published Erratum will adhere to the Retraction Notice publishing guidelines outlined above.
\n\n3.2. CORRIGENDUM
\n\nA Corrigendum will be issued by the Academic Editor when it is determined that a mistake in a Chapter is a result of an Author’s miscalculation or oversight. A published Corrigendum will adhere to the Retraction Notice publishing guidelines outlined above.
\n\n4. FINAL REMARKS
\n\nIntechOpen wishes to emphasize that the final decision on whether a Retraction, Statement of Concern, or a Correction will be issued rests with the Academic Editor. The publisher is obliged to act upon any reports of scientific misconduct in its publications and to make a reasonable effort to facilitate any subsequent investigation of such claims.
\n\nIn the case of Retraction or removal of the Work, the publisher will be under no obligation to refund the APC.
\n\nThe general principles set out above apply to Retractions and Corrections issued in all IntechOpen publications.
\n\nAny suggestions or comments on this Policy are welcome and may be sent to permissions@intechopen.com.
\n\nPolicy last updated: 2017-09-11
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