Spread and control of COVID-19: A mathematical model

2021 ◽  
Author(s):  
O. P. Misra ◽  
Omprakash Singh Sisodiya
Keyword(s):  
Mathematical Model ◽  
Control Measures ◽  
Transition Rates ◽  
Susceptible Population ◽  
Death Rates ◽  
Social Distancing ◽  
The Social ◽  
The Stability ◽  
And Control ◽  
The Mathematical Model

A mathematical model is proposed in this paper to study the transmission and control of COVID-19. The mathematical model is formulated using system of nonlinear ordinary differential equations. The model includes disease-related parameters such as contact rate, disease-induced death rates, immigration rate and transition rates along with parameters for control measures such as implementation of social distancing practices, isolation and quarantine rates. From the stability analysis of the model, it is shown that if the social distancing is practiced by the large number of susceptible population, then the disease will not spread, and it may eventually die out. Further, it is derived from the analysis of the model that if most of the infected populations are isolated or quarantined, then the spread of the disease can be eventually controlled. However, from the analysis of the model, it is observed that if there is constant immigration of asymptomatic infected persons, then the disease will continue to spread and will remain pandemic. For controlling the disease, two more parameters, that is, vaccination and testing rates, are introduced in the original mathematical model and from the numerical analysis of this model, it has been shown that the control strategy involving vaccination and testing in combination can have synergistic effect for minimizing the COVID-19 infected cases.

scholarly journals COVID-19 in South Korea: Proper timing for Easing Mask mandates after COVID-19 Vaccination

2021 ◽  
pp. 1-9
Author(s):  
Yun-Jung Kang
Keyword(s):  
South Korea ◽  
Disease Control ◽  
Prevention And Control ◽  
Control Measures ◽  
Social Distancing ◽  
Proper Timing ◽  
Control And Prevention ◽  
Prevention And Control Measures ◽  
And Control

Abstract As of 25 July 2021, the Korea Disease Control and Prevention Agency reported 1,422 new COVID-19 cases, 188,848 total cases, and 2.073 total deaths (1.10% fatality rates). Since the first SARS-CoV-2 case was reported, efforts to find a treatment and vaccine against COVID-19 have been widespread. Four vaccines are on the WHO’s emergency use listing and are approved of their usage; BNT162b2, mRNA-1273, AZD1222, and Ad26.COV2.S. Vaccines against SARS-CoV-2 need at least 14 days to achieve effectiveness. Thus, people should abide by prevention and control measures, including wearing masks, washing hands, and social distancing. However, a lot of new cases were reported after vaccinations, as many people did not follow the prevention control measures before the end of the 14 days period. There is no doubt we need to break free from mask mandates. But let us not decide the timing in haste. Even if the mask mandates are eased, they should be changed depending on the number of reported cases, vaccinations, as well as prevention and control measures on how circumstances are changing under the influence of mutant coronavirus.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

Stability Analysis and Control Measures of the Kim-Yun-Mine Collapse

2012 ◽  
Vol 594-597 ◽  
pp. 358-361
Author(s):  
Shan Shan Zhang ◽  
Yu Liang Wu
Keyword(s):  
Rock Mass ◽  
Stability Analysis ◽  
Stereographic Projection ◽  
Control Measures ◽  
Collapse Characteristics ◽  
Basic Characteristics ◽  
The Stability ◽  
Mine Collapse ◽  
And Control ◽  
Dangerous Rock Mass

Collapse is one of the major geological disasters all over the world and threats to life and property safety of people. To make a better understanding of the reason it occurs and how to deal with it, the Kim-Yun-Mine collapse is researched. There are one dangerous rock mass and two collapse accumulation body. The basic characteristics of the collapse is described clearly according to the geological exploration data, and the stability of the dangerous rock mass and the collapse accumulated body is analyzed in the way of engineering geology and stereographic projection. At last, we put forward comprehensive control measures based on the results of stability analysis and collapse characteristics.

On A Formulation of the Elastic Stability Equations of Circular Cylindrical Shells Under Variable Internal Pressure

1985 ◽  
Vol 9 (2) ◽  
pp. 64-69
Author(s):  
J.L. Urrutia-Galicia ◽  
A.N. Sherbourne
Keyword(s):  
Mathematical Model ◽  
Internal Pressure ◽  
Cylindrical Shells ◽  
Direct Analysis ◽  
Elastic Stability ◽  
Equilibrium Path ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Variable Internal Pressure ◽  
The Mathematical Model

The mathematical model of the stability analysis of circular cylindrical shells under arbitrary internal pressure is presented. The paper consists of a direct analysis of the equilibrium modes in the neighbourhood of the unperturbed principal equilibrium path. The final stability condition results in a completely symmetric differential operator which is then compared with current theories found in the literature.

scholarly journals An Approach for the Global Stability of Mathematical Model of an Infectious Disease

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1778
Author(s):  
Mojtaba Masoumnezhad ◽  
Maziar Rajabi ◽  
Amirahmad Chapnevis ◽  
Aleksei Dorofeev ◽  
Stanford Shateyi ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Global Stability ◽  
Incidence Rates ◽  
Endemic Equilibrium ◽  
Symmetry Properties ◽  
Nonlinear Incidence Rates ◽  
Lyapunov Matrix ◽  
The Stability ◽  
The Mathematical Model

The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.

scholarly journals Estimates of the ongoing need for social distancing and control measures post-“lockdown” from trajectories of COVID-19 cases and mortality

2020 ◽  
Vol 56 (1) ◽  
pp. 2001483 ◽  
Author(s):  
Mike Lonergan ◽  
James D. Chalmers
Keyword(s):  
Severe Acute Respiratory Syndrome ◽  
Economic Activity ◽  
Regression Models ◽  
Reproduction Number ◽  
Viral Transmission ◽  
Control Measures ◽  
Social Distancing ◽  
And Control ◽  
Doubling Times

By 21 May 2020, severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) had caused more than 5 million cases of coronavirus 2019 (COVID-19) across more than 200 countries. Most countries with significant outbreaks have introduced social distancing or “lockdown” measures to reduce viral transmission. So the key question now is when, how and to what extent these measures can be lifted.Publicly available data on daily numbers of newly confirmed cases and mortality were used to fit regression models estimating trajectories, doubling times and the reproduction number (R0) of the disease, before and under the control measures. These data ran up to 21 May 2020, and were sufficient for analysis in 89 countries.The estimates of R0 before lockdown based on these data were broadly consistent with those previously published: between 2.0 and 3.7 in the countries with the largest number of cases available for analysis (USA, Italy, Spain, France and UK). There was little evidence to suggest that the restrictions had reduced R far below 1 in many places, with France having the most rapid reductions: R0 0.76 (95% CI 0.72–0.82) based on cases, and 0.77 (95% CI 0.73–0.80) based on mortality.Intermittent lockdown has been proposed as a means of controlling the outbreak while allowing periods of increased freedom and economic activity. These data suggest that few countries could have even 1 week per month unrestricted without seeing resurgence of the epidemic. Similarly, restoring 20% of the activity that has been prevented by the lockdowns looks difficult to reconcile with preventing the resurgence of the disease in most countries.

Causes Analysis and Control Measures of Landslide on Expressway from Yangshuo to Pingle in Guangxi

2013 ◽  
Vol 353-356 ◽  
pp. 116-119
Author(s):  
Chan Juan Yu ◽  
Yu Dong Peng
Keyword(s):  
Transfer Coefficient ◽  
Reference Value ◽  
Control Measures ◽  
The Other ◽  
Retaining Structure ◽  
Treatment Measures ◽  
Stability Of Slope ◽  
The Stability ◽  
And Control ◽  
Coefficient Method

According to the analysis on engineering geological and hydrological conditions of landslide on expressway from Yangshuo to Pingle in Guangxi, the formation mechanism of the landslide was summarized. The stability of slope was analyzed by mechanical transfer coefficient method. Then two kinds of effective preventions and treatment measures are proposed: setting retaining structure after drainage, or unloading after drainage. These measures have reference value to the management of the other landslide.

Traffic Management Staff System Based on MARKOV Modal

2014 ◽  
Vol 556-562 ◽  
pp. 4582-4585
Author(s):  
Xing Wei Liu ◽  
Jun Song ◽  
Ya Hui Cheng ◽  
Yi Bo Xu ◽  
Jian Long Ma
Keyword(s):  
Mathematical Model ◽  
Human Resource ◽  
Traffic Management ◽  
Social Progress ◽  
Web Pages ◽  
Cultural Conditions ◽  
Human Situation ◽  
The Social ◽  
Management Staff ◽  
The Mathematical Model

Social progress absolutely doesn’t means a situation that sacrificing the benefits of most people to satisfy the benefits of the minority. This paper will discuss some questions surrounded with the social resources human resource supply chain. This paper also discusses whether ‘promotion changing pattern of common progress’ can be applied to all kinds of industries, and what natural and cultural conditions to meet so that achieving social and human situation [1]. We have found that MARKOV model meet the promotion of such progress law. At the same time, using the MARKOV modal, this article has done a comparative analysis based on a number of growth historical data. We extract an appropriate mathematical model to predict the human resource after correcting the old model. According to the mathematical model we extracted, we analyze and predict the result of questions. Finally, the article give the models and results obtained in the form of web pages so that making readers and managers decide and read more visually and better.

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