scholarly journals A Mathematical Study of COVID-19 Outbreak with Uncertainties of Controlling Parameters

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Prasenjit Mahato ◽  
◽  
Sanat Mahato ◽  
Subhashis Das
Keyword(s):  
Equilibrium Point ◽  
Theoretical Study ◽  
Disease Model ◽  
Existence Condition ◽  
Model Formulation ◽  
Mathematical Study ◽  
Infectious Disease Model ◽  
Proposed Model ◽  
Spreading Disease ◽  
Imprecise Parameters

Rapidly spreading disease, COVID-19 is classified as the human-to-human transmissionable disease and currently it becomes a pandemic in the Globe. In this paper, we propose the conceptual mathematical model and analyze a Susceptible-Exposed-Infected-Quarantined or Isolated-Recovered- Susceptible (SEIRUS) type infectious disease model with imprecise parameters. We have divided the model formulation portion into four subsections. They are namely crisp SEIRUS model, interval SEIRUS model and fuzzy SEIRUS model. The existence condition and boundedness of the solution to our proposed model have been discussed. The asymptotical stability of the system at different equilibrium point is investigated. Also we have explained the global stability at endemic equilibrium point. Application of optimal control of the system is described and solved. Finally, some numerical results have been shown to test the theoretical study of the model. We observed that the population is greatly influenced for the imprecise nature of parameters.

scholarly journals A Novel Prey-Predator Quadratic Harvesting Model via Optimal Control Theory and Hopf Bifurcation

2020 ◽  
Vol 1 ◽  
pp. 1-22
Author(s):  
Prabir Panja ◽  
Dipak Kumar Jana
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Fish Species ◽  
Interaction Model ◽  
Existence Condition ◽  
Optimal Harvesting ◽  
Selling Price ◽  
Type I ◽  
Functional Responses ◽  
Proposed Model

In this investigation, a predator-prey interaction model among Phytoplankton, Zooplankton and Fish has been developed. In the absence of Zooplankton and Fish, it is assumed that Phytoplankton grows logistically. It is assumed that Zooplankton consumes Phytoplankton and Fish consumes Phytoplankton as well as Zooplankton. Holling type I & II functional responses have been considered to formulate the our proposed model. It is considered that Phytoplankton releases some toxin in the aquatic environment which makes some death in Zooplankton population. Quadratic harvesting is considered on Fish species. Boundedness of the solution of our proposed model has also been studied. Local stability of the system around each equilibrium point has been investigated. Also, the global stability of the interior equilibrium point has been studied. Existence condition of Hopf bifurcation of our proposed system has been studied. It is found that half saturation constant (α) can change the system dynamics. It is also found that the harvesting rate of Fish (E) and consumption rate of Zooplankton (γ1) has a significant role in the stability of the system. Again, it is found that the harvesting of Fish species will be increased if the selling price of Fish (p) and the annual discount (δ1) of Fish production cost increases. It is also found that the optimal harvesting rate of Fish decreases due to the increase of cost (c) of harvesting of Fish. Finally, some numerical simulation results have been presented to verify our analytical findings.

Modeling and Analysis of an Imprecise Epidemic System with Optimal Treatment and Vaccination Control

2018 ◽  
Vol 13 (02) ◽  
pp. 37-60
Author(s):  
Anjana Das ◽  
M. Pal
Keyword(s):  
Infectious Disease ◽  
Functional Form ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Disease Model ◽  
Control Parameters ◽  
Interval Numbers ◽  
Modeling And Analysis ◽  
Infectious Disease Model ◽  
Imprecise Parameters

In this paper, we propose and analyze a Susceptible-Vaccinated-Exposed-Infected-Recovered (SVEIR) type infectious disease model with imprecise parameters. Introducing the interval numbers in functional form, the SVEIR model is proposed and formulated. The existence of possible equilibrium points with their feasibility criteria and an explicit value of basic reproduction number is obtained. The asymptotic stability of the system at different equilibrium points are also discussed. Next by considering treatment and vaccination as two control parameters, an optimal control problem is formulated and solved. Finally, some computer simulation works are given in support of our analytical results.

Dynamics of a prey predator disease model with Holling type functional response and stochastic perturbation

2020 ◽  
pp. 471-488
Author(s):  
M. N. Srinivas ◽  
G. Basava Kumar ◽  
V. Madhusudanan
Keyword(s):  
Equilibrium Point ◽  
Disease Model ◽  
Stochastic Perturbation ◽  
Positive Equilibrium ◽  
Type Ii ◽  
Asymptotically Stable ◽  
Unique Positive Solution ◽  
Stochastic Nature ◽  
Research Article ◽  
Positive Equilibrium Point

The present research article constitutes Holling type II and IV diseased prey predator ecosystem and classified into two categories namely susceptible and infected predators.We show that the system has a unique positive solution. The deterministic and stochastic nature of the dynamics of the system is investigated. We check the existence of all possible steady states with local stability. By using Routh-Hurwitz criterion we showed that the positive equilibrium point $E_{7}$ is locally asymptotically stable if $x^{*} > \sqrt{m_{1}}$ .Moreover condition of the global stability of positive equilibrium point $E_{7}$ are also entrenched with help of Lyupunov theorem. Some Numerical simulations are carried out to illustrate our analytical findings.

scholarly journals Analysis of Smooth Implementation of Industry Poverty Alleviation considering Government Supervision

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Haifeng Yao ◽  
Jiangyue Fu
Keyword(s):  
Equilibrium Point ◽  
Evolutionary Game Theory ◽  
Poverty Alleviation ◽  
Equilibrium Points ◽  
Evolutionary Game ◽  
Parameter Design ◽  
Game Model ◽  
Government Supervision ◽  
Proposed Model ◽  
The Government

Vigorous implementation of industrial poverty alleviation is the fundamental path and core power of poverty alleviation in impoverished areas. Enterprises and poor farmers are the main participants in industry poverty alleviation. Government supervision measures regulate their behaviors. This study investigates how to smoothly implement industry poverty alleviation projects considering government supervision. A game model is proposed based on the evolutionary game theory. It analyses the game processes between enterprises and poor farmers with and without government supervision based on the proposed model. It is shown that poverty alleviation projects will fail without government supervision given that the equilibrium point (0, 0) is the ultimate convergent point of the system but will possibly succeed with government supervision since the equilibrium points (0, 0) and (1, 1) are the ultimate convergent point of the system, where equilibrium point (1, 1) is our desired results. Different supervision modes have different effects on the game process. This study considers three supervision modes, namely, only reward mode, only penalty mode, and reward and penalty mode, and investigates the parameter design for the reward and penalty mode. The obtained results are helpful for the government to develop appropriate policies for the smooth implementation of industry poverty alleviation projects.

scholarly journals Obesity as an "infectious" disease

2021 ◽  
Vol 11 (9) ◽  
pp. 534-537
Author(s):  
Daria Żuraw ◽  
Paulina Oleksa ◽  
Mateusz Sobczyk
Keyword(s):  
Infectious Disease ◽  
Disease Model ◽  
Living Environment ◽  
Social Contagion ◽  
Social Discrimination ◽  
Obese People ◽  
Obesity Epidemic ◽  
Global Epidemic ◽  
Infectious Disease Model ◽  
The One

Introduction: Obesity has been recognized as a global epidemic by the WHO, followed by a wealth of empirical evidence supporting its contagiousness. However, the dynamics of the spread of obesity between individuals are rarely studied.  A distinguishing feature of the obesity epidemic is that it is driven by a process of social contagion that cannot be perfectly described by the infectious disease model. There is also social discrimination in the obesity epidemic. Social discrimination against obese people plays quite different roles in two cases: on the one hand, when obesity cannot be eliminated, social discrimination can reduce the number of obese people; on the other hand, when obesity is eradicable, social discrimination can cause it to explode.(1)   Materiał and methods: A literature analysis on obesity epidemic was carried out within the Pubmed, Google scholar and Research Gate platform. The following keywords were used in serach: obesity, epidemy, children, body max index.    Purpose of the work: The aim of the following analysis is to present an obesity as an infectious disease. The steadily increasing percentage of obese people, including children, shows that there is an obesity epidemic. This is the phenomenon of social contagion, which partially explains the concept of homophily, which involves the grouping of people with similar characteristics. Potential explanations are also provided by sharing a living environment with similar access to certain foods and similar opportunities for physical activity, which defines the occurrence of analogous health habits

Study of Donor Centres in n-InSb due to the Temperature Annealing

2005 ◽  
Vol 480-481 ◽  
pp. 197-200
Author(s):  
Y. Sayad ◽  
A. Nouiri
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Annealing Time ◽  
Annealing Temperature ◽  
Theoretical Study ◽  
Donor Concentration ◽  
Model Based ◽  
Proposed Model ◽  
Kinetics Of ◽  
Best Fit

An increasing of donor centres has been detected in n-InSb when it was submitted to anneal/quench with various annealing temperature (450 °C - 850 °C) and various annealing time (5 - 100 hours). A theoretical study of the kinetics of the conduction conversion of n-InSb at temperature annealing above 250 °C has been made. The present analysis indicates that the donor concentration increases with increasing of annealing time. In order to study this variation and to give a model for donor centres generated, a proposed model based on the simple kinetic is used to fit the variation of donor concentration as a function of annealing time. However, from the best fit of experimental data using the proposed model, the activation energy is determined.

Modeling of three-dimensional beam nonlinear vibrations generalizing Hencky’s ideas

2022 ◽  
pp. 108128652110679
Author(s):  
Emilio Turco
Keyword(s):  
Kinetic Energy ◽  
Strain Energy ◽  
Nonlinear Vibrations ◽  
Three Dimensional ◽  
Integration Scheme ◽  
Beam Model ◽  
Model Formulation ◽  
Discrete Approach ◽  
Numerical Integration Scheme ◽  
Proposed Model

In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e., by the kinetic energy and by the potential of conservative forces. Differently from Hencky’s seminal work, which considers only flexibility to compute the buckling load for rectilinear and planar Euler–Bernoulli beams, the proposed model is fully three-dimensional and considers both the extensional and shear deformability contributions to the strain energy and translational and rotational kinetic energy terms. After having introduced the model formulation, some simulations obtained with a numerical integration scheme are presented to show the capabilities of the proposed beam model.

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