scholarly journals A numerical solution by alternative Legendre polynomials on a model for novel coronavirus (COVID-19)

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Elham Hashemizadeh ◽  
Mohammad Ali Ebadi
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
Legendre Polynomials ◽  
Algebraic System ◽  
The Novel ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Runge Kutta Method ◽  
Novel Coronavirus ◽  
The Mathematical Model

Abstract Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. This paper provides a numerical solution for the mathematical model of the novel coronavirus by the application of alternative Legendre polynomials to find the transmissibility of COVID-19. The mathematical model of the present problem is a system of differential equations. The goal is to convert this system to an algebraic system by use of the useful property of alternative Legendre polynomials and collocation method that can be solved easily. We compare the results of this method with those of the Runge–Kutta method to show the efficiency of the proposed method.

Enhancement the Solar Still Performance Using Chimney Exhaust Gases

2021 ◽  
Author(s):  
Hamdy Hassan
Keyword(s):  
Mathematical Model ◽  
Theoretical Study ◽  
Saline Water ◽  
Kutta Method ◽  
Solar Still ◽  
Climate Conditions ◽  
Exhaust Gases ◽  
Runge Kutta Method ◽  
The Impact ◽  
The Mathematical Model

Abstract In this paper, a theoretical study is presented on enhancement of the solar still performance by using the exhaust gases passing inside a chimney under the still basin. The impact of the exhaust gases temperature on the solar still temperature, productivity, and efficiency are considered. The performance of solar still with chimney is compared with that of conventional solar still. The study is carried out under the hot and climate conditions of Upper Egypt. A complete transient mathematical model of the physical model including the solar still regions temperatures, productivity, and heat transfer between the solar still and the exhaust gases are constructed. The mathematical model is solved numerically by using fourth-order Runge-Kutta method and is programmed by using MATLAB. The mathematical model is validated using an experimental work. The results show that the solar still saline water temperature increases and productivity with using and rising the exhaust gases. Furthermore, the impact of using exhaust gases on the still performance in winter is greater than in summer. using chimney exhaust gases at 75 °C and 125 °C enhances the daily freshwater yield of the conventional still by more than three times and about six times in winter, respectively, and about two and half times and more than three times in summer, respectively.

scholarly journals A Note on COVID-19 Diagnosis Number Prediction Model in China

2021 ◽  
Author(s):  
Yi Li ◽  
Xianhong Yin ◽  
Meng Liang ◽  
Xiaoyu Liu ◽  
Meng Hao ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Future Trend ◽  
Disease Prediction ◽  
The Novel ◽  
Limited Impact ◽  
Infected People ◽  
Health Authorities ◽  
Novel Coronavirus ◽  
New Diagnosis ◽  
The Mathematical Model

Abstract Objective: In December 2019, pneumonia infected with the novel coronavirus burst in Wuhan, China. We aimed to use a mathematical model to predict number of diagnosed patients in future to ease anxiety on the emergent situation. Methods: According to all diagnosis number from WHO website and combining with the transmission mode of infectious diseases, the mathematical model was fitted to predict future trend of outbreak. Our model was based on the epidemic situation in China, which could provide referential significance for disease prediction in other countries, and provide clues for prevention and intervention of relevant health authorities. In this retrospective, all diagnosis number from Jan 21 to Feb 10, 2020 reported from China was included and downloaded from WHO website. We develop a simple but accurate formula to predict the next day diagnosis number: ，where N i is the total diagnosed patient till the i th day, and was estimated as 0.904 at Feb 10. Results: Based on this model, it is predicted that the rate of disease infection will decrease exponentially. The total number of infected people is limited; thus, the disease will have limited impact. However, new diagnosis will last to end of March. Conclusions: Through the establishment of our model, we can better predict the trend of the epidemic in China.

scholarly journals DESIGN OF A NONLINEAR SITR FRACTAL MODEL BASED ON THE DYNAMICS OF A NOVEL CORONAVIRUS (COVID-19)

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040026 ◽  
Author(s):  
YOLANDA GUERRERO SÁNCHEZ ◽  
ZULQURNAIN SABIR ◽  
JUAN L. G. GUIRAO
Keyword(s):  
Mathematical Model ◽  
Fractal Model ◽  
Contact Rate ◽  
The Novel ◽  
Nonlinear Mathematical Model ◽  
Huge Number ◽  
Social Distancing ◽  
Natural Stabilization ◽  
Novel Coronavirus ◽  
The Mathematical Model

The aim of the present paper is to state a simplified nonlinear mathematical model to describe the dynamics of the novel coronavirus (COVID-19). The design of the mathematical model is described in terms of four categories susceptible ([Formula: see text], infected ([Formula: see text], treatment ([Formula: see text] and recovered ([Formula: see text], i.e. SITR model with fractals parameters. These days there are big controversy on if is needed to apply confinement measure to the population of the word or if the infection must develop a natural stabilization sharing with it our normal life (like USA or Brazil administrations claim). The aim of our study is to present different scenarios where we draw the evolution of the model in four different cases depending on the contact rate between people. We show that if no confinement rules are applied the stabilization of the infection arrives around 300 days affecting a huge number of population. On the contrary with a contact rate small, due to confinement and social distancing rules, the stabilization of the infection is reached earlier.

scholarly journals A Note on COVID-19 Diagnosis Number Prediction Model in China

2020 ◽  
Author(s):  
Yi Li ◽  
Xianhong Yin ◽  
Meng Liang ◽  
Xiaoyu Liu ◽  
Meng Hao ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Scientific Information ◽  
Future Trend ◽  
The Novel ◽  
Infected People ◽  
The Public ◽  
Health Authorities ◽  
Novel Coronavirus ◽  
New Diagnosis ◽  
The Mathematical Model

AbstractImportanceTo predict the diagnosed COVID-19 patients and the trend of the epidemic in China. It may give the public some scientific information to ease the fear of the epidemic.ObjectiveIn December 2019, pneumonia infected with the novel coronavirus burst in Wuhan, China. We aimed to use a mathematical model to predict number of diagnosed patients in future to ease anxiety on the emergent situation.DesignAccording to all diagnosis number from WHO website and combining with the transmission mode of infectious diseases, the mathematical model was fitted to predict future trend of outbreak.SettingOur model was based on the epidemic situation in China, which could provide referential significance for disease prediction in other countries, and provide clues for prevention and intervention of relevant health authorities.ParticipantsIn this retrospective, all diagnosis number from Jan 21 to Feb 10, 2020 reported from China was included and downloaded from WHO website.Main Outcome(s) and Measure(s)We develop a simple but accurate formula to predict the next day diagnosis number:,where Ni is the total diagnosed patient till the ith day, and α was estimated as 0.904 at Feb 10.ResultsBased on this model, it is predicted that the rate of disease infection will decrease exponentially. The total number of infected people is limited; thus, the disease will have limited impact. However, new diagnosis will last to March.Conclusions and RelevanceThrough the establishment of our model, we can better predict the trend of the epidemic in China.

scholarly journals Novel Dynamic Structures of 2019-nCoV with Nonlocal Operator via Powerful Computational Technique

Biology ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 107 ◽  
Author(s):  
Wei Gao ◽  
P. Veeresha ◽  
D. G. Prakasha ◽  
Haci Mehmet Baskonus
Keyword(s):  
Mathematical Model ◽  
Nonlocal Operator ◽  
Computational Technique ◽  
The Novel ◽  
Adomian Decomposition ◽  
Dynamic Structures ◽  
Novel Coronavirus ◽  
The Mathematical Model ◽  
Natural Decomposition ◽  
The City

In this study, we investigate the infection system of the novel coronavirus (2019-nCoV) with a nonlocal operator defined in the Caputo sense. With the help of the fractional natural decomposition method (FNDM), which is based on the Adomian decomposition and natural transform methods, numerical results were obtained to better understand the dynamical structures of the physical behavior of 2019-nCoV. Such behaviors observe the general properties of the mathematical model of 2019-nCoV. This mathematical model is composed of data reported from the city of Wuhan, China.

Applications of Numerical Simulation of Solar Cooker Type Box With Multi-Step Inner Reflector

Solar Energy ◽  
2003 ◽  
Author(s):  
H. Terre´s-Pen˜a ◽  
P. Quinto-Diez
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Thermal Conversion ◽  
Numerical Results ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Energetic Analysis ◽  
The Mathematical Model ◽  
Solar Rays

It is shown a mathematical model of a solar box cooker with multi-step inner reflector and the numerical results for two applications has been analyzed. These applications are 1. Numerical simulation of operation of solar box cooker with multi-step inner reflector in Tanta, Egypt and 2. Numerical simulation of solar box cooker with multi-step inner reflector for 10 hours of operation. In the case 1, is analyzed a solar box cooker constructed and evaluated in Tanta, Egypt [1]. The experimental results that was obtained are compared with the numerical results that was obtained for the mathematical model. The case 2, is an evaluation of numerical results that was obtained for the operation of 10 hours for solar box cooker constructed in the Laboratorio de Ingenieri´a Te´rmica e Hidra´ulica Aplicada (LABINTHAP) in Me´xico City. [4] The solar box cooker is integrated by a covert that was made with double glass, this is use with two purposes, reduce the loss heat convection with outer and to generated the greenhouse effect with inner of cooker. In the inner of cooker there are a mirrors arrangement in inclined position (inner reflectors) placed in angles of 30°, 45° and 75°, these helped to reflex the solar rays in direction to the cook recipient. The recipient also received the solar rays in the upper part (lid). The mathematical model that was obtained from energetic analysis, is formed for five differential equations system no linear and the fourth Runge-Kutta method is used to resolve it. The numerical solution of the equations system is obtained with a computational software in C++. This work is a contribution to the application of numerical methods and computational for development of the solar energy used in thermal conversion equipments. The use of these techniques to solve the mathematical model is important to contribute in the evaluation and design of solar box cookers with multi-step inner reflector.

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