scholarly journals Determining COVID-19 Dynamics Using Physics Informed Neural Networks

2021 ◽  
Author(s):  
Joseph Malinzi ◽  
Simanga Gwebu ◽  
Sandile Motsa
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Infection Rate ◽  
Recovery Rate ◽  
Death Rate ◽  
System Of Equations ◽  
Governing System

The Physics Informed Neural Networks framework is applied to the understanding of the dynamics of Coronavirus of 2019. To provide the governing system of equations used by the framework, the Susceptible-Infected-Recovered-Death mathematical model is used. The study focused on finding the patterns of the dynamics of the disease which involves predicting the infection rate, recovery rate and death rate; thus predicting the active infections, total recovered, susceptible and deceased at any required time. The study used data that was collected on the dynamics of COVID-19 from the Kingdom of Eswatini between March 2020 and September 2021. The obtained results showed less errors thus making highly accurate predictions.

scholarly journals Contributions to the mathematical theory of epidemics: V. Analysis of experimental epidemics of mouse-typhoid; a bacterial disease conferring incomplete immunity

1939 ◽  
Vol 39 (3) ◽  
pp. 271-288 ◽  
Author(s):  
W. O. Kermack ◽  
A. G. McKendrick
Keyword(s):  
General Theory ◽  
Observational Data ◽  
Life Table ◽  
Infection Rate ◽  
Recovery Rate ◽  
Death Rate ◽  
Mathematical Theory ◽  
Bacterial Disease ◽  
Experimental Conditions ◽  
Published Paper

In a recently published paper (Kermack & McKendrick, 1937) the observational data relating to epidemics of ectromelia in populations of mice maintained under experimental conditions (Greenwood et al. 1936) has been analysed in the light of a mathematical theory of epidemics developed by us during recent years (Kermack & McKendrick, 1927, 1932, 1933, 1936). It was shown that the life table giving the chance of mice surviving for various lengths of time in infected communities is very closely represented by a formula calculated on the assumption that the various rates—infection rate, recovery rate, death rate, etc.—are constants. It is, of course, realized that this simplifying assumption can only be regarded as approximately true. It renders the application of the general theory practicable, and the result of the investigation justifies its use, in so far as the theory so simplified does actually conform to the experimental results.

scholarly journals System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 787
Author(s):  
Olaniyi Iyiola ◽  
Bismark Oduro ◽  
Trevor Zabilowicz ◽  
Bose Iyiola ◽  
Daniel Kenes
Keyword(s):  
Fractional Order ◽  
Recovery Rate ◽  
Death Rate ◽  
Numerical Solutions ◽  
Complex Nature ◽  
Uniqueness Of Solutions ◽  
Fractional Equations ◽  
Effective Contact ◽  
Proposed Model ◽  
Fractional Models

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.

Global Approximation: Performance Comparison of Different Methods, With an Application to Road Vehicle System Engineering

1999 ◽  
Author(s):  
Massimiliano Gobbi ◽  
Giampiero Mastinu
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Linear Interpolation ◽  
Performance Comparison ◽  
Pareto Optimal ◽  
Approximation Methods ◽  
Global Approximation ◽  
Road Vehicle ◽  
Pareto Optimal Set ◽  
Design Variables

Abstract Optimisation of complex mechanical systems has often to be performed by resorting to global approximation. In usual global approximation practice, the original mathematical model is substituted by another mathematical model which gives approximately the same relationships between design variables and performance indexes. This is made to ensure much faster simulations which are of crucial importance to find optimal solutions. In this paper the performances of four global approximation methods (Neural Networks, Kriging, Quadratic Approximation, Linear Interpolation) are compared, with reference to an actual optimal design problem. The performances of a road vehicle suspension system are optimised by varying the system’s design variables. The Pareto-optimal set is derived symbolically. The performances of the different approximation methods taken into consideration are assessed by comparing the numerical- and the analytical-Pareto-optimal results. It is found that Neural Networks obtain the best accuracy.

Public Asylum Reports for 1873

1874 ◽  
Vol 20 (91) ◽  
pp. 464-471
Keyword(s):  
Recovery Rate ◽  
Death Rate ◽  
Annual Report

Newcastle-on-Tyne.—Ninth Annual Report.—Mr. Wickham enters into the following defence of Australian tinned meats, which they, perhaps, hardly required:—“The Australian tinned meats, which are now freely used, at first met with much opposition, and, even now, a few of the more ill-humoured patients object to them. To some of the better disposed ones the flavour is at first a little disagreeable, but the same may be said of fairly intelligent people outside, and they are so very few here that it is impossible to consider them in the arrangement of a diet table. As for its nutritious qualities, I have only to say that the patients eating it (excluding those suffering from wasting diseases) gain, or at least retain, their weight. The recovery rate for the three years I have held office has been 45 9 per cent. as against 33 5 per cent. during the previous five years, and the death rate has been steadily decreasing, while the necessity for ordering extras for the sick is reduced to the very lowest minimum. The Australian meat has been largely used during that time, and, though I do not wish to ascribe these satisfactory results to its agency, it must be apparent that it has not interfered with the primary objects of the institution.”

scholarly journals Development of turning process digital twin based on machine learning

2021 ◽  
pp. 32-41
Author(s):  
D. A. Rastorguev ◽  
◽  
A. A. Sevastyanov ◽  
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Artificial Neural Networks ◽  
Information Technologies ◽  
Cutting Process ◽  
Turning Process ◽  
Force Load ◽  
Cnc Machine ◽  
Digital Twin ◽  
Artificial Neural

Today, manufacturing technologies are developing within the Industry 4.0 concept, which is the information technologies introduction in manufacturing. One of the most promising digital technologies finding more and more application in manufacturing is a digital twin. A digital twin is an ensemble of mathematical models of technological process, which exchanges information with its physical prototype in real-time. The paper considers an example of the formation of several interconnected predictive modules, which are a part of the structure of the turning process digital twin and designed to predict the quality of processing, the chip formation nature, and the cutting force. The authors carried out a three-factor experiment on the hard turning of 105WCr6 steel hardened to 55 HRC. Used an example of the conducted experiment, the authors described the process of development of the digital twin diagnostic module based on artificial neural networks. When developing a mathematical model for predicting and diagnosing the cutting process, the authors revealed higher accuracy, adaptability, and versatility of artificial neural networks. The developed mathematical model of online diagnostics of the cutting process for determining the surface quality and chip type during processing uses the actual value of the cutting depth determined indirectly by the force load on the drive. In this case, the model uses only the signals of the sensors included in the diagnostic subsystem on the CNC machine. As an informative feature reflecting the force load on the machine’s main motion drive, the authors selected the value of the energy of the current signal of the spindle drive motor. The study identified that the development of a digital twin is possible due to the development of additional modules predicting the accuracy of dimensions, geometric profile, tool wear.

scholarly journals Simple MSEIR Model for Measles Transmission

2019 ◽  
pp. 1-11
Author(s):  
Mojeeb Al-Rahman EL-Nor Osman ◽  
Appiagyei Ebenezer ◽  
Isaac Kwasi Adu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Birth Rate ◽  
Reproduction Number ◽  
Progression Rate ◽  
Asymptotically Stable ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an Immunity-Susceptible-Exposed-Infectious-Recovery (MSEIR) mathematical model was used to study the dynamics of measles transmission. We discussed that there exist a disease-free and an endemic equilibria. We also discussed the stability of both disease-free and endemic equilibria.  The basic reproduction number  is obtained. If , then the measles will spread and persist in the population. If , then the disease will die out.  The disease was locally asymptotically stable if  and unstable if  . ALSO, WE PROVED THE GLOBAL STABILITY FOR THE DISEASE-FREE EQUILIBRIUM USING LASSALLE'S INVARIANCE PRINCIPLE OF Lyaponuv function. Furthermore, the endemic equilibrium was locally asymptotically stable if , under certain conditions. Numerical simulations were conducted to confirm our analytic results. Our findings were that, increasing the birth rate of humans, decreasing the progression rate, increasing the recovery rate and reducing the infectious rate can be useful in controlling and combating the measles.

scholarly journals Art of Formulating LPs and IPs from Real Life Problems

2013 ◽  
Vol 61 (2) ◽  
pp. 185-191
Author(s):  
Md Hasib Uddin Molla ◽  
M Babul Hasan
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Real Life ◽  
Linear Constraints ◽  
Decision Problems ◽  
System Of Equations ◽  
Present Formulation ◽  
Real Life Problem ◽  
Life Problems ◽  
Life Decision

Formulation of LPs and IPs is a technique to convert real life decision problems into a mathematical model. This model consists of a linear objective function and a set of linear constraints expressed in the form of a system of equations or inequalities. In this paper, we present formulation from real life problem as an art. We discuss formulation through real life example and solve them using computer techniques AMPL and LINDO. DOI: http://dx.doi.org/10.3329/dujs.v61i2.17068 Dhaka Univ. J. Sci. 61(2): 185-191, 2013 (July)

scholarly journals Estimation of the probability of reinfection with COVID-19 coronavirus by the SEIRUS model

2020 ◽  
Author(s):  
Victor Alexander Okhuese
Keyword(s):  
Recovery Rate ◽  
Death Rate ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Chain Reaction ◽  
Health Community ◽  
Polymerase Chain ◽  
Model Equations ◽  
Disease Free ◽  
Pcr Test

AbstractWith sensitivity of the Polymerase Chain Reaction (PCR) test used to detect the presence of the virus in the human host, the global health community has been able to record a great number of recovered population. Therefore, in a bid to answer a burning question of reinfection in the recovered class, the model equations which exhibits the disease-free equilibrium (E0) state for COVID-19 coronavirus was developed in this study and was discovered to both exist as well as satisfy the criteria for a locally or globally asymptotic stability with a basic reproductive number R0 = 0 for and endemic situation. Hence, there is a chance of no secondary reinfections from the recovered population as the rate of incidence of the recovered population vanishes, that is, B = 0.Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect of the implementation of quarantine and observatory procedures has on the projection of the further spread of the virus globally. Result shows that the proportion of infected population in the absence of curative vaccination will continue to grow globally meanwhile the recovery rate will continue slowly which therefore means that the ratio of infection to recovery rate will determine the death rate that is recorded globally and most significant for this study is the rate of reinfection by the recovered population which will decline to zero over time as the virus is cleared clinically from the system of the recovered class.

scholarly journals Higher Mortality and Infection Rate in a Region or Country Suggest a Longer Time of COVID-19 Disease Pandemic

2020 ◽  
Author(s):  
Tianshu Gu ◽  
Lan Yao ◽  
Tong Sun ◽  
Sara W. Day ◽  
Scott C. Howard ◽  
...  
Keyword(s):  
Infection Rate ◽  
Death Rate ◽  
Positive Relationship ◽  
Disease Duration ◽  
Strong Positive Correlation ◽  
Positive Correlation ◽  
Number Of Patients ◽  
The World ◽  
Total Death ◽  
R Value

Abstract In view of the fact that the 2019-nCoV has spread to most countries in the world, it is necessary to make scientific and well-founded predictions of the current pandemic situation caused by the virus worldwide, which are conducive to public, social and government responses that mitigate and appropriately address the pandemic. We collected data from provinces with more than 200 cases in China and from eight other countries. Our analyses showed that the disease duration has no correlation with the number of patients, with r = 0.184. The number of deaths was not correlated to the disease duration, with r = 0.242. However, a positive correlation between the days of disease duration and infection rate, with a r = 0.626. Furthermore, there is a strong positive correlation between the disease duration and total death rate, with a r = 0.707. Using death rate of first 25 days, we obtained a positive relationship with a r value of 0.597. Based on the data from first 25 days, the minimum and maximum days of COVID-19 pandemic duration of eight countries was estimated between days of 37 and 114 days.

Sign in / Sign up

Export Citation Format

Share Document