A Comprehensive Mathematical Model for SARS-CoV-2 in Caputo Derivative

In the present work, we study the COVID-19 infection through a new mathematical model using the Caputo derivative. The model has all the possible interactions that are responsible for the spread of disease in the community. We first formulate the model in classical differential equations and then extend it into fractional differential equations using the definition of the Caputo derivative. We explore in detail the stability results for the model of the disease-free case when R0<1. We show that the model is stable locally when R0<1. We give the result that the model is globally asymptotically stable whenever R0≤1. Further, to estimate the model parameters, we consider the real data of the fourth wave from Pakistan and provide a reasonable fitting to the data. We estimate the basic reproduction number for the proposed data to be R0=1.0779. Moreover, using the real parameters, we present the numerical solution by first giving a reliable scheme that can numerically handle the solution of the model. In our simulation, we give the graphical results for some sensitive parameters that have a large impact on disease elimination. Our results show that taking into consideration all the possible interactions can describe COVID-19 infection.

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Experimental and Mathematical Model for the Antimalarial Activity of Methanolic Root Extract of Azadirachta indica (Dongoyaro) in Mice Infected with Plasmodium berghei NK65

Journal of Advances in Mathematics and Computer Science ◽

10.9734/jamcs/2020/v35i530283 ◽

2020 ◽

pp. 68-82

Author(s):

Adeniyi Michael Olaniyi ◽

Momoh Johnson Oshiobugie ◽

Aderele Oluwaseun Raphael

Keyword(s):

Mathematical Model ◽

Azadirachta Indica ◽

Plasmodium Berghei ◽

Antimalarial Activity ◽

Equilibrium Points ◽

Standard Procedure ◽

Root Extract ◽

Globally Asymptotically Stable ◽

The Stability ◽

Group B

The study determines the experimental and mathematical model for the anti-plasmodial activity of methanolic root extract of Azadirachta indica in Swiss mice infected with Plasmodium berghei NK65. Phytochemical analyses, antimalarial activity of the methanolic root extract of A. indica was determined in mice infected with Plasmodium berghei NK65 using standard procedure. Liver biomarker enzymes were also determined. The model P. berghei induced free and P. berghei infected equilibrium were determined. The stability of the model equilibrium points was rigorously analyzed. The phytochemicals present in the extract include: alkaloid, flavonoid, saponin and phenolic compounds etc. The experimental study consists of five groups of five mice each per group. Group A, B, C, D and E were healthy, infected without treatment, infected mice treated with fansidar (10 mg/kg), chloroquine (10 mg/kg) and 250 mg/kg body weight of A. indica methanolic root extract respectively. The extract showed anti-plasmodial activity of 73.96%. The result was significant when compared with group B mice, though it was lower than that exhibited by fansidar (88.91%) and chloroquine (92.18%) for suppressive test. There were significant decrease (P<0.05) in plasma AST and ALT levels in the treated infected mice compared to the infected untreated mice. The results of the model showed that the P.berghei induced free equilibrium is locally and globally asymptotically stable at threshold parameter, less than unity and unstable when is greater than unity. Numerical simulations were carried out to validate the analytic results which are in agreement with the experimental analysis of this work.

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Coefficient Identification of Steam Network Model Based on Genetic Algorithm

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.658.555 ◽

2013 ◽

Vol 658 ◽

pp. 555-559

Author(s):

Xiao Feng Zhu ◽

Yong Zhang ◽

Zhao Feng Lu ◽

Yong Ma

Keyword(s):

Genetic Algorithm ◽

Mathematical Model ◽

Network Model ◽

Model Parameters ◽

The Real ◽

Coefficient Identification ◽

Model Based ◽

Test Result

This article establish a coupled thermo-hydraulic mathematical model for steam network by adopting a set of equations. Here, identification is defined as process in which a number of Steam Network model parameters are adjusted until the model mimics behavior of the real Steam Network as closely as possible. Test result indicates the advantage of genetic algorithm.

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Mathematical analysis of an age structured epidemic model with a quarantine class

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2021049 ◽

2021 ◽

Author(s):

Bedreddine AINSEBA ◽

Tarik Touaoula ◽

Zakia Sari

Keyword(s):

Reproduction Number ◽

Asymptotic Behavior Of Solutions ◽

Model Parameters ◽

Qualitative Behavior ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Age Structured ◽

The Stability ◽

The Impact

In this paper, an age structured epidemic Susceptible-Infected-Quarantined-Recovered-Infected (SIQRI) model is proposed, where we will focus on the role of individuals that leave their class of quarantine before being completely recovered and thus will participate again to the transmission of the disease. We investigate the asymptotic behavior of solutions by studying the stability of both trivial and positive equilibria. In order to see the impact of the different model parameters like the relapse rate on the qualitative behavior of our system, we firstly, give the explicit expression of the epidemic reproduction number $R_{0}.$ This number is a combination of the classical epidemic reproduction number for the SIQR model and a new epidemic reproduction number corresponding to the individuals infected by a relapsed person from the R-class. It is shown that, if $R_{0}\leq 1$, the disease free equilibrium is globally asymptotically stable and becomes unstable for $R_{0}>1$. Secondly, while $R_{0}>1$, a suitable Lyapunov functional is constructed to prove that the unique endemic equilibrium is globally asymptotically stable on some subset $\Omega_{0}.$

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Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

10.21203/rs.3.rs-28213/v1 ◽

2020 ◽

Author(s):

Tamer Sanlidag ◽

Nazife Sultanoglu ◽

Bilgen Kaymakamzade ◽

Evren Hincal ◽

Murat Sayan ◽

...

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Real Data ◽

Northern Cyprus ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

Abstract The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2 epidemic.

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Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

10.21203/rs.3.rs-28704/v1 ◽

2020 ◽

Author(s):

Tamer Sanlidag ◽

Nazife Sultanoglu ◽

Bilgen Kaymakamzade ◽

Evren Hincal ◽

Murat Sayan ◽

...

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Real Data ◽

Northern Cyprus ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

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Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2020/4903168 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Bouchaib Khajji ◽

Abderrahim Labzai ◽

Omar Balatif ◽

Mostafa Rachik

Keyword(s):

Alcohol Drinking ◽

Addiction Treatment ◽

Reproduction Number ◽

Dynamical Behavior ◽

Model Parameters ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Modeling And Analysis ◽

Private And Public ◽

The Stability

In this paper, we present a continuous mathematical model PMHTrTpQ of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number R0. We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number R0. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium E0 when R0≤1. When R0>1, drinking present equilibrium E∗ exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium E∗.

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Operational research and cost containment: a general mathematical model of a workstation.

Clinical Chemistry ◽

10.1093/clinchem/30.11.1758 ◽

1984 ◽

Vol 30 (11) ◽

pp. 1758-1764 ◽

Cited By ~ 14

Author(s):

P Winkel

Keyword(s):

Mathematical Model ◽

Operational Research ◽

Working Hours ◽

Real Data ◽

Turnaround Time ◽

Time Of Day ◽

Model Parameters ◽

Specimen Processing ◽

General Mathematical Model ◽

Computer Simulation Technique

Abstract To facilitate planning and management, I have derived a mathematical model describing the dynamics of a workstation that receives a mixture of routine and emergency specimens. The model parameters include the maximal specimen-processing rate (to be defined by personnel representatives) and the longest delay allowed for emergency specimens at the workstation. Based on the model, a computer-simulation technique has been developed to maximize the length of time (planned pauses) during which the workstation could be closed without causing undue delay of routine and emergency specimen results. The application of this technique is illustrated with real data, in which more than 50% of the specimens were emergency specimens. Three pauses, constituting 35% of working hours, could be introduced with a negligible impact on the turnaround time of emergency specimens (mean increase = 8 min). The model may also be used to derive, as a function of time of day, the largest extra workload that may be presented to a workstation without creating overwork. The workload could be increased by 45%, provided that all additional specimens arrived before noon.

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Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications

Journal of Function Spaces ◽

10.1155/2020/8898309 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17 ◽

Cited By ~ 3

Author(s):

Mehnaz Shakeel ◽

Iltaf Hussain ◽

Hijaz Ahmad ◽

Imtiaz Ahmad ◽

Phatiphat Thounthong ◽

...

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Difference Scheme ◽

Caputo Derivative ◽

Time Derivative ◽

Order Derivative ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

Central Difference ◽

Definition Of

In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and complex geometries. Time derivative is approximated by Caputo derivative for the values of α ∈ 0 , 1 and α ∈ 1 , 2 . Forward difference scheme is applied to approximate the 1st order derivative appearing in the definition of Caputo derivative for α ∈ 0 , 1 , whereas central difference scheme is used for the 2nd order derivative in the definition of Caputo derivative for α ∈ 1 , 2 . Numerical problems are given to judge the behaviour of the proposed method for both the cases of α . Error norms are used to asses the accuracy of the method. Both uniform and nonuniform nodes are considered. Numerical simulation is carried out for irregular domain as well. Results are also compared with the existing methods in the literature.

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A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives

Advances in Difference Equations ◽

10.1186/s13662-021-03499-2 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Pushpendra Kumar ◽

Vedat Suat Erturk ◽

Marina Murillo-Arcila ◽

Ramashis Banerjee ◽

A. Manickam

Keyword(s):

Fractional Order ◽

Trust Region ◽

Simulated Data ◽

Real Data ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Order Model ◽

The Real ◽

The Stability ◽

Parameter Values

AbstractIn this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March 03, 2020 to March 29, 2021 which is a data range of more than one complete year. We propose a Atangana–Baleanu type fractional-order model and simulate it by using predictor–corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. We use a well-known effective optimization scheme based on the renowned trust-region-reflective (TRR) method to perform the model calibration. We have plotted the real cases of COVID-19 and compared our integer-order model with the simulated data along with the calculation of basic reproductive number. Concerning fractional-order simulations, first we prove the existence and uniqueness of solution and then write the solution along with the stability of the given P-C method. A number of graphs at various fractional-order values are simulated to predict the future dynamics of the virus in Argentina which is the main contribution of this paper.

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The Error Incurred in Using the Caputo-Derivative Laplace-Transform

Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C ◽

10.1115/detc2009-87648 ◽

2009 ◽

Cited By ~ 9

Author(s):

Tom T. Hartley ◽

Carl F. Lorenzo

Keyword(s):

Differential Equations ◽

Laplace Transform ◽

Fractional Derivative ◽

Fractional Order ◽

Caputo Derivative ◽

Fractional Order Differential Equations ◽

Definition Of

This paper considers the initialization of fractional-order differential equations. The initialization responses obtained using the Caputo derivative are compared with the exact initialization responses from the Riemann-Liouville definition of the fractional derivative. The error incurred in using the Caputo derivative for initialization problems in fractionalorder differential equations is presented.

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