Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases

This study focuses on modeling, prediction, and analysis of confirmed, recovered, and death cases of COVID-19 by using Fractional Calculus in comparison with other models for 8 countries including China, France, Italy, Spain, Turkey, the UK, and the US. First, the dataset is modeled using our previously proposed approach Deep Assessment Methodology, next, one step prediction of the future is made using two methods: Deep Assessment Methodology and Long Short-Term Memory. Later, a Gaussian prediction model is proposed to predict the short-term (30 Days) future of the pandemic, and prediction performance is evaluated. The proposed Gaussian model is compared to a time-dependent susceptible-infected-recovered (SIR) model. Lastly, an analysis of understanding the effect of history is made on memory vectors using wavelet-based denoising and correlation coefficients. Results prove that Deep Assessment Methodology successfully models the dataset with 0.6671%, 0.6957%, and 0.5756% average errors for confirmed, recovered, and death cases, respectively. We found that using the proposed Gaussian approach underestimates the trend of the pandemic and the fastest increase is observed in the US while the slowest is observed in China and Spain. Analysis of the past showed that, for all countries except Turkey, the current time instant is mainly dependent on the past two weeks where countries like Germany, Italy, and the UK have a shorter average incubation period when compared to the US and France.

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“…To directly see the effect of any previous instant, we substitute (48) into (47). In this case, ( ) becomes:…”

Section: E Understanding the Effect Of History By Analyzing The Shormentioning

confidence: 99%

Modeling and Prediction of the Covid-19 Cases With Deep Assessment Methodology and Fractional Calculus

et al. 2020

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“…Rate the infected individuals recover is . More many applications of models fractional [El-Shahed, Ahmed and Abdelstar (2016); Haq, Shahzad, Muhammad et al (2017)]. Researchers and mathematicians used fractional models problems [El-Shahed, Ahmed and Abdelstar (2016); Henderson (1984)].…”

Section: ( )mentioning

confidence: 99%

“…Effectively, the analytic approximate solutions are discussed for two nonlinear systems of biomathematics models such as SI1I2R model for the spread of virus HCV-subtype4a and SIR childhood disease mode. These systems can be seen in El-Shahed et al [El-Shahed, Ahmed and Abdelstar (2016); Haq, Shahzad, Muhammad et al (2017)]. In biomathematics models, they play a major role in various fields, such as Childhood diseases are the most serious infectious diseases.…”

Section: Introductionmentioning

confidence: 99%

Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

Gepree¹,

Mahdy²,

Mohamed³

et al. 2019

Computers, Materials &Amp; Continua

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In this paper, we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model. The reduced differential transforms method (RDTM) is one of the interesting methods for finding the approximate solutions for nonlinear problems. We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model. We discuss the numerical results at some special values of parameters in the approximate solutions. We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions. Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.

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“…These models are designed by using data collected from clinicians and health workers to make prophecies about a disease's development. A tremendous number of models have been formulated, analyzed, and applied, which improved our understanding and predictive ability about a variety of infectious diseases [1][2][3][4][5]. Many of these models also consider time delay in the process of transmissibility of any infection to further study the effect of delays on the spread out of diseases.…”

Section: Introductionmentioning

confidence: 99%

Transmissibility of epidemic diseases caused by delay with local proportional fractional derivative

et al. 2021

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Epidemiological models have been playing a vital role in different areas of biological sciences for the analysis of various contagious diseases. Transmissibility of virulent diseases is being portrayed in the literature through different compartments such as susceptible, infected, recovered (SIR), susceptible, infected, recovered, susceptible (SIRS) or susceptible, exposed, infected, recovered (SEIR), etc. The novelty in this endeavor is the addition of compartments of latency and treatment with vaccination, so the system is designated as susceptible, vaccinated, exposed, latent, infected, treatment, and recovered (SVELITR). The contact of a susceptible individual to an infective individual firstly makes the individual exposed, latent, and then completely infection carrier. Innovatively, the assumption that exposed, latent, and infected individuals enter the treatment compartment at different rates after a time lag is also deliberated through the existence of time delay. The rate of change and constant solutions of each compartment are studied with incorporation of a special case of proportional fractional derivative (PFD). In addition, existence and uniqueness of the system are also comprehensively elaborated. Moreover, novel dynamic assessment of the system is carried out in context with the fractional order index. Succinctly, the manuscript accomplishes cyclic epidemiological behavior of the infectious disease due to the delay in treatment of the infected individuals.

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Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases

Cited by 32 publications

References 11 publications

Modeling and Prediction of the Covid-19 Cases With Deep Assessment Methodology and Fractional Calculus

Modeling and Prediction of the Covid-19 Cases With Deep Assessment Methodology and Fractional Calculus

Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

Transmissibility of epidemic diseases caused by delay with local proportional fractional derivative

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