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Epidemiological Modeling with Application to Covid-19
- 1st Edition - September 2, 2024
- Authors: Abdon Atangana, Seda İğret Araz
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 2 3 8 6 7 - 3
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 2 3 8 6 8 - 0
Epidemiological Modeling with Application to Covid-19 presents information about statistical, numerical, stability, and theoretical analyses for nine different Covid-19 models… Read more
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Request a sales quoteEpidemiological Modeling with Application to Covid-19 presents information about statistical, numerical, stability, and theoretical analyses for nine different Covid-19 models. Those models are considered with classical and fractional derivatives, which is a generalization of the classical analysis. The authors present their newly introduced rate indicator function for the prediction of the waves of Covid-19 spread. Moreover, future prediction of Covid-19 spread is presented for some countries. The authors also provide a new approach to modeling epidemiological issues in general, which has been tested against the spread of COVID-19 in several nations.
This book provides in-depth analysis of the spread of Covid-19, including discussion of theoretical and numerical results, including a novel modeling method called strength numbers that was created under the umbrella of acceleration, which provides a determiner of the power of disease spread. These significant characteristics might be the key to understanding and anticipating the spread of infections and diseases more generally.
This book provides in-depth analysis of the spread of Covid-19, including discussion of theoretical and numerical results, including a novel modeling method called strength numbers that was created under the umbrella of acceleration, which provides a determiner of the power of disease spread. These significant characteristics might be the key to understanding and anticipating the spread of infections and diseases more generally.
- Provides in-depth analysis of the spread of Covid-19, including discussion of theoretical and numerical results
- Introduces a new concept called the rate indicator function for a new perspective on the spread of virological disease in epidemiology
- Presents a novel modeling method called strength numbers created under the umbrella of acceleration, which provides a determiner of the power of disease spread
- Provides a new approach to developing mathematical equations that may be used to show how an infectious disease spreads using the available starting data
Researchers in computational modelling, applied mathematicians, and computer scientists working with researchers and clinicians in biomedical and epidemiological modeling. Researchers, developers, and graduate students in computer science and mathematics interested in calculus and differential equations for mathematical modelling of biomedical and epidemiological phenomena
Chapter 1: History and Data Collection of Covid-19
1.1 Statistical analysis for some African countries
1.2 Statistical analysis for some European countries
1.3 Conclusion
Chapter 2: Statistical Analysis of Collected Data
2.1 Some statistical formulas
2.2 Parameters estimation with some analysis
2.3 Likelihood function with some distributions
2.4 Conclusion
Chapter 3: Nonlocal Operators and Their Properties
3.1 Fractional Differential and Integral Operators
3.2 Some properties of fractional and integral operators
3.3 Numerical approximation of the fractional derivatives
3.4 Geometrical interpretation of fractional derivatives
3.5 Geometry of Riemann-Liouville derivative
3.6 Usefulness of differential operators with singular and nonsingular kernels
3.7 Conclusion
Chapter 4: A New Mathematical Model of Covid-19 Spread with 9 Classes: Application to Cameroon Case
4.1 Numerical Method based on Lagrange polynomial
4.2 Mathematical model of Covid-19 spread with 9 classes
4.3 Analysis of the model: Equilibrium points and reproductive numbers
4.4 Stability analysis of the equilibrium points
4.5 Optimal control for Covid-19 model
4.6 Numerical solution of Covid-19 model
4.7 Effect of non-local operators on Covid-19 model with 9 classes
4.8 Comparison between the suggested model and experimental data by using rate indication function
4.9 Future Prediction for Cameroon
Chapter 5: A SCIRD Mathematical Model of Covid-19 Spread with A Lockdown Functions Applications to Russia Case
5.1 A predictor-corrector scheme based on Newton polynomial
5.2 A mathematical model of Covid-19 outbreak with lockdown function
5.3 Analysis of the model: Equilibrium Points and Reproduction number
5.4 Stability analysis of the equilibrium points
5.5 Optimal control for Covid-19 model
5.6 Numerical solution of Covid-19 model
5.7 Effect of non-local operators on Covid-19 model
5.8 Comparison between the SCIRD model and experimental data
5.9 Future Prediction for Russia
Chapter 6: Mathematical Model of Covid-19 Spread with Super-spreaders and Hospitalized Classes: Application to South Africa Case
6.1 Atangana-Seda numerical scheme
6.2 Mathematical model of Covid-19 transmission
6.3 Analysis of the model: Equilibrium points and basic reproduction number
6.4 Stability analysis of the equilibrium points
6.5 Optimal control for Covid-19 model
6.6 Numerical solution of Covid-19 model
6.7 Effect of non-local operators on Covid-19 model with super-spreader class
6.8 Comparison between the model and experimental data
6.9 Future Prediction for South Africa
Chapter 7: A Covid-19 Spread Model with Two Stages Piecewise Lockdown Function: Application to Turkey case
7.1 Mathematical model of Covid-19 spread with piecewise lockdown function
7.2 Analysis of the model: Equilibrium points and reproductive number
7.3 Stability analysis of the equilibrium points
7.4 Optimal control for Covid-19 model
7.5 Numerical solution of Covid-19 model
7.6 Effect of non-local operators on Covid-19 model
7.7 Comparison between the model and experimental data
7.8 Future Prediction for Turkey
Chapter 8: A SEIARP Model of Covid-19: Application to Italy Case
8.1 Predictor-corrector based on Lagrange interpolation polynomial for a general Cauchy problem
8.2 A model of Covid-19 spread
8.3 Analysis of the model: Equilibrium points and reproduction number
8.4 Stability analysis of the equilibrium points
8.5 Optimal control for Covid-19 model
8.6 Numerical solution of Covid-19 model
8.7 Effect of non-local operators on Covid-19 model
8.8 Comparison between the model and experimental data
8.9 Future Prediction for Italy
Chapter 9: A SEIAQPHR Model of Coronavirus Transmission: Application to Ukraine Case
9.1 A comprehensive model about Covid-19 outbreak
9.2 Analysis of the model: Equilibrium points and reproduction number
9.3 Stability analysis of the equilibrium points
9.4 Optimal control for Covid-19 model
9.5 Numerical solution of Covid-19 model
9.6 Effect of non-local operators on Covid-19 model
9.7 Comparison between the model and experimental data
9.8 Future Prediction for Ukraine
Chapter 10: A Mathematical Model with Exposed and Quarantined Classes: Application to Nigeria Case
10.1 Predictor-corrector based on Newton interpolation polynomial for a general Cauchy
Problem
10.2 A Covid-19 model with exposed and quarantined classes
10.3 Analysis of the model: Equilibrium points and basic reproduction number
10.4 Stability analysis of the equilibrium points.
10.5 Optimal control for Covid-19 model
10.6 Numerical solution of Covid-19 model
10.7 Effect of non-local operators on Covid-19 model.
10.8 Comparison between the model and experimental data
10.9 Future Prediction for Nigeria
Chapter 11: Mathematical Model of Covid-19 Transmission Including a Closely Observed Population: Application to Morocco Case
11.1 Numerical method based on the product integration rule
11.2 A Covid-19 model with closely observed population
11.3 Analysis of the model: Equilibrium points and reproductive number
11.4 Stability analysis of the equilibrium points
11.5 Optimal control for Covid-19 model
11.6 Numerical solution of the model
11.7 Effect of non-local operators on Covid-19 model
11.8 Comparison between the model and experimental data
11.9 Future Prediction for Morocco
Chapter 12: A New Mathematical Model with Two Susceptible and Two Infected Classes: Application to Azerbaijan Case
12.1 Mathematical model of Covid-19 transmission with two susceptible and infected
Classes
12.2 Analysis of the model: Equilibrium points and basic reproduction number
12.3 Stability analysis of the equilibrium points.
12.4 Optimal control for Covid-19 model
12.5 Numerical solution of Covid-19 model
12.6 Effect of non-local operators on Covid-19 model.
12.6.1 Effect of exponential decay on Covid-19 model
12.6.2 Effect of power-law on Covid-19 model . . . .
12.6.3 Effect of Mittag-Leffler kernel on Covid-19 model
12.6.4 Effect of fractal-fractional derivatives on Covid-19 model.
12.7 Comparison between the model and experimental data
12.8 Future Prediction for Azerbaijan
12.9 References
1.1 Statistical analysis for some African countries
1.2 Statistical analysis for some European countries
1.3 Conclusion
Chapter 2: Statistical Analysis of Collected Data
2.1 Some statistical formulas
2.2 Parameters estimation with some analysis
2.3 Likelihood function with some distributions
2.4 Conclusion
Chapter 3: Nonlocal Operators and Their Properties
3.1 Fractional Differential and Integral Operators
3.2 Some properties of fractional and integral operators
3.3 Numerical approximation of the fractional derivatives
3.4 Geometrical interpretation of fractional derivatives
3.5 Geometry of Riemann-Liouville derivative
3.6 Usefulness of differential operators with singular and nonsingular kernels
3.7 Conclusion
Chapter 4: A New Mathematical Model of Covid-19 Spread with 9 Classes: Application to Cameroon Case
4.1 Numerical Method based on Lagrange polynomial
4.2 Mathematical model of Covid-19 spread with 9 classes
4.3 Analysis of the model: Equilibrium points and reproductive numbers
4.4 Stability analysis of the equilibrium points
4.5 Optimal control for Covid-19 model
4.6 Numerical solution of Covid-19 model
4.7 Effect of non-local operators on Covid-19 model with 9 classes
4.8 Comparison between the suggested model and experimental data by using rate indication function
4.9 Future Prediction for Cameroon
Chapter 5: A SCIRD Mathematical Model of Covid-19 Spread with A Lockdown Functions Applications to Russia Case
5.1 A predictor-corrector scheme based on Newton polynomial
5.2 A mathematical model of Covid-19 outbreak with lockdown function
5.3 Analysis of the model: Equilibrium Points and Reproduction number
5.4 Stability analysis of the equilibrium points
5.5 Optimal control for Covid-19 model
5.6 Numerical solution of Covid-19 model
5.7 Effect of non-local operators on Covid-19 model
5.8 Comparison between the SCIRD model and experimental data
5.9 Future Prediction for Russia
Chapter 6: Mathematical Model of Covid-19 Spread with Super-spreaders and Hospitalized Classes: Application to South Africa Case
6.1 Atangana-Seda numerical scheme
6.2 Mathematical model of Covid-19 transmission
6.3 Analysis of the model: Equilibrium points and basic reproduction number
6.4 Stability analysis of the equilibrium points
6.5 Optimal control for Covid-19 model
6.6 Numerical solution of Covid-19 model
6.7 Effect of non-local operators on Covid-19 model with super-spreader class
6.8 Comparison between the model and experimental data
6.9 Future Prediction for South Africa
Chapter 7: A Covid-19 Spread Model with Two Stages Piecewise Lockdown Function: Application to Turkey case
7.1 Mathematical model of Covid-19 spread with piecewise lockdown function
7.2 Analysis of the model: Equilibrium points and reproductive number
7.3 Stability analysis of the equilibrium points
7.4 Optimal control for Covid-19 model
7.5 Numerical solution of Covid-19 model
7.6 Effect of non-local operators on Covid-19 model
7.7 Comparison between the model and experimental data
7.8 Future Prediction for Turkey
Chapter 8: A SEIARP Model of Covid-19: Application to Italy Case
8.1 Predictor-corrector based on Lagrange interpolation polynomial for a general Cauchy problem
8.2 A model of Covid-19 spread
8.3 Analysis of the model: Equilibrium points and reproduction number
8.4 Stability analysis of the equilibrium points
8.5 Optimal control for Covid-19 model
8.6 Numerical solution of Covid-19 model
8.7 Effect of non-local operators on Covid-19 model
8.8 Comparison between the model and experimental data
8.9 Future Prediction for Italy
Chapter 9: A SEIAQPHR Model of Coronavirus Transmission: Application to Ukraine Case
9.1 A comprehensive model about Covid-19 outbreak
9.2 Analysis of the model: Equilibrium points and reproduction number
9.3 Stability analysis of the equilibrium points
9.4 Optimal control for Covid-19 model
9.5 Numerical solution of Covid-19 model
9.6 Effect of non-local operators on Covid-19 model
9.7 Comparison between the model and experimental data
9.8 Future Prediction for Ukraine
Chapter 10: A Mathematical Model with Exposed and Quarantined Classes: Application to Nigeria Case
10.1 Predictor-corrector based on Newton interpolation polynomial for a general Cauchy
Problem
10.2 A Covid-19 model with exposed and quarantined classes
10.3 Analysis of the model: Equilibrium points and basic reproduction number
10.4 Stability analysis of the equilibrium points.
10.5 Optimal control for Covid-19 model
10.6 Numerical solution of Covid-19 model
10.7 Effect of non-local operators on Covid-19 model.
10.8 Comparison between the model and experimental data
10.9 Future Prediction for Nigeria
Chapter 11: Mathematical Model of Covid-19 Transmission Including a Closely Observed Population: Application to Morocco Case
11.1 Numerical method based on the product integration rule
11.2 A Covid-19 model with closely observed population
11.3 Analysis of the model: Equilibrium points and reproductive number
11.4 Stability analysis of the equilibrium points
11.5 Optimal control for Covid-19 model
11.6 Numerical solution of the model
11.7 Effect of non-local operators on Covid-19 model
11.8 Comparison between the model and experimental data
11.9 Future Prediction for Morocco
Chapter 12: A New Mathematical Model with Two Susceptible and Two Infected Classes: Application to Azerbaijan Case
12.1 Mathematical model of Covid-19 transmission with two susceptible and infected
Classes
12.2 Analysis of the model: Equilibrium points and basic reproduction number
12.3 Stability analysis of the equilibrium points.
12.4 Optimal control for Covid-19 model
12.5 Numerical solution of Covid-19 model
12.6 Effect of non-local operators on Covid-19 model.
12.6.1 Effect of exponential decay on Covid-19 model
12.6.2 Effect of power-law on Covid-19 model . . . .
12.6.3 Effect of Mittag-Leffler kernel on Covid-19 model
12.6.4 Effect of fractal-fractional derivatives on Covid-19 model.
12.7 Comparison between the model and experimental data
12.8 Future Prediction for Azerbaijan
12.9 References
- No. of pages: 400
- Language: English
- Edition: 1
- Published: September 2, 2024
- Imprint: Morgan Kaufmann
- Paperback ISBN: 9780443238673
AA
Abdon Atangana
Dr. Abdon Atangana is Academic Head of Department and Professor of Applied Mathematics at the University of the Free State, Bloemfontein, Republic of South Africa. He obtained his honours and master’s degrees from the Department of Applied Mathematics at the UFS with distinction. He obtained his PhD in applied mathematics from the Institute for Groundwater Studies. He was included in the 2019 (Maths), 2020 (Cross-field) and the 2021 (Maths) Clarivate Web of Science lists of the World's top 1% scientists, and he was awarded The World Academy of Sciences (TWAS) inaugural Mohammed A. Hamdan award for contributions to science in developing countries. In 2018 Dr. Atangana was elected as a member of the African Academy of Sciences and in 2021 a member of The World Academy of Sciences. He also ranked number one in the world in mathematics, number 186 in the world in all fields, and number one in Africa in all fields, according to the Stanford University list of top 2% scientists in the world. He was one of the first recipients of the Obada Award in 2018. Dr. Atangana published a paper that was ranked by Clarivate in 2017 as the most cited mathematics paper in the world. Dr. Atangana serves as an editor for 20 international journals, lead guest editor for 10 journals, and is also a reviewer of more than 200 international accredited journals. His research interests include methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modelling. Dr. Atangana is a pioneer in research on fractional calculus with non-local and non-singular kernels popular in applied mathematics today. He is the author of numerous books, including Integral Transforms and Engineering: Theory, Methods, and Applications, Taylor and Francis/CRC Press; Numerical Methods for Fractal-Fractional Differential Equations and Engineering: Simulations and Modeling, Taylor and Francis/CRC Press; Numerical Methods for Fractional Differentiation, Springer; Fractional Stochastic Differential Equations, Springer; Fractional Order Analysis, Wiley; Applications of Fractional Calculus to Modeling in Dynamics and Chaos, Taylor and Francis/CRC Press; Fractional Operators with Constant and Variable Order with Application to Geo-hydrology, Elsevier/Academic Press; Derivative with a New Parameter: Theory, Methods, and Applications, Elsevier/Academic Press; and New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications, Elsevier/Academic Press; among others.
Affiliations and expertise
Academic Head, Department and Professor of Applied Mathematics, University of the Free State, Bloemfontein, South AfricaSA
Seda İğret Araz
Dr. Seda İğret Araz is an Assistant Professor of Mathematics at Siirt University, Siirt, Turkey. She obtained her master’s and PhD at Ataturk University, Turkey. She is the author of more than 15 papers published in top-tier journals. She has acted as guest editor on special issues in Q1 journals. Dr. Araz is the co-author with Dr. Atangana of New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications, Elsevier/Academic Press; and Fractional Stochastic Differential Equations, Springer
Affiliations and expertise
Assistant Professor of Mathematics, Department of Mathematics, Siirt University, Siirt, Turkey