Fractional Stochastic Differential Equations: Applications to Covid-19 Modeling

This book discusses the spread modeling of Covid-19 using stochastics nonlocal differential and integral operators with singular and non-singular kernels, covering the global dynamic of Covid-19 spread behavior from December 2019 to September 2021.

Format: Paperback / softback
Length: 540 pages
Publication date: 23 April 2023
Publisher: Springer Verlag, Singapore

This comprehensive book delves into the intricate foundations of COVID-19 spread modeling, employing stochastics nonlocal differential and integral operators with singular and non-singular kernels. It offers a detailed exploration of the dynamic nature of COVID-19 spread worldwide, highlighting the observed nonlocal behaviors that resemble power law, fading memory, crossover, and stochastic phenomena. Consequently, fractional stochastic differential equations are utilized to model the spread behaviors across various regions of the globe. The content encompasses a brief historical overview of COVID-19's global spread from December 2019 to September 2021, accompanied by a statistical analysis of the collected data for infected, deceased, and recovered individuals.

The book begins by providing a foundational introduction to stochastics, emphasizing its applications in modeling complex systems. It then delves into the theoretical framework of nonlocal differential and integral operators, highlighting their significance in capturing the intricate dynamics of COVID-19 spread. The authors introduce various kernels, including singular and non-singular ones, to model different aspects of the spread process.

The subsequent chapters delve into the application of nonlocal operators to model COVID-19 spread behavior. The authors discuss the use of fractional stochastic differential equations to capture the non-stationary and non-linear characteristics of the spread dynamic. They present examples of how these equations can be used to simulate the spread of COVID-19 in different parts of the world, accounting for factors such as population density, mobility patterns, and healthcare infrastructure.

Throughout the book, the authors emphasize the importance of statistical analysis in understanding the spread of COVID-19. They discuss various statistical models and methodologies used to analyze the collected data, including regression analysis, time series analysis, and spatial analysis. The results of these analyses are used to draw insights into the factors that influence COVID-19 spread, such as age, gender, vaccination status, and geographical location.

The book also includes case studies and real-world examples to illustrate the practical applications of nonlocal differential and integral operators in COVID-19 spread modeling. These examples showcase the challenges faced by different countries in combating the pandemic and the strategies employed to mitigate the spread of the virus.

In conclusion, this book provides a comprehensive and in-depth exploration of the foundations of COVID-19 spread modeling, employing stochastics nonlocal differential and integral operators with singular and non-singular kernels. It offers valuable insights into the dynamic nature of COVID-19 spread worldwide, highlighting the observed nonlocal behaviors and the use of fractional stochastic differential equations to model these behaviors. The book also emphasizes the importance of statistical analysis in understanding the spread of COVID-19 and provides practical examples and case studies to illustrate the applications of nonlocal operators in real-world scenarios. This book is a valuable resource for researchers, policymakers, and healthcare professionals interested in understanding and combating the COVID-19 pandemic.

Weight: 842g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811907319
Edition number: 1st ed. 2022