2024_An Improved Mathematical Analysis Of Infectious Disease Stochastic Models
| Format: | General Document |
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| country | Malaysia |
| date | 2024-07-17 |
| format | General Document |
| id | 16177 |
| institution | UniSZA |
| originalfilename | 16177_2dcdfa52232ca62.pdf |
| person | Hussain Shah |
| recordtype | oai_dc |
| resourceurl | https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16177 |
| sourcemedia | Server storage Scanned document |
| spelling | 16177 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16177 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection3 General Document Malaysia Library Staff (Top Management) Library Staff (Management) Library Staff (Support) Terengganu Faculty of Informatics & Computing English application/pdf 1.5 158 Server storage Scanned document Universiti Sultan Zainal Abidin UniSZA Private Access UNIVERSITI SULTAN ZAINAL ABIDIN SAMBox 3.0.10; modified using iTextSharp™ 5.5.10 ©2000-2016 iText Group NV (AGPL-version) Copyright©PWB2025 2024-07-17 16177_2dcdfa52232ca62.pdf Hussain Shah Stochastic processes 2024_An Improved Mathematical Analysis Of Infectious Disease Stochastic Models Epidemiology is the field that uses surveys, data analysis, models, and evaluation to determine the impact of risk factors and intervention measures on public health during an epidemic outbreak. Mathematical modeling is very helpful for describing the dynamics of infectious diseases and forecasting possible future situations. Environmental variations play a crucial role in the spread of infectious diseases, and stochastic models are the most accurate and realistic approach to simulate and exploring the dynamics of such epidemics. COVID-19 and influenza are among those infectious diseases that are highly prone to environmental fluctuations, and thus, the dynamics of these diseases should be investigated keeping in mind their economic burden and associated risks to society. The objective of this study is to formulate a generalized stochastic Susceptible-Infectious-Recovered (SIR) type of model and then improve the model to capture the real dynamics of the epidemics of COVID-19 and influenza. This model will help health professionals derive strategies that lead to the prevention, control, and elimination of both COVID-19 and influenza, as well as various other infectious diseases. The deterministic model is transferred into stochastic models by implementing Brownian motions or white noises. New model is obtained by dividing subclasses as well as introducing new compartments. Next, a compartmental modeling technique is implemented, and their dimensionality is checked accordingly. The wellposedness of the models is studied by showing that they possess a unique positive solution. This study investigated other dynamical behaviors of the proposed model while performing the formulation of the Lyapunov function and implementing Ito's formula. Thus, this study implemented Lyapunov stability theory and Ito's formula to show the persistence of diseases. The analytical results are verified numerically by developing a scheme for the model using the standard numerical method. This study suggests and explores novel, broad, and unconventional ways of illustrating interesting aspects of perturbed models such as global existence, positivity, persistence, disease extinction, and the distinction between stochastic and deterministic behavior within an appropriate hypothetical framework. Each new model is concluded with numerical simulations that illustrate the accuracy of the determined conditions and thresholds to justify the theoretical findings. This study introduces novel approaches for addressing and evaluating the growing complexity of biological and epidemiological systems, and better explains stochastic theory, particularly in mathematical epidemiology. Dissertations, Academic Stochastic Models Infectious Disease Modeling Epidemiological Modeling Thesis |
| spellingShingle | 2024_An Improved Mathematical Analysis Of Infectious Disease Stochastic Models |
| state | Terengganu |
| subject | Stochastic processes Dissertations, Academic |
| summary | Epidemiology is the field that uses surveys, data analysis, models, and evaluation to determine the impact of risk factors and intervention measures on public health during an epidemic outbreak. Mathematical modeling is very helpful for describing the dynamics of infectious diseases and forecasting possible future situations. Environmental variations play a crucial role in the spread of infectious diseases, and stochastic models are the most accurate and realistic approach to simulate and exploring the dynamics of such epidemics. COVID-19 and influenza are among those infectious diseases that are highly prone to environmental fluctuations, and thus, the dynamics of these diseases should be investigated keeping in mind their economic burden and associated risks to society. The objective of this study is to formulate a generalized stochastic Susceptible-Infectious-Recovered (SIR) type of model and then improve the model to capture the real dynamics of the epidemics of COVID-19 and influenza. This model will help health professionals derive strategies that lead to the prevention, control, and elimination of both COVID-19 and influenza, as well as various other infectious diseases. The deterministic model is transferred into stochastic models by implementing Brownian motions or white noises. New model is obtained by dividing subclasses as well as introducing new compartments. Next, a compartmental modeling technique is implemented, and their dimensionality is checked accordingly. The wellposedness of the models is studied by showing that they possess a unique positive solution. This study investigated other dynamical behaviors of the proposed model while performing the formulation of the Lyapunov function and implementing Ito's formula. Thus, this study implemented Lyapunov stability theory and Ito's formula to show the persistence of diseases. The analytical results are verified numerically by developing a scheme for the model using the standard numerical method. This study suggests and explores novel, broad, and unconventional ways of illustrating interesting aspects of perturbed models such as global existence, positivity, persistence, disease extinction, and the distinction between stochastic and deterministic behavior within an appropriate hypothetical framework. Each new model is concluded with numerical simulations that illustrate the accuracy of the determined conditions and thresholds to justify the theoretical findings. This study introduces novel approaches for addressing and evaluating the growing complexity of biological and epidemiological systems, and better explains stochastic theory, particularly in mathematical epidemiology. |
| title | 2024_An Improved Mathematical Analysis Of Infectious Disease Stochastic Models |
| title_full | 2024_An Improved Mathematical Analysis Of Infectious Disease Stochastic Models |
| title_fullStr | 2024_An Improved Mathematical Analysis Of Infectious Disease Stochastic Models |
| title_full_unstemmed | 2024_An Improved Mathematical Analysis Of Infectious Disease Stochastic Models |
| title_short | 2024_An Improved Mathematical Analysis Of Infectious Disease Stochastic Models |
| title_sort | 2024_an improved mathematical analysis of infectious disease stochastic models |