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Title: A Mathematical Anaysis and Modeling on the Transmissions Dynamics in Epidemiology
Authors: Raza, Ali
Keywords: Physical Sciences
Issue Date: 2021
Publisher: The University of Lahore, Lahore.
Abstract: Mathematical modeling has proven to be an essential tool for the development of control strategies and in distinguishing driving factors in disease dynamics. A key determinant of a given model’s potential to aid in such measures is the availability of data to parameterize the model. For developing countries in particular, data is often difficult to collect. It is, therefore, important to understand the types of data that are necessary for a modeling project, to be successful. Infectious diseases are a persistent problem throughout the world, potentially threatening everyone who comes in contact with them. This thesis attempts to improve our understanding of infectious diseases by developing mathematical models of the cellular dynamics of human infectious diseases. This has been carried out through the investigation of the interaction between infectious agents and cells of the humoral and cell-mediated immune response. Additionally, dynamics of the infectious agent in an infected cell are described through the development of descriptive mathematical models. In this thesis, we consider the models for Hepatitis B, pine wilt disease, Ebola virus and HIV/AIDS mathematical model. Sensitivity analysis of these models are provided by threshold or reproductive number as well as analysed qualitatively, also check the stability analysis of these epidemiological models. Numerical simulation derived through figures and tables which support the accuracy and better conver gence results of the problems. These results are very helpful to control and study the dynamical behavior of the diseases in the society. A mathematical model is employed to study and assess the dynamics of pine wilt disease in a wild life. We prove the essential properties, bounded, positivity and well-posed, also local and global stability analysis has been made for the epidemic model. An unconditionally convergent nonstandard finite difference scheme has been employed to solve model with different compartment. Finally, numerical results are depicted graphically and discussed quantitatively. A nonlinear fractional order Ebola virus mathematical model discusses for the complex transmission of the epidemic problems. Qualitative analysis has been made to verify the steady state and uniqueness of the system is also developed for reliable results. Caputo fractional derivative operator of order φi ∈ (0, 1] works to achieve the fractional differential equations. Laplace with Adomian Decomposition Method successfully solved the fractional differential equations. Ultimately, numerical simu lations are also developed to evaluate the effects of the device parameter on spread of disease and effect of fractional parameter φi on obtained solution which can also be assessed by tabulated results. A fractional order HIV/AIDS mathematical model discusses epidemic problems for the complex transmission of the disease. The Caputo-Fabrizio fractional deriva tive operator of order β ∈ (0, 1) is used to obtain fractional differential equations structure. The stability fractional order model was developed and the unique non negative solution was tested. The numerical simulations are performed using an iterative technique. Some new results are being viewed with the help of Sumudu transform. Nonetheless, according to Banach, the related findings are given nonlin ear functional analysis and fixed point theory. However, mathematical simulations are also acknowledged to evaluate the impact of the model’s parameter by decreasing the fractional values and showing the effect of the β fractional parameter on our ob tained solutions. The impact of various parameters is represented graphically. This model will assist the public health planner in framing a disease control policy. In addition, we will expand the model incorporating determinist and stochastic model comparisons with fractional technique, as well as using optimal control theory for new outcomes. We can measure estimated parameter value in graphs with respect to time. These results are also helpful to overcome effects of HIV/AIDS in our society.
Gov't Doc #: 23614
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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