http://hdl.handle.net/20.500.12228/49 2026-04-08T01:52:39Z http://hdl.handle.net/20.500.12228/464 Mathematical Analysis of Epidemiological Model of Virus Transmission Dynamics in Perspective of Bangladesh Islam, Rafiqul Infectious diseases cause great suffering all over the world like Japan, USA, India, China, Ghana, Bangladesh etc. every year. The cause of infectious diseases are mainly virus and bacteria, they are becoming resistant against existing drugs. Therefore, infectious diseases become great concern in public health. But the spread of infectious disease can be controlled by some preventive steps. To get the control strategy, we have to know the transmission dynamics of the viruses. Mathematical modeling plays a vital role in understanding the transmission dynamics of the virus. In order to find out the control strategy of the infectious diseases, several mathematical models are available in the literatures. SIR and SEIR are the most well-known models regarding the transmission dynamics of the infectious diseases. In this thesis we have applied mathematical model namely SEIR model to realize the dynamics of Influenza A (H1N1) virus and Nipah Virus. By analyzing sensitivity of their disease free equilibrium and endemic equilibrium we have got two controlling strategies –decrease of contact rate and/or increase of recovery rate. Moreover, we have got herd immunity threshold for them by basic reproduction number regarding data of Bangladesh. Our result suggests that vaccinating 15.31% population could be controlled spread out of Influenza A (H1N1) virus and keeping away 77.25% (susceptible) population from close contact with infected people could be controlled outbreak of Nipah virus in Bangladesh at their initial outbreak respectively. Using the above control strategy we have proposed vaccine induced SEIR model for Influenza A (H1N1) virus and controlled induced SEIR model for Nipah virus. For Influenza A (H1N1) virus, we considered 15.31% of the susceptible population will be vaccinated whereas for Nipah virus, 77.25% of the susceptible population will not be in close contact (by awareness) with infected population. Numerical solutions of the proposed vaccine induced SEIR model as well as control induced SEIR model regarding data of Bangladesh reveal the control of the outbreak of both diseases respectively. Moreover numerical simulation have been performed to analyze the performance of SEIR models and proposed control induced SEIR models for both the viruses. This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Philosophy in Mathematics, June 2018.; Cataloged from PDF Version of Thesis.; Includes bibliographical references (pages 65-68). 2018-06-01T00:00:00Z http://hdl.handle.net/20.500.12228/454 Dufour Effect on Combined Heat and Mass Transfer by Laminar Mixed Convection Flow from a Vertical Surface under the Influence of an Induced Magnetic Field Khatun, Mst. Moslema In this study the laminar mixed free and force convection flow and heat transfer of viscous incompressible electrically conducting fluid above a vertical porous continuously moving surface is considered under the action of a transverse applied magnetic field. The Dufbur or diffusion-thermo effect in the presence of induced magnetic tiled is taken into account. The governing differential equations relevant to the problem are solved by using the perturbation technique. On introducing the non-dimensional concept and initialing the idea of usual Boussinesq's approximation, the solutions for velocity field, temperature distribution, induced magnetic field and current density are obtained under certain assumptions. The influences of various establish dimensionless parameters on the velocity and temperature profiles, induced magnetic fields as well as on the shear stress are studied graphically. The numerical results have also shown that the diffusion-thermo (Dufour) effect has a great influence in the study of flow and heat transfer process of some types of fluids considered. This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Philosophy in Mathematics, December, 2010.; Cataloged from PDF Version of Thesis.; Includes bibliographical references (pages 67-71). 2010-12-01T00:00:00Z http://hdl.handle.net/20.500.12228/405 Similarity Solution of Unsteady Natural Convection Boundary Layer Flow above a Semi-infinite Porous Horizontal Plate with Suction and Blowing Mojumder, Rita The present study deals with the similarity solutions of laminar boundary layer equations for the unsteady free convection flow over a heated horizontal semi-infinite porous plate. The Boussinesq approximation is employed firstly in order to simplify the governing boundary layer equations. Secondly, similarity requirements for an incompressible fluid are sought on the basis of detailed analysis in order to reduce the governing coupled partial differential equations into a set of ordinary differential equations. The influence of suction and blowing on the flow and temperature fields and other flow factors like skin friction and heat transfer coefficients are extensively investigated under different similarity cases. Sixth order R-K method is used to solved the simplified equations and the obtained numerical results are displayed graphically for some selected values of the controlling parameters provided by the similarity transformation. It is found that a small value of suction or blowing play a vital role on the patterns of flow and temperature fields as well as on the coefficients of skin friction and heat transfer and pressure distribution. This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Philosophy in Mathematics, December 2011.; Cataloged from PDF Version of Thesis.; Includes bibliographical references (pages 62-65). 2011-12-01T00:00:00Z http://hdl.handle.net/20.500.12228/403 Study of Solving Linear Equations by Hybrid Evolutionary Computation Techniques Jamali, Abdur Rakib Muhammad Jalal Uddin Solving a set of simultaneous linear equations is a fundamental problem that occurs in diverse applications. For solving large sets of linear equations, iterative methods are preferred over other methods specially when the coefficient matrix of the linear system is sparse. The rate of convergence of iterative (Jacobi & Gauss-Seidel) methods is increased by using successive relaxation (SR) technique. But SR technique is very sensitive to relaxation factor, . Recently, hybridization of evolutionary computation techniques with classical Gauss-Seidel-based SR method has successfully been used to solve large set of linear equations in which relaxation factors are self-adapted. Under this paradigm, this research work has developed a new class of hybrid evolutionary algorithms for solving system of linear equations. The first algorithm is the Jacobi-Based Uniform Adaptive (JBUA) hybrid algorithm, which has been developed within the framework of contemporary Gauss-Seidel-Based Uniform Adaptive (GSBUA) hybrid algorithm, and classical Jacobi method. The proposed JBUA hybrid algorithm can be implemented, inherently, in parallel processing environment efficiently whereas GSBUA hybrid algorithm cannot be implemented in parallel processing environment efficiently. The second algorithm is the Gauss-Seidel-Based Time-Variant Adaptive (GSBTVA) hybrid algorithm that has been developed within the framework of contemporary GSBUA hybrid algorithm and time-variant adaptive technique. In this algorithm two new time-variant adaptive operators have been introduced based on some observed biological evidences. The third algorithm is the Jacobi-Based Time-Variant Adaptive (JBTVA) hybrid algorithm that has been developed within the framework of GSBTVA and JBUA hybrid algorithms. This proposed JBTVA algorithm also can be implemented, inherently, in parallel processing environment efficiently. All the proposed hybrid algorithms have been tested on some test problems and compared with other hybrid evolutionary algorithms and classical iterative methods. Also the validity of the rapid convergence of the proposed algorithms are proved theoretically. The proposed hybrid algorithms outperform the contemporary GSBUA hybrid algorithm as well as classical iterative methods in terms of convergence speed and effectiveness. This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Philosophy in Mathematics, October 2004.; Cataloged from PDF Version of Thesis.; Includes bibliographical references (pages 90-95). 2004-10-01T00:00:00Z