Document Details

Document Type : Thesis 
Document Title :
MATHEMATICAL ANALYSIS OF HUMAN VIRAL INFECTION MODELS
التحليل الرياضي لنماذج الإصابة الفيروسية البشرية
 
Subject : Faculty of Science 
Document Language : Arabic 
Abstract : The coronavirus disease 2019 (COVID-19) has caused fatal consequences in people with underlying illnesses. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infects the respiratory tract's epithelial cells (ECs) and causes COVID-19. Human T-cell lymphotropic virus type I (HTLV-I) is a retrovirus that infects CD4^+T cells and causes fatal and chronic illnesses. Asymptomatic HTLV-I carriers' immune systems can decline. Mathematical models aid biological and medical research on human viral infections. The global stability of viral infection models is an important and unsolved scientific challenge. Infection treatment techniques and thresholds require such results. This thesis aims to create new mathematical models to characterize the co-dynamics of SARS-CoV-2 and HTLV- in a host of ordinary differential equations (ODEs), delay differential equations (DDEs), and partial differential equations (PDEs). The second goal of this thesis is to design and study a class of general models that describes the within-host dynamics of HTLV-I under Cytotoxic T-Lymphocytes (CTLs) immunity. Infected cells undergo mitosis. General nonlinear functions for cell formation, proliferation, and clearance are considered. Using a general nonlinear function, infection incidence is modeled. These general functions are supposed to satisfy adequate requirements and encompass numerous literature-presented forms. Each of our proposed models' core properties—existence, uniqueness, nonnegativity, and boundedness of solutions—indicate biological acceptability. We compute the equilibria and derive their threshold parameter-dependent existence conditions. We develop general function requirements that prove the model's equilibria exist and are globally stable. Using Lyapunov functions and LaSalle's invariance principle, we prove the global stability of the equilibria in general incidence (LIP). To clarify theoretical results and derive key implications, numerical simulations utilizing MATLAB and MATHEMATICA programs backed analytical results. This thesis' results are published in ISI International Journals. 
Supervisor : Dr. Ahmed Aliu 
Thesis Type : Doctorate Thesis 
Publishing Year : 1445 AH
2023 AD 
Added Date : Tuesday, October 17, 2023 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
عبد السلام سعيد شفلوتShaflot, Abdul ALSalam SaeedResearcherDoctorate 

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