Document Details

Document Type : Thesis 
Document Title :
Global stability of coronavirus infection dynamics models
الاستقرار الشمولي لنماذج ديناميكا الإصابة بفيروس كورونا
 
Subject : Faculty of Science 
Document Language : Arabic 
Abstract : In this thesis, we formulate and analyze a class of coronavirus disease 2019 (COVID-19) dynamics models with latent infection and logistic growth of healthy epithelial cells. These models are given by delay differential equations (DDEs) or by systems of partial differential equations (PDEs) with suitable initial and boundary conditions. In this study, we consider the following: (i) Two forms of viral incidence rate of infection, bilinear incidence and general incidence. (ii) Two classes of infected cells, latent infected cells and active infected cells. (iii) Four mixed (distributed/discrete) time delays are involved, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) particles. (iv) Two types of immune response, which mainly depend on B Lymphocytes and Cytotoxic T Lymphocytes (CTLs). CTLs kill the viral-infected cells (CTL immune response), while B cells produce antibodies to neutralize viruses (humoral or antibody immune response). (v) Diffusion which is an inherent feature of biological systems. For each of our proposed models, we study the basic properties of the models including the nonnegativity and boundedness of solutions; which indicate that the models are biologically acceptable. Further, we compute all steady states and determining their existence conditions which depend on threshold parameters. In case of general incidence we establish a set of conditions on the general functions which are sufficient to prove the existence and global stability of all steady states of the model. We prove the global stability of the steady states by constructing suitable Lyapunov functions and applying LaSalle’s invariance principle (LIP). We preform some numerical simulations to illustrate the obtained theoretical results and draw some important conclusions. We have shown that the delay plays the same significant role of antiviral treatments. The outcomes of this thesis are published in several ISI International Journals. Keywords: SARS-CoV-2; humoral immunity; CTL immunity; time delay; global stability. 
Supervisor : Prof. Ahmed Mohamed Elaiw 
Thesis Type : Doctorate Thesis 
Publishing Year : 1444 AH
2023 AD 
Co-Supervisor : Prof. Aatef Hobiny 
Added Date : Monday, June 5, 2023 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
عبدالله جميل الحربيAlharbi, Abdullah JameelResearcherDoctorate 

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