Document Details

Document Type : Thesis 
Document Title :
GLOBAL PROPERTIES OF A CLASS OF DISCRETE-TIME VIRAL INFECTION MODELS
الخواص الشمولية لفئة من نماذج الإصابة الفيروسية ذات الزمن المتقطع
 
Subject : faculty of science 
Document Language : Arabic 
Abstract : Global properties of a class of discrete-time viral infection models By Matuqah Atallah Daifallah Alshaikh Supervised by Prof. Ahmed Mohamed Elaiw Abstract In this thesis, we study a class of mathematical viral infection models. These models are given by systems of ordinary differential equations (ODEs) or by systems of delay differential equations (DDEs). We discretize the continuous-time models by using nonstandard finite difference scheme. In this study we consider the following: (i) Different forms of cellular and viral incidence rates of infection such as bilinear, saturation, Holling type-II and general incidence. (ii) Different categories of infected cells such as latently infected cells, short-lived infected cells, long-lived infected cells and actively infected cells. (iii) Different types of time delays. We show that the delay plays the same significant role of antiviral treatments. (iv) Two types of immune response, humoral immune response and cell-mediated immune response. For each discrete-time model, we show that the model is biologically compatible by showing that the solutions of the model are positive and bounded. We derive threshold parameters which fully determine the existence and stability of the equilibria of the model. In case of the general viral infection model, we establish a set of conditions on the general functions which are sufficient to prove the existence and global stability of all equilibria of the model. We establish the global stability of all equilibria by using the Lyapunov method. We conduct numerical simulations and show that both the theoretical and numerical results are consistent. The outcomes of this thesis are published in several ISI International Journals. 
Supervisor : Prof. Ahmed Mohamed Elaiw 
Thesis Type : Doctorate Thesis 
Publishing Year : 1441 AH
2020 AD 
Added Date : Monday, June 22, 2020 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
معتوقه عطا الله الشيخAlshaikh, Matuqah AtallahResearcherDoctorate 

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