Browsing Department of Mathematics by Author "Kojouharov, Hristo"
Now showing items 1-11 of 11
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A Mathematical Model of Hepatitis C Virus Infection Incorporating Immune Responses and Cell Proliferation
Hadi, Huda Amer; 0000-0003-3052-0886 (2017-08-03)This thesis introduces a mathematical model of differential equations for the chronic hepatitis C virus (HCV) infection, which is a contagious disease that infects the liver cells. Firstly, we present the early mathematical ... -
Advancements And Applications Of Nonstandard Finite Difference Methods
Wood, DanielA class of dynamically consistent numerical methods are analyzed for general n-dimensional productive-destructive systems (PDS). Using this analysis, a methodology for constructing positive and elementary stable nonstandard ... -
Comparative Analysis Of Various Continuous-time Deterministic Models Of Tumor-immune Interactions
Childress, Robert Paul (Mathematics, 2015)Cancer is historically a leading cause of death in the United States. In 2013,cancer was the second leading cause of death with 584,881 deaths \cite{CDC}.Having solely been responsible for 22.5\% of all deaths in 2013 ... -
From Discrete To Continuous Models Of Cell Movement: An Application To Medical Implants
Prieto Langarica, Alicia (Mathematics, 2013-03-20)Mathematical modeling of cell movement is needed to aid in the deeper understanding of vital processes such as embryogenesis, angiogenesis, tumor metastasis, and immune reactions to foreign bodies. In this work, cell ... -
Mathematical Analysis Of Allelopathy And Resource Competition Models
Martines, Ian Pablo (Mathematics, 2008-08-08)Mathematical population models of nutrient recycling and allelopathy are presented. The chemostat limited-resource model forms the basis for each of the models, amended with the dynamics of nutrient recycling and allelopathy. ... -
A Mathematical Model For Swine Flu 2009 With Vaccination
Turk, Irfan (Mathematics, 2011-10-11)H1N1 influenza is one of the deadliest diseases in human's history. Swine Flu 2009 is the same virus and it was named in 2009. Vaccination is of the most common ways to control a disease. We offer a new vaccination model ... -
Mathematical Modeling of the Bone Remodeling Process
Alvarado, Iris Lizeth (2018-08-10)The skeleton is a very important organ that needs to be continuously remodeled due to microdamage, changes in mechanical loading, or mineral homeostasis. The bone remodeling process is responsible for maintaining the ... -
Mathematical Models Of Nutrient Recycling And Toxin Production In A Gradostat
Dong, Xiaoyang (Mathematics, 2013-10-23)We discuss several gradostat models in which a microbial population excretes a biochemical that can get recycled back into the system as a nutrient source. Each mathematical model consists of six ordinary differential ... -
MODELING THE EFFECTS OF THE IMMUNE SYSTEM ON BONE FRACTURE HEALING
Trejo Lorenzo, Imelda (2019-05-14)Bone fracture healing is a complex biological process that results in a full reconstruction of the bone. However, it is not always an easy and successful process. Indeed, in some unfavorable conditions, the bone fracture ... -
Multiple Linear Regression Model Of Visceral Leishmaniasis In Bihar, India
Sheets, Darren (Mathematics, 2009-09-16)Visceral Leishmaniasis (VL) is one of the world's worst parasitic killers, second only to Malaria, claiming nearly 500,000 lives each year. The disease attacks the spleen, liver, and bone marrow, and if left untreated is ... -
ON SOME PROBLEMS IN SPARSE HYBRID IMAGING, NON-STANDARD FINITE DIFFERENCE METHODS, AND FOKKER-PLANCK FRAMEWORKS IN ESOPHAGEAL CANCER
Gupta, Madhu; 0000-0002-7668-3114 (2022-08-16)In this thesis, we first discuss nonlinear optimization frameworks for the sparsity- based on nonlinear reconstruction of parameters in hybrid imaging modalities such as current density impedance imaging (CDII) and two-photon ...