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Mathematical Modeling

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Full-Text Articles in Disease Modeling

Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov Apr 2023

Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov

CODEE Journal

An inquiry-based project that discusses immune system dynamics during HIV infection using differential equations is presented. The complex interactions between healthy T-cells, latently infected T-cells, actively infected T-cells, and the HIV virus are modeled using four nonlinear differential equations. The model is adapted to simulate long term HIV dynamics, including the AIDS state, and is used to simulate the long term effects of the traditional antiretroviral therapy (ART). The model is also used to test viral rebound over time of combined application of ART and a new drug that blocks the reactivation of the viral genome in the infected cells …

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An Application Of Differential Mathematical Modeling Techniques To Study The Ongoing Rabies Epizootic In China, Christopher Turner May 2022

An Application Of Differential Mathematical Modeling Techniques To Study The Ongoing Rabies Epizootic In China, Christopher Turner

Electronic Theses and Dissertations

Rabies remains a global public health issue with a wide variety of neurological symptoms such as confusion, slight paralysis, hypersalivation, and hydrophobia. Rabies is usually fatal once symptoms appear. Many species are reservoirs for rabies, such as foxes, racoons, and wild dogs, which in turn can transmit the disease to humans, leading to complex transmission chains. There is a long latent period of rabies, between 1 to 3 months after infection, which further complicates control efforts. Mathematical modeling is a valuable tool in the study of infectious disease outbreaks and there have been many models applied to rabies outbreaks. However, …

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H-Discrete Fractional Model Of Tumor Growth And Anticancer Effects Of Mono And Combination Therapies, Kamala Dadashova Apr 2020

H-Discrete Fractional Model Of Tumor Growth And Anticancer Effects Of Mono And Combination Therapies, Kamala Dadashova

Masters Theses & Specialist Projects

In this thesis, we focus on h–discrete and h–discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model which describes tumor growth considering time on hNa, where h>0. First, we introduce some definitions, lemmas and theorems on both h–discrete and h–discrete fractional calculus in the preliminary section. In Chapter 3, we work on the PD model with delay by exam ining nabla h–discrete equations and nabla h–discrete fractional equations as well as variation of constants formulas, accordingly. We introduce our model and solve it using theorems we proved in the last section of the indicated chapter. When we do simulation for …

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A Multiscale Modeling Study Of The Mammary Gland, Joseph D. Butner Jul 2017

A Multiscale Modeling Study Of The Mammary Gland, Joseph D. Butner

Biomedical Engineering ETDs

Multiscale, hybrid computer modeling has emerged as a valuable tool in the fields of computational systems biology and mathematical oncology. In this work, we present an overview of the motivations for, and development and implementation of, three hybrid multiscale models of the mammary gland system and early stage ductal carcinoma in situ (DCIS) in the gland. Pubertal mammary gland development was described first using a two-dimensional, lattice-based hybrid agent-based model description of the mammary terminal end bud (TEB), and then with a three-dimensional lattice-free TEB model. Both models implement a discrete, agent-based description of the cell scale, and a continuum, …

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