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Title: A MATHEMATICAL STUDY OF MALARIA MODELS OF ROSS AND NGWA.
Creator: Plemmons, William, Rollins, David, University of Central Florida
Abstract / Description: Malaria is a vector borne disease that has been plaguing mankind since before recorded history. The disease is carried by three subspecies of mosquitoes Anopheles gambiae, Anopheles arabiensis and Anopheles funestu. These mosquitoes carry one of four type of Plasmodium specifically: P. falciparum, P. vivax, P. malariae or P. ovale. The disease is a killer; the World Health Organization (WHO) estimates that about 40% of the world's total populations live in areas where malaria is an...
Show moreMalaria is a vector borne disease that has been plaguing mankind since before recorded history. The disease is carried by three subspecies of mosquitoes Anopheles gambiae, Anopheles arabiensis and Anopheles funestu. These mosquitoes carry one of four type of Plasmodium specifically: P. falciparum, P. vivax, P. malariae or P. ovale. The disease is a killer; the World Health Organization (WHO) estimates that about 40% of the world's total populations live in areas where malaria is an endemic disease and as global warming occurs, endemic malaria will spread to more areas. The malaria parasite kills a child every 30 seconds. In Africa alone, as many as one million children die annually from malaria before they reach the age of 5. The World Health Organization has an estimate of 100-200 million victims annually. Malaria has many mathematical models and this paper will examine several different models in order to achieve a greater understanding of this disease.
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Date Issued: 2006
Identifier: CFE0001406, ucf:47070
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0001406

Title: MATHEMATICAL MODELING OF SMALLPOX WITHOPTIMAL INTERVENTION POLICY.
Creator: LAWOT, NIWAS, ROLLINS, DAVID, University of Central Florida
Abstract / Description: In this work, two differential equation models for smallpox are numerically solved to find the optimal intervention policy. In each model we look for the range of values of the parameters that give rise to the worst case scenarios. Since the scale of an epidemic is determined by the number of people infected, and eventually dead, as a result of infection, we attempt to quantify the scale of the epidemic and recommend the optimum intervention policy. In the first case study, we mimic a densely...
Show moreIn this work, two differential equation models for smallpox are numerically solved to find the optimal intervention policy. In each model we look for the range of values of the parameters that give rise to the worst case scenarios. Since the scale of an epidemic is determined by the number of people infected, and eventually dead, as a result of infection, we attempt to quantify the scale of the epidemic and recommend the optimum intervention policy. In the first case study, we mimic a densely populated city with comparatively big tourist population, and heavily used mass transportation system. A mathematical model for the transmission of smallpox is formulated, and numerically solved. In the second case study, we incorporate five different stages of infection: (1) susceptible (2) infected but asymptomatic, non infectious, and vaccine-sensitive; (3) infected but asymptomatic, noninfectious, and vaccine-in-sensitive; (4) infected but asymptomatic, and infectious; and (5) symptomatic and isolated. Exponential probability distribution is used for modeling this case. We compare outcomes of mass vaccination and trace vaccination on the final size of the epidemic.
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Date Issued: 2006
Identifier: CFE0001193, ucf:46848
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0001193

Title: EPIDEMIOLOGICAL MODELS FOR MUTATING PATHOGENS WITH TEMPORARY IMMUNITY.
Creator: Singh, Neeta, Rollins, David, University of Central Florida
Abstract / Description: Significant progress has been made in understanding different scenarios for disease transmissions and behavior of epidemics in recent years. A considerable amount of work has been done in modeling the dynamics of diseases by systems of ordinary differential equations. But there are very few mathematical models that deal with the genetic mutations of a pathogen. In-fact, not much has been done to model the dynamics of mutations of pathogen explaining its effort to escape the host's immune...
Show moreSignificant progress has been made in understanding different scenarios for disease transmissions and behavior of epidemics in recent years. A considerable amount of work has been done in modeling the dynamics of diseases by systems of ordinary differential equations. But there are very few mathematical models that deal with the genetic mutations of a pathogen. In-fact, not much has been done to model the dynamics of mutations of pathogen explaining its effort to escape the host's immune defense system after it has infected the host. In this dissertation we develop an SIR model with variable infection age for the transmission of a pathogen that can mutate in the host to produce a second infectious mutant strain. We assume that there is a period of temporary immunity in the model. A temporary immunity period along with variable infection age leads to an integro-differential-difference model. Previous efforts on incorporating delays in epidemic models have mainly concentrated on inclusion of latency periods (this assumes that the force of infection at a present time is determined by the number of infectives in the past). We begin with reviewing some basic models. These basic models are the building blocks for the later, more detailed models. Next we consider the model for mutation of pathogen and discuss its implications. Finally, we improve this model for mutation of pathogen by incorporating delay induced by temporary immunity. We examine the influence of delay as we establish the existence, and derive the explicit forms of disease-free, boundary and endemic equilibriums. We will also investigate the local stability of each of these equilibriums. The possibility of Hopf bifurcation using delay as the bifurcation parameter is studied using both analytical and numerical solutions.
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Date Issued: 2006
Identifier: CFE0001043, ucf:46801
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0001043

Title: ANALYTIC & NUMERICAL STUDY OF A VORTEX MOTION EQUATION.
Creator: Bueller, Daniel, Rollins, David, University of Central Florida
Abstract / Description: A nonlinear second order differential equation related to vortex motion is derived. This equation is analyzed using various numerical and analytical techniques including finding approximate solutions using a perturbative approach.
Date Issued: 2011
Identifier: CFE0003720, ucf:48802
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0003720

Title: Semi-Analytical Solutions of Non-linear Differential Equations Arising in Science and Engineering.
Creator: Dewasurendra, Mangalagama, Vajravelu, Kuppalapalle, Mohapatra, Ram, Rollins, David, Kumar, Ranganathan, University of Central Florida
Abstract / Description: Systems of coupled non-linear differential equations arise in science and engineering are inherently nonlinear and difficult to find exact solutions. However, in the late nineties, Liao introduced Optimal Homotopy Analysis Method (OHAM), and it allows us to construct accurate approximations to the systems of coupled nonlinear differential equations.The drawback of OHAM is, we must first choose the proper auxiliary linear operator and then solve the linear higher-order deformation equation by...
Show moreSystems of coupled non-linear differential equations arise in science and engineering are inherently nonlinear and difficult to find exact solutions. However, in the late nineties, Liao introduced Optimal Homotopy Analysis Method (OHAM), and it allows us to construct accurate approximations to the systems of coupled nonlinear differential equations.The drawback of OHAM is, we must first choose the proper auxiliary linear operator and then solve the linear higher-order deformation equation by spending lots of CPU time. However, in the latest innovation of Liao's " Method of Directly Defining inverse Mapping (MDDiM)" which he introduced to solve a single nonlinear ordinary differential equation has great freedom to define the inverse linear map directly. In this way, one can solve higher order deformation equations quickly, and it is unnecessary to calculate an inverse linear operator.Our primary goal is to extend MDDiM to solve systems of coupled nonlinear ordinary differential equations. In the first chapter, we will introduce MDDiM and briefly discuss the advantages of MDDiM Over OHAM. In the second chapter, we will study a nonlinear coupled system using OHAM. Next three chapters, we will apply MDDiM to coupled non-linear systems arise in mechanical engineering to study fluid flow and heat transfer. In chapter six we will apply this novel method to study coupled non-linear systems in epidemiology to investigate how diseases spread throughout time. In the last chapter, we will discuss our conclusions and will propose some future work. Another main focus is to compare MDDiM with OHAM.
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Date Issued: 2019
Identifier: CFE0007624, ucf:52551
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0007624

Title: Modeling Mass Care Resource Provision Post Hurricane.
Creator: Muhs, Tammy, Kincaid, John, Rollins, David, Dorman, Teresa, Taylor, Gregory, University of Central Florida
Abstract / Description: Determining the amount of resources needed, specifically food and water, following a hurricane is not a straightforward task. Through this research effort, an estimating tool was developed that takes into account key demographic and evacuation behavioral effects, as well as hurricane storm specifics to estimate the number of meals required for the first fourteen days following a hurricane making landfall in the State of Florida. The Excel based estimating tool was created using data collected...
Show moreDetermining the amount of resources needed, specifically food and water, following a hurricane is not a straightforward task. Through this research effort, an estimating tool was developed that takes into account key demographic and evacuation behavioral effects, as well as hurricane storm specifics to estimate the number of meals required for the first fourteen days following a hurricane making landfall in the State of Florida. The Excel based estimating tool was created using data collected from four hurricanes making landfall in Florida during 2004-2005. The underlying model used in the tool is a Regression Decision Tree with predictor variables including direct impact, poverty level, and hurricane impact score. The hurricane impact score is a hurricane classification system resulting from this research that includes hurricane category, intensity, wind field size, and landfall location. The direct path of a hurricane, a higher than average proportion of residents below the poverty level, and the hurricane impact score were all found to have an effect on the number of meals required during the first fourteen days following a hurricane making landfall in the State of Florida.
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Date Issued: 2011
Identifier: CFE0004143, ucf:49053
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0004143

Title: Convective Heat Transfer in Nanofluids.
Creator: Schraudner, Steven, Vajravelu, Kuppalapalle, Mohapatra, Ram, Rollins, David, University of Central Florida
Abstract / Description: In recent years, the study of fluid flow with nanoparticles in base fluids has attracted the attention of several researchers due to its various applications to science and engineering problems. Recent investigations on convective heat transfer in nanofluids indicate that the suspended nanoparticles markedly change the transport properties and thereby the heat transfer characteristics. Convection in saturated porous media with nanofluids is also an area of growing interest. In this thesis, we...
Show moreIn recent years, the study of fluid flow with nanoparticles in base fluids has attracted the attention of several researchers due to its various applications to science and engineering problems. Recent investigations on convective heat transfer in nanofluids indicate that the suspended nanoparticles markedly change the transport properties and thereby the heat transfer characteristics. Convection in saturated porous media with nanofluids is also an area of growing interest. In this thesis, we study the effects of radiation on the heat and mass transfer characteristics of nanofluid flows over solid surfaces. In Chapter 2, an investigation is made into the effects of radiation on mixed convection over a wedge embedded in a saturated porous medium with nanofluids, while in Chapter 3 results are presented for the effects of radiation on convection heat transfer about a cone embedded in a saturated porous medium with nanofluids. The resulting governing equations are non-dimensionalized and transformed into a non-similar form and then solved by Keller box method. A comparison is made with the available results in the literature, and the results are found to be in very good agreement. The numerical results for the velocity, temperature, volume fraction, the local Nusselt number and the Sherwood number are presented graphically. The salient features of the results are analyzed and discussed for several sets of values of the pertinent parameters. Also, the effects of the Rosseland diffusion and the Brownian motion are discussed.
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Date Issued: 2012
Identifier: CFE0004214, ucf:49024
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0004214

Title: On Hall Magnetohydrodynamics: X-type Neutral Point and Parker Problem.
Creator: Reger, Kyle, Shivamoggi, Bhimsen, Rollins, David, Eastes, Richard, University of Central Florida
Abstract / Description: The framework for the Hall magnetohydrodynamic (MHD) model for plasma physics is built up from kinetic theory and used to analytically solve problems of interest in the field. The Hall MHD model describes fast magnetic reconnection processes in space and laboratory plasmas. Specifically, the magnetic reconnection process at an X-type neutral point, where current sheets form and store enormous amounts of magnetic energy which is later released as magnetic storms when the sheets break up, is...
Show moreThe framework for the Hall magnetohydrodynamic (MHD) model for plasma physics is built up from kinetic theory and used to analytically solve problems of interest in the field. The Hall MHD model describes fast magnetic reconnection processes in space and laboratory plasmas. Specifically, the magnetic reconnection process at an X-type neutral point, where current sheets form and store enormous amounts of magnetic energy which is later released as magnetic storms when the sheets break up, is investigated. The phenomena of magnetic flux pile-up driving the merging of antiparallel magnetic fields at an ion stagnation-point flow in a thin current sheet, called the Parker problem, also receives rigorous mathematical analysis.
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Date Issued: 2012
Identifier: CFE0004428, ucf:49345
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0004428

Title: computational study of traveling wave solutions and global stability of predator-prey models.
Creator: Zhu, Yi, Qi, Yuanwei, Rollins, David, Shuai, Zhisheng, Zhai, Lei, University of Central Florida
Abstract / Description: In this thesis, we study two types of reaction-diffusion systems which have direct applications in understanding wide range of phenomena in chemical reaction, biological pattern formation and theoretical ecology.The first part of this thesis is on propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two...
Show moreIn this thesis, we study two types of reaction-diffusion systems which have direct applications in understanding wide range of phenomena in chemical reaction, biological pattern formation and theoretical ecology.The first part of this thesis is on propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will bestudied. The first is autocatalytic chemical reaction of order $m$ without decay. The second is chemical reaction of order $m$ with a decay of order $l$, where $m$ and $l$ are positive integers and $m(>)l\ge1$. A typical system is $A + 2B \rightarrow3B$ and $B\rightarrow C$ involving three chemical species, a reactant A and an auto-catalyst B and C an inert chemical species.We use numerical computation to give more accurate estimates on minimum speed of traveling waves for autocatalytic reaction without decay, providing useful insight in the study of stability of traveling waves. For autocatalytic reaction of order $m = 2$ with linear decay $l = 1$, which hasa particular important role in biological pattern formation, it is shown numerically that there exist multiple traveling waves with 1, 2 and 3 peaks with certain choices of parameters.The second part of this thesis is on the global stability of diffusive predator-prey system of Leslie Type and Holling-Tanner Type in a bounded domain $\Omega\subset R^N$ with no-flux boundary condition. By using a new approach, we establish much improved global asymptotic stability of a unique positiveequilibrium solution. We also show the result can be extended to more general type of systems with heterogeneous environment and/or other kind of kinetic terms.
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Date Issued: 2016
Identifier: CFE0006519, ucf:51359
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0006519

Title: Smooth and Non-Smooth Traveling Wave Solutions of Some Generalized Camassa-Holm Equations.
Creator: Rehman, Taslima, Choudhury, Sudipto, Nevai, Andrew, Rollins, David, University of Central Florida
Abstract / Description: In this thesis we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of recently derived integrable family of generalized Camassa-Holm (GCH) equations. In the first part, a novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of four GCH equations, i.e. the possible non-smooth peakon, cuspon and compacton solutions. Two of the GCH equations do no support singular traveling...
Show moreIn this thesis we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of recently derived integrable family of generalized Camassa-Holm (GCH) equations. In the first part, a novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of four GCH equations, i.e. the possible non-smooth peakon, cuspon and compacton solutions. Two of the GCH equations do no support singular traveling waves. We generalize an existing theorem to establish the existence of peakon solutions of the third GCH equation. This equation is found to also support four segmented, non-smooth M-wave solutions. While the fourth supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes.In the second part of the thesis, smooth traveling waves of the four GCH equations are considered. Here, we use a recent technique to derive convergent multi-infinite series solutions for the homoclinic and heteroclinic orbits of their traveling-wave equations, corresponding to pulse and front (kink or shock) solutions respectively of the original PDEs. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. Of course, the convergence rate is not comparable to typical asymptotic series. However, asymptotic solutions for global behavior along a full homoclinic/heteroclinic orbit are currently not available.
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Date Issued: 2013
Identifier: CFE0004918, ucf:49637
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0004918

Title: Numerical Simulations for the Flow of Rocket Exhaust Through a Granular Medium.
Creator: Kraakmo, Kristina, Moore, Brian, Brennan, Joseph, Rollins, David, University of Central Florida
Abstract / Description: Physical lab experiments have shown that the pressure caused by an impinging jet on a granular bed has the potential to form craters. This poses a danger to landing success and nearby spacecraft for future rocket missions. Current numerical simulations for this process do not accurately reproduce experimental results. Our goal is to produce improved simulations to more accurately and efficiently model the changes in pressure as gas flows through a porous medium. A two-dimensional model in...
Show morePhysical lab experiments have shown that the pressure caused by an impinging jet on a granular bed has the potential to form craters. This poses a danger to landing success and nearby spacecraft for future rocket missions. Current numerical simulations for this process do not accurately reproduce experimental results. Our goal is to produce improved simulations to more accurately and efficiently model the changes in pressure as gas flows through a porous medium. A two-dimensional model in space known as the nonlinear Porous Medium Equation as it is derived from Darcy's law is used. An Alternating-Direction Implicit (ADI) temporal scheme is presented and implemented which reduces our multidimensional problem into a series of one-dimensional problems. We take advantage of explicit approximations for the nonlinear terms using extrapolation formulas derived from Taylor-series, which increases efficiency when compared to other common methods. We couple our ADI temporal scheme with different spatial discretizations including a second-order Finite Difference (FD) method, a fourth-order Orthogonal Spline Collocation (OSC) method, and an Nth-order Chebyshev Spectral method. Accuracy and runtime are compared among the three methods for comparison in a linear analogue of our problem. We see the best results for accuracy when using an ADI-Spectral method in the linear case, but discuss possibilities for increased efficiency using an ADI-OSC scheme. Nonlinear results are presented using the ADI-Spectral method and the ADI-FD method.
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Date Issued: 2013
Identifier: CFE0005017, ucf:49998
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0005017

Title: Partially Integrable PT-Symmetric Hierarchies of Some Canonical Nonlinear Partial Differential Equations.
Creator: Pecora, Keri, Choudhury, Sudipto, Schober, Constance, Rollins, David, Christodoulides, Demetrios, University of Central Florida
Abstract / Description: We generalize the work of Bender and co-workers to derive new partially-integrable hierarchies of various PT-symmetric, nonlinear partial differential equations. The possible integrable members are identified employing the Painlev(&)#232; Test, a necessary but not sufficient integrability condition, and are indexed by the integer n, corresponding to the negative of the order of the dominant pole in the singular part of the Painlev(&)#232; expansion for the solution.For the PT-symmetric KdV...
Show moreWe generalize the work of Bender and co-workers to derive new partially-integrable hierarchies of various PT-symmetric, nonlinear partial differential equations. The possible integrable members are identified employing the Painlev(&)#232; Test, a necessary but not sufficient integrability condition, and are indexed by the integer n, corresponding to the negative of the order of the dominant pole in the singular part of the Painlev(&)#232; expansion for the solution.For the PT-symmetric KdV equation, as with some other hierarchies, the first or n=1 equation fails the test, the n=2 member corresponds to the regular KdV equation, while the remainder form an entirely new, possibly integrable hierarchy. Integrability properties of the n=3 and n=4 members, typical of partially-integrable systems, including B(&)#228;cklund Transformations, a 'near-Lax Pair', and analytic solutions are derived. The solutions, or solitary waves, prove to be algebraic in form, and the extended homogeneous balance technique appears to be the most efficient in exposing the Lax Pair.The PT-symmetric Burgers' equation fails the Painlev(&)#232; Test for its n=2 case, but special solutions are nonetheless obtained. Also, PT-symmetric hierarchies of 2+1 Burgers' and Kadomtsev-Petviashvili equations, which may prove useful in applications, are analyzed. Extensions of the Painlev(&)#232; Test and Invariant Painlev(&)#232; analysis to 2+1 dimensions are utilized, and BTs and special solutions are found for those cases that pass the Painlev(&)#232; Test.
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Date Issued: 2013
Identifier: CFE0004736, ucf:49843
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0004736

Analytical method (1)	+ -
Brownian motion (1)	+ -
Camassa-Holm Equations (1)	+ -
Computer simulation of smallpox (1)	+ -
Cuspons (1)	+ -

Darcy flow (1)	+ -
Directly defining inverse mapping (1)	+ -
Epidemiology (1)	+ -
Florida (1)	+ -
Fluid flow (1)	+ -
HSI (1)	+ -
Hall magnetohydrodynamics (1)	+ -
Heat transfer (1)	+ -
Heteroclinic orbits (1)	+ -
Homoclinic orbits (1)	+ -
Homotopy analysis method (1)	+ -
Hopf bifurcation (1)	+ -
Mathematical modeling of smallpox (1)	+ -
Nanofluid (1)	+ -
Non-linear systems (1)	+ -
Numerical Methods (1)	+ -
ODE (1)	+ -
Peakons (1)	+ -
Perturbation (1)	+ -
Reversible and non-reversible systems (1)	+ -
Stability (1)	+ -
Stretching surface (1)	+ -
Superfluid (1)	+ -
Traveling wave solutions (1)	+ -
Vortex (1)	+ -

University of Central Florida (12)	+ -
Rollins, David (11)	+ -
Choudhury, Sudipto (2)	+ -
Mohapatra, Ram (2)	+ -
Vajravelu, Kuppalapalle (2)	+ -

Brennan, Joseph (1)	+ -
Bueller, Daniel (1)	+ -
Christodoulides, Demetrios (1)	+ -
Dewasurendra, Mangalagama (1)	+ -
Dorman, Teresa (1)	+ -
Eastes, Richard (1)	+ -
Kincaid, John (1)	+ -
Kraakmo, Kristina (1)	+ -
Kumar, Ranganathan (1)	+ -
LAWOT, NIWAS (1)	+ -
Moore, Brian (1)	+ -
Muhs, Tammy (1)	+ -
Nevai, Andrew (1)	+ -
Pecora, Keri (1)	+ -
Plemmons, William (1)	+ -
Qi, Yuanwei (1)	+ -
ROLLINS, DAVID (1)	+ -
Reger, Kyle (1)	+ -
Rehman, Taslima (1)	+ -
Schober, Constance (1)	+ -
Schraudner, Steven (1)	+ -
Shivamoggi, Bhimsen (1)	+ -
Shuai, Zhisheng (1)	+ -
Singh, Neeta (1)	+ -
Taylor, Gregory (1)	+ -

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