Current Search: Rollins, David (x)
View All Items
 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 100200 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.
Show less  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 vaccinesensitive; (3) infected but asymptomatic, noninfectious, and vaccineinsensitive; (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.
Show less  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. Infact, 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. Infact, 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 integrodifferentialdifference 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 diseasefree, 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.
Show less  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
 SemiAnalytical Solutions of Nonlinear 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 nonlinear 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 higherorder deformation equation by...
Show moreSystems of coupled nonlinear 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 higherorder 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 nonlinear systems arise in mechanical engineering to study fluid flow and heat transfer. In chapter six we will apply this novel method to study coupled nonlinear 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.
Show less  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 20042005. 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.
Show less  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 nondimensionalized and transformed into a nonsimilar 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.
Show less  Date Issued
 2012
 Identifier
 CFE0004214, ucf:49024
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004214
 Title
 On Hall Magnetohydrodynamics: Xtype 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 Xtype 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 Xtype 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 pileup driving the merging of antiparallel magnetic fields at an ion stagnationpoint flow in a thin current sheet, called the Parker problem, also receives rigorous mathematical analysis.
Show less  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 predatorprey 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 reactiondiffusion 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 reactiondiffusion 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 reactiondiffusion 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 reactiondiffusion 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 autocatalyst 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 predatorprey system of Leslie Type and HollingTanner Type in a bounded domain $\Omega\subset R^N$ with noflux 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.
Show less  Date Issued
 2016
 Identifier
 CFE0006519, ucf:51359
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006519
 Title
 Smooth and NonSmooth Traveling Wave Solutions of Some Generalized CamassaHolm 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 CamassaHolm (GCH) equations. In the first part, a novel application of phaseplane analysis is employed to analyze the singular traveling wave equations of four GCH equations, i.e. the possible nonsmooth 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 CamassaHolm (GCH) equations. In the first part, a novel application of phaseplane analysis is employed to analyze the singular traveling wave equations of four GCH equations, i.e. the possible nonsmooth 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, nonsmooth Mwave 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 multiinfinite series solutions for the homoclinic and heteroclinic orbits of their travelingwave 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.
Show less  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 twodimensional 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 twodimensional model in space known as the nonlinear Porous Medium Equation as it is derived from Darcy's law is used. An AlternatingDirection Implicit (ADI) temporal scheme is presented and implemented which reduces our multidimensional problem into a series of onedimensional problems. We take advantage of explicit approximations for the nonlinear terms using extrapolation formulas derived from Taylorseries, which increases efficiency when compared to other common methods. We couple our ADI temporal scheme with different spatial discretizations including a secondorder Finite Difference (FD) method, a fourthorder Orthogonal Spline Collocation (OSC) method, and an Nthorder 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 ADISpectral method in the linear case, but discuss possibilities for increased efficiency using an ADIOSC scheme. Nonlinear results are presented using the ADISpectral method and the ADIFD method.
Show less  Date Issued
 2013
 Identifier
 CFE0005017, ucf:49998
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005017
 Title
 Partially Integrable PTSymmetric 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 coworkers to derive new partiallyintegrable hierarchies of various PTsymmetric, 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 PTsymmetric KdV...
Show moreWe generalize the work of Bender and coworkers to derive new partiallyintegrable hierarchies of various PTsymmetric, 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 PTsymmetric 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 partiallyintegrable systems, including B(&)#228;cklund Transformations, a 'nearLax 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 PTsymmetric Burgers' equation fails the Painlev(&)#232; Test for its n=2 case, but special solutions are nonetheless obtained. Also, PTsymmetric hierarchies of 2+1 Burgers' and KadomtsevPetviashvili 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.
Show less  Date Issued
 2013
 Identifier
 CFE0004736, ucf:49843
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004736