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MODELING TRANSMISSION DYNAMICS OF TUBERCULOSIS INCLUDING VARIOUS LATENT PERIODS
Title
MODELING TRANSMISSION DYNAMICS OF TUBERCULOSIS INCLUDING VARIOUS LATENT PERIODS.
Creator
Atkins, Tracy, Mohapatra, Ram, University of Central Florida
Abstract / Description
The systems of equations created by Blower et al. (1995) and Jia et al. (2007) designed to model the dynamics of Tuberculosis are solved using the computer software SIMULINK. The results are first employed to examine the intrinsic transmission dynamics of the disease through two models developed by Blower et al. (1995). The "simple transmission model" was used primarily to give insight to the behavior of the susceptible, latent, and infectious groups of individuals. Then, we consider a more...
Show moreThe systems of equations created by Blower et al. (1995) and Jia et al. (2007) designed to model the dynamics of Tuberculosis are solved using the computer software SIMULINK. The results are first employed to examine the intrinsic transmission dynamics of the disease through two models developed by Blower et al. (1995). The "simple transmission model" was used primarily to give insight to the behavior of the susceptible, latent, and infectious groups of individuals. Then, we consider a more detailed transmission model which includes several additional factors. This model captures the dynamics of not only the susceptible, latent and infectious groups but also the non-infectious cases and the recovered cases. Using the SIMULINK results, it can be shown that the intrinsic dynamics of the disease contribute to the rise and decline of the disease seen in historical accounts. Next, the simulation results are used to study the equilibrium points of the disease which can be obtained by varying the parameters and therefore changing the value for the basic reproduction ratio (R0 ). Our model uses the system of equations developed by Jia et al. (2007). The SIMULINK results are used to visually confirm the hypothesis proposed by Jia et al. (2007) that the equilibrium behavior of the system when R0 > 1 is globally asymptotically stable.
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Date Issued
2008
Identifier
CFE0002030, ucf:47606
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0002030
RIGOROUS ANALYSIS OF AN EDGE-BASED NETWORK DISEASE MODEL
Title
RIGOROUS ANALYSIS OF AN EDGE-BASED NETWORK DISEASE MODEL.
Creator
Mai, Sabrina, Shuai, Zhisheng, University of Central Florida
Abstract / Description
Edge-based network disease models, in comparison to classic compartmental epidemiological models, better capture social factors affecting disease spread such as contact duration and social heterogeneity. We reason that there should exist infinitely many equilibria rather than only an endemic equilibrium and a disease-free equilibrium for the edge-based network disease model commonly used in the literature, as there do not exist any changes in demographic in the model. We modify the commonly...
Show moreEdge-based network disease models, in comparison to classic compartmental epidemiological models, better capture social factors affecting disease spread such as contact duration and social heterogeneity. We reason that there should exist infinitely many equilibria rather than only an endemic equilibrium and a disease-free equilibrium for the edge-based network disease model commonly used in the literature, as there do not exist any changes in demographic in the model. We modify the commonly used network model by relaxing some assumed conditions and factor in a dependency on initial conditions. We find that this modification still accounts for realistic dynamics of disease spread (such as the probability of contracting a disease based off your neighbors' susceptibility to the disease) based on the basic reproduction number. Specifically, if the basic reproduction number is below 1, then the infection dies out; while if the basic reproduction number is above 1, then there is possibility of an epidemic.
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Date Issued
2019
Identifier
CFH2000537, ucf:45651
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFH2000537
SOCIAL PATHOGENIC SOURCES OF POOR COMMUNITY HEALTH
Title
SOCIAL PATHOGENIC SOURCES OF POOR COMMUNITY HEALTH.
Creator
Smith, Hayden, Wan, Thomas, University of Central Florida
Abstract / Description
The United States currently provides a health care system that is neither efficient nor equitable. Despite outspending the world on health care, over three-fourths of developed countries produce better health outcomes (Auerbach et al., 2000). Simultaneously, the "Ecological School of Thought" has documented the large impact that social, economic, and environmental circumstances play in health outcomes. Unfortunately, these 'ecological" studies are frequently conducted without theoretical...
Show moreThe United States currently provides a health care system that is neither efficient nor equitable. Despite outspending the world on health care, over three-fourths of developed countries produce better health outcomes (Auerbach et al., 2000). Simultaneously, the "Ecological School of Thought" has documented the large impact that social, economic, and environmental circumstances play in health outcomes. Unfortunately, these 'ecological" studies are frequently conducted without theoretical justification, and rely solely on a cross-sectional research design and a myriad of unrelated variables. This study represents an important step towards the development of a true theory of "ecology". More specifically, we argue that the adversity associated with socio-economic disadvantage, social disorganization, and a lack of health care resources, leads to adverse health outcomes, represented by sentinel health events. This research employs both a cross-sectional (2000) and longitudinal designs (1990 – 2000) to assess the antecedents of sentinel health events in 309 United States counties. Structural Equation Modeling was the statistical technique employed in the study. Findings revealed that socioeconomic disadvantage remains a primary contributor to sentinel health. Indeed the economic growth between 1990 and 2000 was associated with increased rates of sentinel health events. Social disorganization was identified as a primary contributor to sentinel health events at a specific time point (2000), but was not significant over time (1990 -2000). Conversely, the inadequacy of health care resources was non-significant in the cross-sectional model (2000), but significant in the longitudinal model (1990 -2000). In both models, racial characteristics were fundamentally linked to ecological predictors of health We found support for the notion that sentinel health events would be reduced through economic equity and the development of healthy environments where community ties are reinforced. Less support is found for saturating given geographical areas with health care resources in order to reduce sentinel health events. Future research should be directed by the theoretical advancements made by this study. More specifically, future studies should examine independent cross-level effects, that is, through the inclusion of behavior variables as mediating factors for ecological constructs.
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Date Issued
2007
Identifier
CFE0001577, ucf:47108
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001577
Analysis and Simulation for Homogeneous and Heterogeneous SIR Models
Title
Analysis and Simulation for Homogeneous and Heterogeneous SIR Models.
Creator
Wilda, Joseph, Shuai, Zhisheng, Brennan, Joseph, Nevai, A, University of Central Florida
Abstract / Description
In mathematical epidemiology, disease transmission is commonly assumed to behave in accordance with the law of mass action; however, other disease incidence terms also exist in the literature. A homogeneous Susceptible-Infectious-Removed (SIR) model with a generalized incidence term is presented along with analytic and numerical results concerning effects of the generalization on the global disease dynamics. The spatial heterogeneity of the metapopulation with nonrandom directed movement...
Show moreIn mathematical epidemiology, disease transmission is commonly assumed to behave in accordance with the law of mass action; however, other disease incidence terms also exist in the literature. A homogeneous Susceptible-Infectious-Removed (SIR) model with a generalized incidence term is presented along with analytic and numerical results concerning effects of the generalization on the global disease dynamics. The spatial heterogeneity of the metapopulation with nonrandom directed movement between populations is incorporated into a heterogeneous SIR model with nonlinear incidence. The analysis of the combined effects of the spatial heterogeneity and nonlinear incidence on the disease dynamics of our model is presented along with supporting simulations. New global stability results are established for the heterogeneous model utilizing a graph-theoretic approach and Lyapunov functions. Numerical simulations confirm nonlinear incidence gives raise to rich dynamics such as synchronization and phase-lock oscillations.
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Date Issued
2015
Identifier
CFE0005906, ucf:50872
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005906
Semi-Analytical Solutions of Non-linear Differential Equations Arising in Science and Engineering
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
Infectious Disease Risks in Developing Countries: A Non-Market Valuation Exercise
Title
Infectious Disease Risks in Developing Countries: A Non-Market Valuation Exercise.
Creator
Samajpati, Shreejata, Gerking, Shelby, Dickie, Mark, Caputo, Michael, Roy, Joyashree, University of Central Florida
Abstract / Description
This dissertation focuses on the non-market valuation of health-risks of malaria, an infectious disease that imposes a substantive public health burden across the globe, hitting particularly hard the tropical developing nations of Africa and Asia. The United Nations Millennium Development Goals include malaria control as a priority and large investments are underway to promote effective prevention and treatment. Despite such concerted supply-side efforts, malaria-related mortality and...
Show moreThis dissertation focuses on the non-market valuation of health-risks of malaria, an infectious disease that imposes a substantive public health burden across the globe, hitting particularly hard the tropical developing nations of Africa and Asia. The United Nations Millennium Development Goals include malaria control as a priority and large investments are underway to promote effective prevention and treatment. Despite such concerted supply-side efforts, malaria-related mortality and morbidity still abound due to a complex interface of factors like climate-change, poverty, inadequate control behavior, infection and prevention externalities, parasite resistance etc. This research project digs into the demand-side of the health problem, considers the "externality" dimension to prevention, and primarily asks the question: how do individuals in developing countries view competing disease-control (prevention) measures, viz. a publicly-administered community-level malaria control measure as against private preventive choices. A theoretical model is developed to help explore the public-private interplay of health risks of malaria. The malaria-endemic regions of Kolkata (India) and its rural fringes comprise the site for an empirical investigation. A field survey (Malaria Risk and Prevention Survey, October-December, 2011) incorporating a mix of stated and revealed preference techniques of health valuation is implemented. Risk-perceptions of respondents are elicited using a measurable visual-aid and individuals' perceived valuations of health-risk reductions, randomly offered with the public and private health treatments, are empirically ascertained. Using a Likelihood Ratio Test on the structural risk parameters, it is seen that individuals' valuations of health risk reductions are the same across the private and public treatments. The comparative valuation exercise, thus, corroborates the externality dimension to malaria control, calling for greater public action to combat malaria. The viability of such a scaled-up public malaria program, in the context of Kolkata, is discussed by comparing the public treatment willingness to pay estimates with the annual estimated costs that the Kolkata Municipal Corporation, the civic body in the city of Kolkata, maintains on account of vector control. Results from the comparative valuation exercises also support the idea that private prevention is generally responsive to prevention costs, indicating the importance of price incentives to induce greater prevention. The issues of health valuation and price sensitivity are further explored across various split-samples differentiated on the basis of socio-economic attributes, disease exposure, actual prevention efforts and perceived malaria risks of survey respondents. Such auxiliary exercises help analyze the valuation question in greater depth, and generate policy insights into the potential factors that shape private prevention behavior.
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Date Issued
2012
Identifier
CFE0004594, ucf:49195
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004594