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USING MODELING AND SIMULATION TO EVALUATE DISEASE CONTROL MEASURES
Title
USING MODELING AND SIMULATION TO EVALUATE DISEASE CONTROL MEASURES.
Creator
Atkins, Tracy, Clarke, Thomas, University of Central Florida
Abstract / Description
This dissertation introduced several issues concerning the analysis of diseases by showing how modeling and simulation could be used to assist in creating health policy by estimating the effects of such policies. The first question posed was how would education, vaccination and a combination of these two programs effect the possible outbreak of meningitis on a college campus. After creating a model representative of the transmission dynamics of meningitis and establishing parameter values...
Show moreThis dissertation introduced several issues concerning the analysis of diseases by showing how modeling and simulation could be used to assist in creating health policy by estimating the effects of such policies. The first question posed was how would education, vaccination and a combination of these two programs effect the possible outbreak of meningitis on a college campus. After creating a model representative of the transmission dynamics of meningitis and establishing parameter values characteristic of the University of Central Florida main campus, the results of a deterministic model were presented in several forms. The result of this model was the combination of education and vaccination would eliminate the possibility of an epidemic on our campus. Next, we used simulation to evaluate how quarantine and treatment would affect an outbreak of influenza on the same population. A mathematical model was created specific to influenza on the UCF campus. Numerical results from this model were then presented in tabular and graphical form. The results comparing the simulations for quarantine and treatment show the best course of action would be to enact a quarantine policy on the campus thus reducing the maximum number of infected while increasing the time to reach this peak. Finally, we addressed the issue of performing the analysis stochastically versus deterministically. Additional models were created with the progression of the disease occurring by chance. Statistical analysis was done on the mean of 100 stochastic simulation runs comparing that value to the one deterministic outcome. The results for this analysis were inconclusive, as the results for meningitis were comparable while those for influenza appeared to be different.
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Date Issued
2010
Identifier
CFE0003232, ucf:48535
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0003232
Mathematical Investigation of the Spatial Spread of an Infectious Disease in a Heterogeneous Environment
Title
Mathematical Investigation of the Spatial Spread of an Infectious Disease in a Heterogeneous Environment.
Creator
Gaudiello, Arielle, Shuai, Zhisheng, Nevai, A, Song, Zixia, Mohapatra, Ram, Quintana-Ascencio, Pedro, University of Central Florida
Abstract / Description
Outbreaks of infectious diseases can devastate a population. Researchers thus study the spread of an infection in a habitat to learn methods of control. In mathematical epidemiology, disease transmission is often assumed to adhere to the law of mass action, yet there are numerous other incidence terms existing in the literature. With recent global outbreaks and epidemics, spatial heterogeneity has been at the forefront of these epidemiological models.We formulate and analyze a model for...
Show moreOutbreaks of infectious diseases can devastate a population. Researchers thus study the spread of an infection in a habitat to learn methods of control. In mathematical epidemiology, disease transmission is often assumed to adhere to the law of mass action, yet there are numerous other incidence terms existing in the literature. With recent global outbreaks and epidemics, spatial heterogeneity has been at the forefront of these epidemiological models.We formulate and analyze a model for humans in a homogeneous population with a nonlinear incidence function and demographics of birth and death. We allow for the combination of host immunity after recovery from infection or host susceptibility once the infection has run its course in the individual. We compute the basic reproduction number, R0, for the system and determine the global stability of the equilibrium states. If R0(<)= 1, the population tends towards a disease-free state. If R0 (>)1, an endemic equilibrium exists, and the disease is persistent in the population. This work provides the framework needed for a spatially heterogeneous model. The model is then expanded to include a set of cities (or patches), each of which is structured from the homogeneous model. Movement is introduced, allowing travel between the cities at different rates. We assume there always exists a potentially non-direct route between two cities, and the movement need not be symmetric between two patches. Further, each city has its own nonlinear incidence function, demographics, and recovery rates, allowing for realistic interpretations of country-wide network structures. New global stability results are established for the disease-free equilibrium and endemic equilibrium, the latter utilizing a graph theoretic approach and Lyapunov functions. Asymptotic profiles are determined for both the disease-free equilibrium and basic reproduction number as the diffusion of human individuals is faster than the disease dynamics. A numerical investigation is performed on a star network, emulating a rural-urban society with a center city and surrounding suburbs. Numerical simulations give rise to similar and contrasting behavior for symmetric movement to the proposed asymmetric movement. Conjectures are made for the monotonicty of the basic reproduction number in terms of the diffusion of susceptible and infectious individuals. The limiting behavior of the system as the diffusion of susceptibles halts is shown to experience varying behavior based on the location of hot spots and biased movement.
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Date Issued
2019
Identifier
CFE0007637, ucf:52463
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0007637
EPIDEMIOLOGICAL MODELS FOR MUTATING PATHOGENS WITH TEMPORARY IMMUNITY
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
A mathematical model for feral cat ecology with application to disease.
Title
A mathematical model for feral cat ecology with application to disease.
Creator
Sharpe, Jeff, Nevai, A, Shuai, Zhisheng, Qi, Yuanwei, Quintana-Ascencio, Pedro, University of Central Florida
Abstract / Description
We formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to Lotka-Volterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also...
Show moreWe formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to Lotka-Volterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also considered, including additional competition and abandonment into the feral population. Control measures are also modeled in the form of per-capita removal rates. We compute the net reproduction number (R_0) for the colony and consider its influence. In the absence of abandonment, if R_0(>)1, the population always persists at a positive equilibrium and if R_0 (<)= 1, the population always tends toward local extinction. This work will be referred to as the core model.The model is then expanded to include a set of colonies (patches) such as those in the core model (this time neglecting the effect of abandonment). Adult females and kittens remain in their native patch while adult males spend a fixed proportion of their time in each patch. Adult females experience competition from both the adult females living in the same patch as well as the visiting adult males. The proportion of adult males in patch j suffer competition from both adult females resident to that patch as well the proportion of adult males also in the patch. We formulate a net reproduction number for each patch (a patch reproduction number) R_j. If R_j(>)1 for at least one patch, then the collective population always persists at some nontrivial (but possibly semitrivial) steady state. We consider the number of possible steady states and their properties. This work will be referred to as the patch model.Finally, the core model is expanded to include the introduction of the feline leukemia virus. Since this disease has many modes of transmission, each of which depends on the host's gender and life-stage, we regard this as a model disease. A basic reproduction number R_0 for the disease is defined and analyzed. Vaccination terms are included and their role in disease propagation is analyzed. Necessary and sufficient conditions are given under which the disease-free equilibrium is stable.
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Date Issued
2016
Identifier
CFE0006502, ucf:51389
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0006502