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Modeling Disease Impact of Vibrio-Phage Interactions
Title
Modeling Disease Impact of Vibrio-Phage Interactions.
Creator
Botelho, Christopher, Shuai, Zhisheng, Nevai, A, Zhang, Teng, Teter, Kenneth, University of Central Florida
Abstract / Description
Since the work of John Snow, scientists and medical professionals have understood that individuals develop cholera by means of consuming contaminated water. Despite the knowledge(&)nbsp;of cholera's route of infection, many countries have experienced and still experience endemic cholera. Cholera is caused by the Vibrio cholerae (V. cholerae) bacterium and presents with acute diarrhea and vomiting. If untreated, infected individuals may die due to dehydration. Cholera is a disease that most...
Show moreSince the work of John Snow, scientists and medical professionals have understood that individuals develop cholera by means of consuming contaminated water. Despite the knowledge(&)nbsp;of cholera's route of infection, many countries have experienced and still experience endemic cholera. Cholera is caused by the Vibrio cholerae (V. cholerae) bacterium and presents with acute diarrhea and vomiting. If untreated, infected individuals may die due to dehydration. Cholera is a disease that most commonly affects countries with poor infrastructure and water sanitation. Despite efforts to control cholera in such countries, the disease persists. One such example is Haiti which has been experiencing a cholera outbreak since 2010. While there has been much research in the field of microbiology to understand V. cholerae, there has been comparably less research in the field of mathematical biology to understand the dynamics of V. cholerae in the environment. A mathematical model of V. cholerae incorporating a phage population is coupled with a SIRS disease model to examine the impact of vibrio and phage interaction. It is shown that there might exist two endemic equilibria, besides the disease free equilibrium: one in which phage persist in the environment and one in which the phage fail to persist. Existence and stability of these equilibria are established. Disease control strategies based on vibrio and phage interactions are discussed.
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Date Issued
2019
Identifier
CFE0007604, ucf:52544
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0007604
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
Modeling Network Worm Outbreaks
Title
Modeling Network Worm Outbreaks.
Creator
Foley, Evan, Shuai, Zhisheng, Kaup, David, Nevai, A, University of Central Florida
Abstract / Description
Due to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible,...
Show moreDue to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible, Infectious, Treatment, and Antidotal. We shall show that allocating resources into treating infectious computers leads to a reduced peak of infections across the infection period, while pouring resources into treating susceptible computers decreases the total amount of infections throughout the infection period. This is assuming both methods are receiving resources without loss. This result reveals an interesting notion of balance between protecting computers and removing computers from infections, ultimately depending on the business executives' goals and/or preferences.
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Date Issued
2015
Identifier
CFE0005948, ucf:50816
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005948
Modeling and analysis of a three-species food web with facilitated and intraguild predation
Title
Modeling and analysis of a three-species food web with facilitated and intraguild predation.
Creator
Castro, Joshua, Weishampel, John, Quintana-Ascencio, Pedro, Nevai, A, University of Central Florida
Abstract / Description
Biotic interactions are known to shape natural community assemblages and biodiversity. Positive interactions such as facilitation have recently received attention in ecological food webs. Mechanistic models have improved our understanding of these complex food web interactions. Here, focus is given to a three-species food web system with a beach dune natural community in mind. In the last decade, there has been a series of studies investigating intraguild predation between two major...
Show moreBiotic interactions are known to shape natural community assemblages and biodiversity. Positive interactions such as facilitation have recently received attention in ecological food webs. Mechanistic models have improved our understanding of these complex food web interactions. Here, focus is given to a three-species food web system with a beach dune natural community in mind. In the last decade, there has been a series of studies investigating intraguild predation between two major loggerhead sea turtle nest predators, North American raccoons and Atlantic ghost crabs. Studies have also highlighted that ghost crab predation assists raccoons in finding nests (i.e., facilitated predation). However, the combined effects of these two intraguild interactions and their consequences on nests have not been examined explicitly. The aims of this study were to (i) develop a three-species, ordinary differential equation model (ii) implement a sensitivity analysis to understand the influence of facilitation and other factors in driving species richness and abundance and (iii) characterize the dynamic interactions between intraguild predators and their effects on a shared resource. Interactions between ghost crabs and sea turtle eggs and facilitation can yield a wide variety of species abundance responses and were influential factors in the model. I found that high secondary sea turtle egg depredation and low facilitated predation by raccoons led to three species co-existence regions in the model. Controlling for nest predators at higher abundance levels showed that ghost crabs had a larger negative effect on sea turtle egg abundance responses when compared to raccoons. This suggests that interactions between sea turtle eggs and ghost crabs appear to be important and potential sea turtle nest management implications are discussed such as the use of ghost crab exclusion devices.
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Date Issued
2015
Identifier
CFE0005771, ucf:50074
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005771
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
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