Lenhart, Suzanne
Overview
Works:  20 works in 36 publications in 1 language and 412 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Author 
Publication Timeline
.
Most widely held works by
Suzanne Lenhart
Mathematics for the life sciences by
Erin N Bodine(
Book
)
8 editions published in 2014 in English and held by 299 WorldCat member libraries worldwide
"The life sciences deal with a vast array of problems at different spatial, temporal, and organizational scales. The mathematics necessary to describe, model, and analyze these problems is similarly diverse, incorporating quantitative techniques that are rarely taught in standard undergraduate courses. This textbook provides an accessible introduction to these critical mathematical concepts, linking them to biological observation and theory while also presenting the computational tools needed to address problems not readily investigated using mathematics alone. Proven in the classroom and requiring only a background in high school math, Mathematics for the Life Sciences doesn't just focus on calculus as do most other textbooks on the subject. It covers deterministic methods and those that incorporate uncertainty, problems in discrete and continuous time, probability, graphing and data analysis, matrix modeling, difference equations, differential equations, and much more. The book uses MATLAB throughout, explaining how to use it, write code, and connect models to data in examples chosen from across the life sciences. Provides undergraduate life science students with a succinct overview of major mathematical concepts that are essential for modern biology, Covers all the major quantitative concepts that national reports have identified as the ideal components of an entrylevel course for life science students, Provides good background for the MCAT, which now includes databased and statistical reasoning Explicitly links data and math modeling, Includes endofchapter homework problems, endofunit student projects, and select answers to homework problems, Uses MATLAB throughout, and MATLAB mfiles with an R supplement are available online Prepares students to read with comprehension the growing quantitative literature across the life sciences, Online answer key, solution guide, and illustration package (available to professors)"
8 editions published in 2014 in English and held by 299 WorldCat member libraries worldwide
"The life sciences deal with a vast array of problems at different spatial, temporal, and organizational scales. The mathematics necessary to describe, model, and analyze these problems is similarly diverse, incorporating quantitative techniques that are rarely taught in standard undergraduate courses. This textbook provides an accessible introduction to these critical mathematical concepts, linking them to biological observation and theory while also presenting the computational tools needed to address problems not readily investigated using mathematics alone. Proven in the classroom and requiring only a background in high school math, Mathematics for the Life Sciences doesn't just focus on calculus as do most other textbooks on the subject. It covers deterministic methods and those that incorporate uncertainty, problems in discrete and continuous time, probability, graphing and data analysis, matrix modeling, difference equations, differential equations, and much more. The book uses MATLAB throughout, explaining how to use it, write code, and connect models to data in examples chosen from across the life sciences. Provides undergraduate life science students with a succinct overview of major mathematical concepts that are essential for modern biology, Covers all the major quantitative concepts that national reports have identified as the ideal components of an entrylevel course for life science students, Provides good background for the MCAT, which now includes databased and statistical reasoning Explicitly links data and math modeling, Includes endofchapter homework problems, endofunit student projects, and select answers to homework problems, Uses MATLAB throughout, and MATLAB mfiles with an R supplement are available online Prepares students to read with comprehension the growing quantitative literature across the life sciences, Online answer key, solution guide, and illustration package (available to professors)"
Modeling paradigms and analysis of disease transmission models by
Abba B Gumel(
Book
)
6 editions published in 2010 in English and held by 86 WorldCat member libraries worldwide
This volume stems from two DIMACS activities, the U.S.Africa Advanced Study Institute and the DIMACS Workshop, both on Mathematical Modeling of Infectious Diseases in Africa, held in South Africa in the summer of 2007. It contains both tutorial papers and research papers. Students and researchers should find the papers on modeling and analyzing certain diseases currently affecting Africa very informative. In particular, they can learn basic principles of disease modeling and stability from the tutorial papers where continuous and discrete time models, optimal control, and stochastic features
6 editions published in 2010 in English and held by 86 WorldCat member libraries worldwide
This volume stems from two DIMACS activities, the U.S.Africa Advanced Study Institute and the DIMACS Workshop, both on Mathematical Modeling of Infectious Diseases in Africa, held in South Africa in the summer of 2007. It contains both tutorial papers and research papers. Students and researchers should find the papers on modeling and analyzing certain diseases currently affecting Africa very informative. In particular, they can learn basic principles of disease modeling and stability from the tutorial papers where continuous and discrete time models, optimal control, and stochastic features
Control of partial differential equations by
Suzanne Lenhart(
Book
)
4 editions published in 2000 in English and held by 6 WorldCat member libraries worldwide
4 editions published in 2000 in English and held by 6 WorldCat member libraries worldwide
Dynamic aspects of competition, adaptation, and patchiness in ecology(
Book
)
1 edition published in 2005 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 3 WorldCat member libraries worldwide
Partial differential equations from dynamic programming equations by
Suzanne Lenhart(
Book
)
2 editions published in 1981 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1981 in English and held by 2 WorldCat member libraries worldwide
Modeling and control of natural resources(
Book
)
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
Optimal control of a heat flux in a parabolic partial differential equation by Katherine Renee Deaton(
Book
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
We consider the problem of controlling the solution of a parabolic partial differential equation with nonhomogeneous Neumann boundary conditions, taking the flux as the control. We take as our cost functional the sum of the L² norms of the control and the difference between the temperature distribution attained and the desired temperature profile. We establish the existence of an optimal control that minimizes the cost functional. The optimal control is characterized in a constructive way through the solution to the optimality system, which is the original problem coupled with an adjoint problem. We establish existence and uniqueness of the solution of the optimality system. Thus, we find the unique optimal control in terms of the solution to the optimality system
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
We consider the problem of controlling the solution of a parabolic partial differential equation with nonhomogeneous Neumann boundary conditions, taking the flux as the control. We take as our cost functional the sum of the L² norms of the control and the difference between the temperature distribution attained and the desired temperature profile. We establish the existence of an optimal control that minimizes the cost functional. The optimal control is characterized in a constructive way through the solution to the optimality system, which is the original problem coupled with an adjoint problem. We establish existence and uniqueness of the solution of the optimality system. Thus, we find the unique optimal control in terms of the solution to the optimality system
A dynamical model for bark beetle outbreaks(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Abstract: Treekilling bark beetles are major disturbance agents affecting coniferous forest ecosystems. The role of environmental conditions on driving beetle outbreaks is becoming increasingly important as global climatic change alters environmental factors, such as drought stress, that, in turn, govern tree resistance. Furthermore, dynamics between beetles and trees are highly nonlinear, due to complex aggregation behaviors exhibited by beetles attacking trees. Models have a role to play in helping unravel the effects of variable tree resistance and beetle aggregation on bark beetle outbreaks. In this article we develop a new mathematical model for bark beetle outbreaks using an analogy with epidemiological models. Because the model operates on several distinct time scales, singular perturbation methods are used to simplify the model. The result is a dynamical system that tracks populations of uninfested and infested trees. A limiting case of the model is a discontinuous function of state variables, leading to solutions in the Filippov sense. The model assumes an extensive seedbank so that tree recruitment is possible even if trees go extinct. Two scenarios are considered for immigration of new beetles. The first is a single tree stand with beetles immigrating from outside while the second considers two forest stands with beetle dispersal between them. For the seedbank driven recruitment rate, when beetle immigration is low, the forest stand recovers to a beetlefree state. At high beetle immigration rates beetle populations approach an endemic equilibrium state. At intermediate immigration rates, the model predicts bistability as the forest can be in either of the two equilibrium states: a healthy forest, or a forest with an endemic beetle population. The model bistability leads to hysteresis. Interactions between two stands show how a less resistant stand of trees may provide an initial toehold for the invasion, which later leads to a regional beetle outbreak in the resistant stand. Abstract : Highlights: A new epidemiological model for bark beetle outbreaks is developed. This model considers beetle aggregation dynamics and tree resistance to infestation. The resulting model is described by a differential equation with discontinuous righthand side. Conditions that relate tree resistance, forest regeneration rate, rate of infestation by beetles, and immigration to the forest state are given. Analytical conditions when forest dies, recovers, or infestation becomes endemic are given. The case of infestation spread between patches is studied using a two stand system
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Abstract: Treekilling bark beetles are major disturbance agents affecting coniferous forest ecosystems. The role of environmental conditions on driving beetle outbreaks is becoming increasingly important as global climatic change alters environmental factors, such as drought stress, that, in turn, govern tree resistance. Furthermore, dynamics between beetles and trees are highly nonlinear, due to complex aggregation behaviors exhibited by beetles attacking trees. Models have a role to play in helping unravel the effects of variable tree resistance and beetle aggregation on bark beetle outbreaks. In this article we develop a new mathematical model for bark beetle outbreaks using an analogy with epidemiological models. Because the model operates on several distinct time scales, singular perturbation methods are used to simplify the model. The result is a dynamical system that tracks populations of uninfested and infested trees. A limiting case of the model is a discontinuous function of state variables, leading to solutions in the Filippov sense. The model assumes an extensive seedbank so that tree recruitment is possible even if trees go extinct. Two scenarios are considered for immigration of new beetles. The first is a single tree stand with beetles immigrating from outside while the second considers two forest stands with beetle dispersal between them. For the seedbank driven recruitment rate, when beetle immigration is low, the forest stand recovers to a beetlefree state. At high beetle immigration rates beetle populations approach an endemic equilibrium state. At intermediate immigration rates, the model predicts bistability as the forest can be in either of the two equilibrium states: a healthy forest, or a forest with an endemic beetle population. The model bistability leads to hysteresis. Interactions between two stands show how a less resistant stand of trees may provide an initial toehold for the invasion, which later leads to a regional beetle outbreak in the resistant stand. Abstract : Highlights: A new epidemiological model for bark beetle outbreaks is developed. This model considers beetle aggregation dynamics and tree resistance to infestation. The resulting model is described by a differential equation with discontinuous righthand side. Conditions that relate tree resistance, forest regeneration rate, rate of infestation by beetles, and immigration to the forest state are given. Analytical conditions when forest dies, recovers, or infestation becomes endemic are given. The case of infestation spread between patches is studied using a two stand system
Applications of optimal control by Katherine Renee Fister(
Book
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
In this dissertation, we investigate optimal control of partial and ordinary differential equations. We prove the existence of an optimal control for which the objective functional is maximized. The goal is to characterize the optimal control in terms of the solution of the optimality system. The optimality system consists of the state equations coupled with the adjoint equations. To obtain the optimality system we differentiate the objective functional with respect to the control. This process is applied to harvesting in a predatorprey parabolic system, to analyzing surface runoff in a parabolic problem, and to controlling the effect of the HIV virus on T cells in an AIDS patient. In the predatorprey problem, the profit associated with harvesting is shown to be positive under certain constraints. In the runoff problem, the concentration of contaminants being deposited into a major river flow is modeled as point sources. To explicitly characterize the optimal controls, two choices of the revenue function are used. One revenue function is a MichaelisMenton function and the other is a quadratic function. In the HIV problem, we control the effect that HIV has on the T cells in the immune system. We seek to maximize the number of T cells, minimize the free virus, and minimize the systemic cost to the body
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
In this dissertation, we investigate optimal control of partial and ordinary differential equations. We prove the existence of an optimal control for which the objective functional is maximized. The goal is to characterize the optimal control in terms of the solution of the optimality system. The optimality system consists of the state equations coupled with the adjoint equations. To obtain the optimality system we differentiate the objective functional with respect to the control. This process is applied to harvesting in a predatorprey parabolic system, to analyzing surface runoff in a parabolic problem, and to controlling the effect of the HIV virus on T cells in an AIDS patient. In the predatorprey problem, the profit associated with harvesting is shown to be positive under certain constraints. In the runoff problem, the concentration of contaminants being deposited into a major river flow is modeled as point sources. To explicitly characterize the optimal controls, two choices of the revenue function are used. One revenue function is a MichaelisMenton function and the other is a quadratic function. In the HIV problem, we control the effect that HIV has on the T cells in the immune system. We seek to maximize the number of T cells, minimize the free virus, and minimize the systemic cost to the body
Application of optimal control theory to in situ bioremediation by
University of Minnesota(
Book
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Optimal control of integrodifference equations in a pestpathofen system by Marco V Martinez(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
"We develop the theory of optimal control for a system of integrodifference equations modelling a pestpathogen system. Integrodifference equations incorporate continuous space into a system of discrete time equations. We design an objective functional to minimize the damaged cost generated by an invasive species and the cost of controlling the population with a pathogen. Existence, characterization, and uniqueness results for the optimal control and corresponding states have been completed. We use a forwardbackward sweep numerical method to implement our optimization which produces spatiotemporal control strategies for the gypsy moth case study."Abstract
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
"We develop the theory of optimal control for a system of integrodifference equations modelling a pestpathogen system. Integrodifference equations incorporate continuous space into a system of discrete time equations. We design an objective functional to minimize the damaged cost generated by an invasive species and the cost of controlling the population with a pathogen. Existence, characterization, and uniqueness results for the optimal control and corresponding states have been completed. We use a forwardbackward sweep numerical method to implement our optimization which produces spatiotemporal control strategies for the gypsy moth case study."Abstract
Modeling feral hogs in Great Smoky Mountains National Park by Benjamin Anthony Levy(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Feral Hogs (Sus scrofa) are an invasive species that have occupied the Great Smoky Mountains National Park since the early 1900s. Recent studies have revitalized interest in the pest and have produced useful data. The Park has kept detailed records on mast abundance as well as every removal since 1980 including geographic location and disease sampling. Data obtained via Lidar includes both overstory as well as understory vegetation information. In this dissertation, three models were created and analyzed using the detailed data on vegetation, mast, and harvest history. The first model is discrete in time and space and was formulated to represent hog dynamics in the park. The second is a spatial model of the niche of the population that relates known presence locations to environmental predictors. The third model is a compartmental disease model for pseudorabies in the population. Together, these projects assess the importance of the existing control program, predict suitable locations for hog presence in the Park, and quantify possible transmission routes for Pseudorabies
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Feral Hogs (Sus scrofa) are an invasive species that have occupied the Great Smoky Mountains National Park since the early 1900s. Recent studies have revitalized interest in the pest and have produced useful data. The Park has kept detailed records on mast abundance as well as every removal since 1980 including geographic location and disease sampling. Data obtained via Lidar includes both overstory as well as understory vegetation information. In this dissertation, three models were created and analyzed using the detailed data on vegetation, mast, and harvest history. The first model is discrete in time and space and was formulated to represent hog dynamics in the park. The second is a spatial model of the niche of the population that relates known presence locations to environmental predictors. The third model is a compartmental disease model for pseudorabies in the population. Together, these projects assess the importance of the existing control program, predict suitable locations for hog presence in the Park, and quantify possible transmission routes for Pseudorabies
Population modeling for resource allocation and antimicrobial stewardship by Jason Bintz(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This dissertation contains two types of population models with applications in conservation biology and epidemiology. In particular, it considers models for resource allocation and antimicrobial stewardship. In a population model with a parabolic differential equation and density dependent growth, we study the problem of allocating resources to maximize the net benefit in the conservation of a single species while the cost of the resource allocation is minimized. The net benefit is measured in terms of maximizing population abundance and the goal of maximizing abundance is divided between the goal of maximizing the overall abundance across space and time and the goal of maximizing abundance at the final time. We consider cases that model a fixed amount of resource as well as cases without this constraint. We regard the resource coefficient as a control and we consider cases where this coefficient varies in space and time as well as cases where it varies only in space. We establish the existence and uniqueness of the solution to the state system given a control and the existence of an optimal control. We establish the characterization of the optimal control and demonstrate uniqueness of the optimal control. Numerical simulations illustrate several cases with Dirichlet and Neumann boundary conditions. We implement an agentbased model for Clostridium difficile transmission in hospitals that accounts for several processes and individual factors including environmental and antibiotic heterogeneity in order to evaluate the efficacy of various control measures aimed at reducing environmental contamination and mitigating the effects of antibiotic use on transmission. In particular, we account for local contamination levels that contribute to the probability of colonization and we account for both the number and type of antibiotic treatments given to patients. Simulations illustrate the relative efficacy of several strategies for the reduction of nosocomial colonizations and nosocomial diseases
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This dissertation contains two types of population models with applications in conservation biology and epidemiology. In particular, it considers models for resource allocation and antimicrobial stewardship. In a population model with a parabolic differential equation and density dependent growth, we study the problem of allocating resources to maximize the net benefit in the conservation of a single species while the cost of the resource allocation is minimized. The net benefit is measured in terms of maximizing population abundance and the goal of maximizing abundance is divided between the goal of maximizing the overall abundance across space and time and the goal of maximizing abundance at the final time. We consider cases that model a fixed amount of resource as well as cases without this constraint. We regard the resource coefficient as a control and we consider cases where this coefficient varies in space and time as well as cases where it varies only in space. We establish the existence and uniqueness of the solution to the state system given a control and the existence of an optimal control. We establish the characterization of the optimal control and demonstrate uniqueness of the optimal control. Numerical simulations illustrate several cases with Dirichlet and Neumann boundary conditions. We implement an agentbased model for Clostridium difficile transmission in hospitals that accounts for several processes and individual factors including environmental and antibiotic heterogeneity in order to evaluate the efficacy of various control measures aimed at reducing environmental contamination and mitigating the effects of antibiotic use on transmission. In particular, we account for local contamination levels that contribute to the probability of colonization and we account for both the number and type of antibiotic treatments given to patients. Simulations illustrate the relative efficacy of several strategies for the reduction of nosocomial colonizations and nosocomial diseases
Modeling Interventions in the Owned Cat Population to Decrease Numbers, Knox County, TN(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Abstract : To find management strategies for controlling the owned cat population in Knox County, TN, the authors formulated a mathematical model using biological properties of such nonhuman animals and spay actions on certain age classes. They constructed this discretetime model to predict the future owned cat population in this county and to evaluate intervention strategies to surgically sterilize some proportion of the population. Using the predicted population size and the number of surgeries for specific scenarios, they showed that focusing on specific age classes can be an effective feature in spay programs
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Abstract : To find management strategies for controlling the owned cat population in Knox County, TN, the authors formulated a mathematical model using biological properties of such nonhuman animals and spay actions on certain age classes. They constructed this discretetime model to predict the future owned cat population in this county and to evaluate intervention strategies to surgically sterilize some proportion of the population. Using the predicted population size and the number of surgeries for specific scenarios, they showed that focusing on specific age classes can be an effective feature in spay programs
Special issue on movement and dispersal in ecology, epidemiology and environmental science by Epidemiology and Environmental Science Everything Disperses to Miami: the Role of Movement and Dispersal in Ecology(
Book
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
Linking Teachers and Mathematicians: The AWM Teacher Partnership Program by
Paosheng Hsu(
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
Optimal Control of Gypsy Moth Populations by Andrew Whittle(
)
1 edition published in 2008 in Undetermined and held by 1 WorldCat member library worldwide
This study investigates an optimal strategy for the cost effective control of gypsy moth populations. Gypsy moth populations cycle between low sparse numbers to high outbreak levels and it is during the outbreak levels that the moths cause extensive damage to plant foliage which can lead to deforestation. Deforestation can result in significant economic damage to infested areas, and consequently, there have been many efforts to control moth populations. One effective method of control is the use of the biocontrol agent, Gypchek, but its production is costly. We develop a mathematical model which combines population dynamics and optimal control of the moth population to explore strategies by which the total cost of the gypsy moth problem (economic damage and cost of Gypchek) can be minimized
1 edition published in 2008 in Undetermined and held by 1 WorldCat member library worldwide
This study investigates an optimal strategy for the cost effective control of gypsy moth populations. Gypsy moth populations cycle between low sparse numbers to high outbreak levels and it is during the outbreak levels that the moths cause extensive damage to plant foliage which can lead to deforestation. Deforestation can result in significant economic damage to infested areas, and consequently, there have been many efforts to control moth populations. One effective method of control is the use of the biocontrol agent, Gypchek, but its production is costly. We develop a mathematical model which combines population dynamics and optimal control of the moth population to explore strategies by which the total cost of the gypsy moth problem (economic damage and cost of Gypchek) can be minimized
Anthrax models involving immunology, epidemiology and controls by Buddhi Raj Pantha(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
This dissertation is divided in two parts. Chapters 2 and 3 consider the use of optimal control theory in anthrax epidemiological models. Models consisting of systems of ordinary differential equations (ODEs) and partial differential differential equations (PDEs) are considered to describe the dynamics of infection spread. Two controls, vaccination of animals and disposal of infected carcasses, are considered and their optimal management strategies are investigated. Chapter 4 involves modeling early host pathogen interaction in an inhalational anthrax infection which consists a system of ODEs that describes early dynamics of bacteriaphagocytic cell interaction associated to an inhalational anthrax infection. First we consider an anthrax epizootic model with system of ODEs describing the disease dynamics between in an animal population. Stability analysis is performed for our system and basic reproduction number is calculated for our system. Two controls representing vaccination of animals and disposal of infected carcasses are investigated in order to minimize the number of infected animals, number of infected carcasses and the cost of vaccination and carcass disposal. Model parameters are estimated using outbreak data, and some numerical results for the optimal control problem are presented. We extend the model to a system of PDEs coupled with ODEs to include animal movement within a region. Both time and space dependent controls are applied into this hybrid system. Existence and uniqueness results are established for weak solutions of the system. The existence of an optimal control pair is proven and the characterization of the controls are derived from corresponding adjoint systems. Numerical results are completed to illustrate various scenarios. The immunological model in Chapter 4 consists of a system of ODEs that consists of the early host pathogen interaction within a lung. The modeling assumptions are derived from an experimental setting and the model parameters are estimated using these experimental data. Our goal is to understand the early processes such as the spore phagocytosis, spore germination, killing of the germinated spores and their replication. Different functional forms for germination and killing are considered and two different models based on bacterial stage are considered to better fit the experimental data
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
This dissertation is divided in two parts. Chapters 2 and 3 consider the use of optimal control theory in anthrax epidemiological models. Models consisting of systems of ordinary differential equations (ODEs) and partial differential differential equations (PDEs) are considered to describe the dynamics of infection spread. Two controls, vaccination of animals and disposal of infected carcasses, are considered and their optimal management strategies are investigated. Chapter 4 involves modeling early host pathogen interaction in an inhalational anthrax infection which consists a system of ODEs that describes early dynamics of bacteriaphagocytic cell interaction associated to an inhalational anthrax infection. First we consider an anthrax epizootic model with system of ODEs describing the disease dynamics between in an animal population. Stability analysis is performed for our system and basic reproduction number is calculated for our system. Two controls representing vaccination of animals and disposal of infected carcasses are investigated in order to minimize the number of infected animals, number of infected carcasses and the cost of vaccination and carcass disposal. Model parameters are estimated using outbreak data, and some numerical results for the optimal control problem are presented. We extend the model to a system of PDEs coupled with ODEs to include animal movement within a region. Both time and space dependent controls are applied into this hybrid system. Existence and uniqueness results are established for weak solutions of the system. The existence of an optimal control pair is proven and the characterization of the controls are derived from corresponding adjoint systems. Numerical results are completed to illustrate various scenarios. The immunological model in Chapter 4 consists of a system of ODEs that consists of the early host pathogen interaction within a lung. The modeling assumptions are derived from an experimental setting and the model parameters are estimated using these experimental data. Our goal is to understand the early processes such as the spore phagocytosis, spore germination, killing of the germinated spores and their replication. Different functional forms for germination and killing are considered and two different models based on bacterial stage are considered to better fit the experimental data
An obstacle control problem with a source by David R Adams(
Book
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
Investigating advection control in competitive PDE systems and environmental transmission in Johne's disease ODE models by Kokum Rekha De Silva(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
We extend the work on optimal control of advective direction in a reactiondiffusion population model to a system representing two competing populations. We investigate the choice of movement direction to benefit a population. First, the advective direction in one of the populations in a competition model is the control. Next, we extend the work by taking the advective directions of both populations as controls. In both these cases the objective is to maximize a weighted combination of the two populations while minimizing the cost involved in the species movement. Mathematical analysis is completed to derive the optimality system and numerical results illustrating solutions of this system are presented. Johne's disease is a bacterial infection caused by Mycobacterium avium subspecies paratuberculosis (MAP). It is a chronic, progressive, and infectious disease which has a long incubation period and probably not curable. The main problem with the disease is the reduction of milk production in infected dairy cows. We develop a deterministic model to describe the dynamics of the Johne's disease in a dairy farm. In this model we use a system of ordinary differential equations to describe the behavior of Johne's disease among dairy cows considering the progression of the disease and the age structure of the cows. We analyze the behavior of the Johne's disease by investigating the effects of the persistence of the bacteria in the environment. Stability and numerical results are computed
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
We extend the work on optimal control of advective direction in a reactiondiffusion population model to a system representing two competing populations. We investigate the choice of movement direction to benefit a population. First, the advective direction in one of the populations in a competition model is the control. Next, we extend the work by taking the advective directions of both populations as controls. In both these cases the objective is to maximize a weighted combination of the two populations while minimizing the cost involved in the species movement. Mathematical analysis is completed to derive the optimality system and numerical results illustrating solutions of this system are presented. Johne's disease is a bacterial infection caused by Mycobacterium avium subspecies paratuberculosis (MAP). It is a chronic, progressive, and infectious disease which has a long incubation period and probably not curable. The main problem with the disease is the reduction of milk production in infected dairy cows. We develop a deterministic model to describe the dynamics of the Johne's disease in a dairy farm. In this model we use a system of ordinary differential equations to describe the behavior of Johne's disease among dairy cows considering the progression of the disease and the age structure of the cows. We analyze the behavior of the Johne's disease by investigating the effects of the persistence of the bacteria in the environment. Stability and numerical results are computed
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
Useful Links
Associated Subjects
BiologyMathematical models Boundary value problems Communicable diseasesTransmissionMathematical models Control theory Difference equations Differential equations Differential equations, Parabolic Differential equations, Partial Diffusion of innovationsMathematical models Dynamic programming EpidemiologyMathematical models Feral swineControl HeatTransmission Introduced organisms Mast (Nuts) Mathematical optimization Mathematics Multiagent systems Paratuberculosis Public healthMathematical models Reactiondiffusion equations Resource allocationMathematical models United StatesGreat Smoky Mountains National Park Vegetation surveys
Covers
Alternative Names
Lenhart, Suzanne M. 1954
Suzanne Lenhart American mathematician
Languages