Page 1. NATURAL RESOURCE MODELING Volume 18, Number 3, Fall 2005 CONTROL OF A METAPOPULATION HARV... more Page 1. NATURAL RESOURCE MODELING Volume 18, Number 3, Fall 2005 CONTROL OF A METAPOPULATION HARVESTING MODEL FOR BLACK BEARS RENÉ A. SALINAS Department of Mathematical Sciences Appalachian ...
ABSTRACT Soil heterotrophic respiration depends not only on temperature but also on the dynamic p... more ABSTRACT Soil heterotrophic respiration depends not only on temperature but also on the dynamic properties of soil organic carbon (SOC). In modeling study, it is necessary to separate the SOC into multiple pools according to their turnover time. The pool sizes and their turnover time can only be determined indirectly. In this study, we show how the assimilation of carbon flux data into a soil carbon model can be used to obtain the needed information. An adjoint system is applied to minimize the difference between the flux data and the model simulation. It also provides the sensitivity of the model to each control variable.
ABSTRACT We study the problem of allocating resources to maximize the net benefit in the conserva... more ABSTRACT 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 population model is a parabolic differential equation with density dependent growth and spatial-temporal resource control coefficient. The existence of an optimal control and the uniqueness and characterization of the optimal control are established. Numerical simulations illustrate several cases with Dirichlet and Neumann boundary conditions.
... For a background on stochastic models applied to biological populations, see books by Allen [... more ... For a background on stochastic models applied to biological populations, see books by Allen [3], Ricciardi [4], and Ludwig [5]. For more specific examples of optimal harvesting in stochastic environments, see articles: Hanson and Ryan [6], Ludwig and Varah [7, 8]. Salinas et al. ...
We consider a bilinear optimal control problem with the state equation being a Kirchho plate equa... more We consider a bilinear optimal control problem with the state equation being a Kirchho plate equation. The control is a function of the spatial variables and acts as a multiplier of the velocity term. The unique optimal control, driving the state solution close to a desired evolution function, is characterized in terms of the solution of the optimality system.
Therapeutic strategies to correct an excessive immune response to pathogenic infection is investi... more Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory response to a pathogenic insult with two therapeutic control inputs which have either a direct pro- or anti-inflammatory effect in the given system. We use Pontryagin's maximum principle and discuss necessary optimality conditions. We consider both an L(1) type objective functional as well as an L(2) type objective. For the former, the presence of singular control will be addressed. For each case, numerical simulations using a nonlinear programming optimization solver to acquire different drug treatment strategies are presented and discussed. The results provide insight for possible treatment strategies and the methods could be a relevant tool for future practice to assist in better prediction of clinical outcomes and subsequently better trea...
Use of enzyme-linked immunosorbent assay (ELISA) is recommended for control of Johne's diseas... more Use of enzyme-linked immunosorbent assay (ELISA) is recommended for control of Johne's disease (JD) in the cattle industry. A recent report showed that prevalence of JD in dairy farms could be reduced by applying an ELISA-based control strategy, even though the sensitivity of the current ELISA has been reported to be lower than 30%. We previously developed a more sensitive ELISA test (EVELISA; Ethanol Vortex ELISA) for diagnosis of JD and, in this report, aimed to evaluate cost-effectiveness of the EVELISA in JD control compared to that of a current ELISA test. For simulation of population dynamics, we developed a deterministic, discrete-time mathematical model incorporating contact structure, possibility of adult infection and the concept of order of events. In our model, the number of animals infected with the causative agent of JD, Mycobacterium avium subsp. paratuberculosis (MAP), increases in a 10-year simulation if no JD control measure is applied. When test results of ELI...
Page 1. NATURAL RESOURCE MODELING Volume 18, Number 3, Fall 2005 CONTROL OF A METAPOPULATION HARV... more Page 1. NATURAL RESOURCE MODELING Volume 18, Number 3, Fall 2005 CONTROL OF A METAPOPULATION HARVESTING MODEL FOR BLACK BEARS RENÉ A. SALINAS Department of Mathematical Sciences Appalachian ...
ABSTRACT Soil heterotrophic respiration depends not only on temperature but also on the dynamic p... more ABSTRACT Soil heterotrophic respiration depends not only on temperature but also on the dynamic properties of soil organic carbon (SOC). In modeling study, it is necessary to separate the SOC into multiple pools according to their turnover time. The pool sizes and their turnover time can only be determined indirectly. In this study, we show how the assimilation of carbon flux data into a soil carbon model can be used to obtain the needed information. An adjoint system is applied to minimize the difference between the flux data and the model simulation. It also provides the sensitivity of the model to each control variable.
ABSTRACT We study the problem of allocating resources to maximize the net benefit in the conserva... more ABSTRACT 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 population model is a parabolic differential equation with density dependent growth and spatial-temporal resource control coefficient. The existence of an optimal control and the uniqueness and characterization of the optimal control are established. Numerical simulations illustrate several cases with Dirichlet and Neumann boundary conditions.
... For a background on stochastic models applied to biological populations, see books by Allen [... more ... For a background on stochastic models applied to biological populations, see books by Allen [3], Ricciardi [4], and Ludwig [5]. For more specific examples of optimal harvesting in stochastic environments, see articles: Hanson and Ryan [6], Ludwig and Varah [7, 8]. Salinas et al. ...
We consider a bilinear optimal control problem with the state equation being a Kirchho plate equa... more We consider a bilinear optimal control problem with the state equation being a Kirchho plate equation. The control is a function of the spatial variables and acts as a multiplier of the velocity term. The unique optimal control, driving the state solution close to a desired evolution function, is characterized in terms of the solution of the optimality system.
Therapeutic strategies to correct an excessive immune response to pathogenic infection is investi... more Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory response to a pathogenic insult with two therapeutic control inputs which have either a direct pro- or anti-inflammatory effect in the given system. We use Pontryagin's maximum principle and discuss necessary optimality conditions. We consider both an L(1) type objective functional as well as an L(2) type objective. For the former, the presence of singular control will be addressed. For each case, numerical simulations using a nonlinear programming optimization solver to acquire different drug treatment strategies are presented and discussed. The results provide insight for possible treatment strategies and the methods could be a relevant tool for future practice to assist in better prediction of clinical outcomes and subsequently better trea...
Use of enzyme-linked immunosorbent assay (ELISA) is recommended for control of Johne's diseas... more Use of enzyme-linked immunosorbent assay (ELISA) is recommended for control of Johne's disease (JD) in the cattle industry. A recent report showed that prevalence of JD in dairy farms could be reduced by applying an ELISA-based control strategy, even though the sensitivity of the current ELISA has been reported to be lower than 30%. We previously developed a more sensitive ELISA test (EVELISA; Ethanol Vortex ELISA) for diagnosis of JD and, in this report, aimed to evaluate cost-effectiveness of the EVELISA in JD control compared to that of a current ELISA test. For simulation of population dynamics, we developed a deterministic, discrete-time mathematical model incorporating contact structure, possibility of adult infection and the concept of order of events. In our model, the number of animals infected with the causative agent of JD, Mycobacterium avium subsp. paratuberculosis (MAP), increases in a 10-year simulation if no JD control measure is applied. When test results of ELI...
Uploads