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485 results on '"Martcheva, Maia"'

1. Solving Singular Control Problems in Mathematical Biology, Using PASA

Author

Atkins, Summer, Aghaee, Mahya, Martcheva, Maia, and Hager, William

Subjects
Mathematics - Optimization and Control
Abstract

In this paper, we will demonstrate how to use a nonlinear polyhedral constrained optimization solver called the Polyhedral Active Set Algorithm (PASA) for solving a general singular control problem. We present methods of discretizing a general optimal control problem that involves the use of the gradient of the Lagrangian for computing the gradient of the cost functional so that PASA can be applied. When a numerical solution contains artifacts that resemble "chattering'', a phenomenon where the control oscillates wildly along the singular region, we recommend a method of regularizing the singular control problem by adding a term to the cost functional that measures a scalar multiple of the total variation of the control, where the scalar is viewed as a tuning parameter. We then demonstrate PASA's performance on three singular control problems that give rise to different applications of mathematical biology. We also provide some exposition on the heuristics that we use in determining an appropriate size for the tuning parameter.

Published
2020

3. Modeling the effects of prosocial awareness on COVID-19 dynamics: A case study on Colombia

Author

Ghosh, Indrajit and Martcheva, Maia

Subjects
Quantitative Biology - Populations and Evolution, Physics - Physics and Society
Abstract

The ongoing COVID-19 pandemic has affected most of the countries on Earth. It has become a pandemic outbreak with more than 24 million confirmed infections and above 840 thousand deaths worldwide. In this study, we consider a mathematical model on COVID-19 transmission with the prosocial awareness effect. The proposed model can have four equilibrium states based on different parametric conditions. The local and global stability conditions for awareness free, disease-free equilibrium is studied. Using Lyapunov function theory and LaSalle Invariance Principle, the disease-free equilibrium is shown globally asymptotically stable under some parametric constraints. The existence of unique awareness free, endemic equilibrium and unique endemic equilibrium is presented. We calibrate our proposed model parameters to fit daily cases and deaths from Colombia. Sensitivity analysis indicates that the transmission rate and learning factor related to awareness of susceptibles are very crucial for reduction in disease related deaths. Finally, we assess the impact of prosocial awareness during the outbreak and compare this strategy with popular control measures. Results indicate that prosocial awareness has competitive potential to flatten the curve.

Published
2020
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9. Class Age-Structured Epidemic Models

Author

Li, Xue-Zhi, Yang, Junyuan, Martcheva, Maia, Bloch, Anthony, Series Editor, Glass, L., Advisory Editor, Kohn, R., Advisory Editor, Epstein, Charles L., Series Editor, Krishnaprasad, P. S., Advisory Editor, Goriely, Alain, Series Editor, Greengard, Leslie, Series Editor, Fowler, Andrew, Advisory Editor, Peskin, C., Advisory Editor, Sastry, S. S., Advisory Editor, Sneyd, J., Advisory Editor, Durrett, Rick, Advisory Editor, Li, Xue-Zhi, Yang, Junyuan, and Martcheva, Maia

Published
2020
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10. Metapopulation and Multigroup Age-Structured Models

Author

Li, Xue-Zhi, Yang, Junyuan, Martcheva, Maia, Bloch, Anthony, Series Editor, Glass, L., Advisory Editor, Kohn, R., Advisory Editor, Epstein, Charles L., Series Editor, Krishnaprasad, P. S., Advisory Editor, Goriely, Alain, Series Editor, Greengard, Leslie, Series Editor, Fowler, Andrew, Advisory Editor, Peskin, C., Advisory Editor, Sastry, S. S., Advisory Editor, Sneyd, J., Advisory Editor, Durrett, Rick, Advisory Editor, Li, Xue-Zhi, Yang, Junyuan, and Martcheva, Maia

Published
2020
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11. Vector-Borne Age-Structured Models

Author

Li, Xue-Zhi, Yang, Junyuan, Martcheva, Maia, Bloch, Anthony, Series Editor, Glass, L., Advisory Editor, Kohn, R., Advisory Editor, Epstein, Charles L., Series Editor, Krishnaprasad, P. S., Advisory Editor, Goriely, Alain, Series Editor, Greengard, Leslie, Series Editor, Fowler, Andrew, Advisory Editor, Peskin, C., Advisory Editor, Sastry, S. S., Advisory Editor, Sneyd, J., Advisory Editor, Durrett, Rick, Advisory Editor, Li, Xue-Zhi, Yang, Junyuan, and Martcheva, Maia

Published
2020
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12. Age-Since-Infection Structured Models Based on Game Theory

Author

Li, Xue-Zhi, Yang, Junyuan, Martcheva, Maia, Bloch, Anthony, Series Editor, Glass, L., Advisory Editor, Kohn, R., Advisory Editor, Epstein, Charles L., Series Editor, Krishnaprasad, P. S., Advisory Editor, Goriely, Alain, Series Editor, Greengard, Leslie, Series Editor, Fowler, Andrew, Advisory Editor, Peskin, C., Advisory Editor, Sastry, S. S., Advisory Editor, Sneyd, J., Advisory Editor, Durrett, Rick, Advisory Editor, Li, Xue-Zhi, Yang, Junyuan, and Martcheva, Maia

Published
2020
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13. Age-Structured Epidemic Models

Author

Li, Xue-Zhi, Yang, Junyuan, Martcheva, Maia, Bloch, Anthony, Series Editor, Glass, L., Advisory Editor, Kohn, R., Advisory Editor, Epstein, Charles L., Series Editor, Krishnaprasad, P. S., Advisory Editor, Goriely, Alain, Series Editor, Greengard, Leslie, Series Editor, Fowler, Andrew, Advisory Editor, Peskin, C., Advisory Editor, Sastry, S. S., Advisory Editor, Sneyd, J., Advisory Editor, Durrett, Rick, Advisory Editor, Li, Xue-Zhi, Yang, Junyuan, and Martcheva, Maia

Published
2020
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14. Age Structured Models on Complex Networks

Author

Li, Xue-Zhi, Yang, Junyuan, Martcheva, Maia, Bloch, Anthony, Series Editor, Glass, L., Advisory Editor, Kohn, R., Advisory Editor, Epstein, Charles L., Series Editor, Krishnaprasad, P. S., Advisory Editor, Goriely, Alain, Series Editor, Greengard, Leslie, Series Editor, Fowler, Andrew, Advisory Editor, Peskin, C., Advisory Editor, Sastry, S. S., Advisory Editor, Sneyd, J., Advisory Editor, Durrett, Rick, Advisory Editor, Li, Xue-Zhi, Yang, Junyuan, and Martcheva, Maia

Published
2020
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15. Nested Immuno-Epidemiological Models

Author

Li, Xue-Zhi, Yang, Junyuan, Martcheva, Maia, Bloch, Anthony, Series Editor, Glass, L., Advisory Editor, Kohn, R., Advisory Editor, Epstein, Charles L., Series Editor, Krishnaprasad, P. S., Advisory Editor, Goriely, Alain, Series Editor, Greengard, Leslie, Series Editor, Fowler, Andrew, Advisory Editor, Peskin, C., Advisory Editor, Sastry, S. S., Advisory Editor, Sneyd, J., Advisory Editor, Durrett, Rick, Advisory Editor, Li, Xue-Zhi, Yang, Junyuan, and Martcheva, Maia

Published
2020
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16. Linear Age-Structured Population Models as a Base of Age-Structured Epidemic Models

Author

Li, Xue-Zhi, Yang, Junyuan, Martcheva, Maia, Bloch, Anthony, Series Editor, Glass, L., Advisory Editor, Kohn, R., Advisory Editor, Epstein, Charles L., Series Editor, Krishnaprasad, P. S., Advisory Editor, Goriely, Alain, Series Editor, Greengard, Leslie, Series Editor, Fowler, Andrew, Advisory Editor, Peskin, C., Advisory Editor, Sastry, S. S., Advisory Editor, Sneyd, J., Advisory Editor, Durrett, Rick, Advisory Editor, Li, Xue-Zhi, Yang, Junyuan, and Martcheva, Maia

Published
2020
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17. Validation of a Multi-Strain HIV Within-Host Model with AIDS Clinical Studies.

Author

Tuncer, Necibe, Ghods, Kia, Sreejithkumar, Vivek, Garbowit, Adin, Zagha, Mark, and Martcheva, Maia

Subjects
VIRAL load, STRAIN rate, DRUG resistance, STRUCTURAL models, AIDS
Abstract

We used a previously introduced HIV within-host model with sensitive and resistant strains and validated it with two data sets. The first data set is from a clinical study that investigated multi-drug treatments and measured the total CD4+ cell count and viral load. All nine patients in this data set experienced virologic failure. The second data set includes a unique patient who was treated with a unique drug and for whom both the sensitive and resistant strains were measured as well as the CD4+ cells. We studied the structural identifiability of the model with respect to each data set. With respect to the first data set, the model was structurally identifiable when the viral production rate of the sensitive strain was fixed and distinct from the viral production rate of the resistant strain. With respect to the second data set, the model was always structurally identifiable. We fit the model to the first data set using nonlinear mixed effect modeling in Monolix and estimated the population-level parameters. We inferred that the average time to emergence of a resistant strain is 844 days after treatment starts. We fit the model to the second data set and found out that the all the parameters except the mutation rate were practically identifiable. [ABSTRACT FROM AUTHOR]

Published
2024
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27. Forward Hysteresis and Backward Bifurcation Caused by Culling in an Avian Influenza Model

Author

Gulbudak, Hayriye and Martcheva, Maia

Subjects
Quantitative Biology - Populations and Evolution
Abstract

The emerging threat of a human pandemic caused by the H5N1 avian influenza virus strain magnifies the need for controlling the incidence of H5N1 infection in domestic bird populations. Culling is one of the most widely used control measures and has proved effective for isolated outbreaks. However, the socio-economic impacts of mass culling, in the face of a disease which has become endemic in many regions of the world, can affect the implementation and success of culling as a control measure. We use mathematical modeling to understand the dynamics of avian influenza under different culling approaches. We incorporate culling into an SI model by considering the per capita culling rates to be general functions of the number of infected birds. Complex dynamics of the system, such as backward bifurcation and forward hysteresis, along with bi-stability, are detected and analyzed for two distinct culling scenarios. In these cases, employing other control measures temporarily can drastically change the dynamics of the solutions to a more favorable outcome for disease control.

Published
2013

32. Fitting Models to Data

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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33. Multistrain Disease Dynamics

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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34. Control Strategies

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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35. Analysis of Complex ODE Epidemic Models: Global Stability

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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36. Techniques for Computing

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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37. Vector-Borne Diseases

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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38. Introduction to Epidemic Modeling

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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39. The SIR Model with Demography: General Properties of Planar Systems

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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40. Introduction

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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41. Discrete Epidemic Models

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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42. Immuno-Epidemiological Modeling

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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43. Spatial Heterogeneity in Epidemiological Models

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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44. Class-Age Structured Epidemic Models

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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45. Age-Structured Epidemic Models

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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46. Zoonotic Disease, Avian Influenza, and Nonautonomous Models

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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47. Ecological Context of Epidemiology

Author

Martcheva, Maia, Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Newton, Paul, Series editor, Holmes, Philip, Editor-in-chief, Keener, James, Series editor, Kohn, Robert, Series editor, Pego, Robert, Series editor, Witelski, Thomas, Series editor, Peskin, Charles, Series editor, Singer, Amit, Series editor, Stevens, Angela, Series editor, Stuart, Andrew, Series editor, Ryzhik, Lenya, Series editor, and Martcheva, Maia

Published
2015
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