American Institute of Mathematical Sciences

Advanced
2006, 3(4): 635-660. doi: 10.3934/mbe.2006.3.635

Modeling shrimp biomass and viral infection for production of biological countermeasures

H. Thomas Banks 1, , V. A. Bokil 1, , Shuhua Hu 1, , A. K. Dhar 2, , R. A. Bullis 2, , C. L. Browdy 3, and  F.C.T. Allnutt 2,

1. 

Center for Research in Scientific Computation, Raleigh, NC 27695-8205, United States, United States
2. 

Advanced Bionutrition Corporation, 6430 Dobbin Road, Columbia, MD 21045, Colombia, Colombia, Colombia
3. 

Marine Resources Research Institute, South Carolina Department of Natural Resources, 217 Ft. Johnson Rd. (P.O. Box 12559), Charleston, SC 29422, United States

Received  December 2005 Revised  April 2006 Published  August 2006

In this paper we develop a mathematical model for the rapid production of large quantities of therapeutic and preventive countermeasures. We couple equations for biomass production with those for vaccine production in shrimp that have been infected with a recombinant viral vector expressing a foreign antigen. The model system entails both size and class-age structure.
Keywords: latently-acutely infected., size/class-age structured population models, shrimp growth/viral pro-gression dynamics.
Mathematics Subject Classification: 92D25, 92D30, 35L60, 65M0.
Citation: H. Thomas Banks, V. A. Bokil, Shuhua Hu, A. K. Dhar, R. A. Bullis, C. L. Browdy, F.C.T. Allnutt. Modeling shrimp biomass and viral infection for production of biological countermeasures. Mathematical Biosciences & Engineering, 2006, 3 (4) : 635-660. doi: 10.3934/mbe.2006.3.635
[1]

L. M. Abia, O. Angulo, J.C. López-Marcos. Size-structured population dynamics models and their numerical solutions. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 1203-1222. doi: 10.3934/dcdsb.2004.4.1203
[2]

Sebastian Aniţa, Ana-Maria Moşsneagu. Optimal harvesting for age-structured population dynamics with size-dependent control. Mathematical Control and Related Fields, 2019, 9 (4) : 607-621. doi: 10.3934/mcrf.2019043
[3]

Jacek Banasiak, Wilson Lamb. Coagulation, fragmentation and growth processes in a size structured population. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 563-585. doi: 10.3934/dcdsb.2009.11.563
[4]

Frédérique Billy, Jean Clairambault, Franck Delaunay, Céline Feillet, Natalia Robert. Age-structured cell population model to study the influence of growth factors on cell cycle dynamics. Mathematical Biosciences & Engineering, 2013, 10 (1) : 1-17. doi: 10.3934/mbe.2013.10.1
[5]

Yicang Zhou, Paolo Fergola. Dynamics of a discrete age-structured SIS models. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 841-850. doi: 10.3934/dcdsb.2004.4.841
[6]

Patrick W. Nelson, Michael A. Gilchrist, Daniel Coombs, James M. Hyman, Alan S. Perelson. An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells. Mathematical Biosciences & Engineering, 2004, 1 (2) : 267-288. doi: 10.3934/mbe.2004.1.267
[7]

Zhihua Liu, Hui Tang, Pierre Magal. Hopf bifurcation for a spatially and age structured population dynamics model. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1735-1757. doi: 10.3934/dcdsb.2015.20.1735
[8]

Jacques Henry. For which objective is birth process an optimal feedback in age structured population dynamics?. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 107-114. doi: 10.3934/dcdsb.2007.8.107
[9]

Z.-R. He, M.-S. Wang, Z.-E. Ma. Optimal birth control problems for nonlinear age-structured population dynamics. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 589-594. doi: 10.3934/dcdsb.2004.4.589
[10]

Tristan Roget. On the long-time behaviour of age and trait structured population dynamics. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2551-2576. doi: 10.3934/dcdsb.2018265
[11]

Yicang Zhou, Zhien Ma. Global stability of a class of discrete age-structured SIS models with immigration. Mathematical Biosciences & Engineering, 2009, 6 (2) : 409-425. doi: 10.3934/mbe.2009.6.409
[12]

Hal L. Smith, Horst R. Thieme. Persistence and global stability for a class of discrete time structured population models. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4627-4646. doi: 10.3934/dcds.2013.33.4627
[13]

Yolanda Guerrero–Sánchez, Muhammad Umar, Zulqurnain Sabir, Juan L. G. Guirao, Muhammad Asif Zahoor Raja. Solving a class of biological HIV infection model of latently infected cells using heuristic approach. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3611-3628. doi: 10.3934/dcdss.2020431
[14]

Thomas Lorenz. Nonlocal hyperbolic population models structured by size and spatial position: Well-posedness. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4547-4628. doi: 10.3934/dcdsb.2019156
[15]

Mustapha Mokhtar-Kharroubi, Quentin Richard. Spectral theory and time asymptotics of size-structured two-phase population models. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 2969-3004. doi: 10.3934/dcdsb.2020048
[16]

Yingli Pan, Ying Su, Junjie Wei. Bistable waves of a recursive system arising from seasonal age-structured population models. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 511-528. doi: 10.3934/dcdsb.2018184
[17]

Yacouba Simporé, Oumar Traoré. Null controllability of a nonlinear age, space and two-sex structured population dynamics model. Mathematical Control and Related Fields, 2021  doi: 10.3934/mcrf.2021052
[18]

Fred Brauer. A model for an SI disease in an age - structured population. Discrete and Continuous Dynamical Systems - B, 2002, 2 (2) : 257-264. doi: 10.3934/dcdsb.2002.2.257
[19]

Zhihua Liu, Rong Yuan. Takens–Bogdanov singularity for age structured models. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : 2041-2056. doi: 10.3934/dcdsb.2019201
[20]

Mohammed Nor Frioui, Tarik Mohammed Touaoula, Bedreddine Ainseba. Global dynamics of an age-structured model with relapse. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : 2245-2270. doi: 10.3934/dcdsb.2019226

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (35)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy