Mathematical Biosciences and Engineering, 2008, 5(3): 549-565. doi: 10.3934/mbe.2008.5.549.

Primary: 92B05, 37N25; Secondary: 37G10.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

An extension of the Beretta-Kuang model of viral diseases

1. Institut für Umweltsystemforschung, Universität Osnabrück
2. Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino

A model for the complete life cycle of marine viruses is presented. The Beretta-Kuang model introduces an explicit equation for viral particles but the replication process of viral particles in their hosts is not considered. The extended model keeps the structure of the original model. This makes it possible to estimate the growth parameters of the viruses for a given parametrisation of the Beretta-Kuang model.
  Figure/Table
  Supplementary
  Article Metrics

Keywords viral replication; lytic viral infection; Hopf bifurcation.

Citation: Ivo Siekmann, Horst Malchow, Ezio Venturino. An extension of the Beretta-Kuang model of viral diseases. Mathematical Biosciences and Engineering, 2008, 5(3): 549-565. doi: 10.3934/mbe.2008.5.549

 

This article has been cited by

  • 1. Banamali Maji, Joydeb Bhattacharyya, Samares Pal, Potential effects of invasive Pterois volitans in coral reefs, Letters in Biomathematics, 2016, 3, 1, 119, 10.1080/23737867.2016.1213146
  • 2. Joydeb Bhattacharyya, Samares Pal, Stage-structured cannibalism with delay in maturation and harvesting of an adult predator, Journal of Biological Physics, 2013, 39, 1, 37, 10.1007/s10867-012-9284-6
  • 3. Joydeb Bhattacharyya, Samares Pal, Stage-Structured Cannibalism in a Ratio-Dependent System with Constant Prey Refuge and Harvesting of Matured Predator, Differential Equations and Dynamical Systems, 2016, 24, 3, 345, 10.1007/s12591-016-0299-5
  • 4. Nicholas R. Record, David Talmy, Selina Våge, Quantifying Tradeoffs for Marine Viruses, Frontiers in Marine Science, 2016, 3, 10.3389/fmars.2016.00251
  • 5. A.K. Misra, Alok Gupta, Ezio Venturino, Cholera dynamics with Bacteriophage infection: A mathematical study, Chaos, Solitons & Fractals, 2016, 91, 610, 10.1016/j.chaos.2016.08.008
  • 6. À. Calsina, J.J. Rivaud, A size structured model for bacteria–phages interaction, Nonlinear Analysis: Real World Applications, 2014, 15, 100, 10.1016/j.nonrwa.2013.06.004
  • 7. Joydeb Bhattacharyya, Samares Pal, Macroalgal allelopathy in the emergence of coral diseases, Discrete and Continuous Dynamical Systems - Series B, 2017, 22, 5, 26, 10.3934/dcdsb.2017146
  • 8. Joydeb Bhattacharyya, Samares Pal, The role of space in stage-structured cannibalism with harvesting of an adult predator, Computers & Mathematics with Applications, 2013, 66, 3, 339, 10.1016/j.camwa.2013.05.011
  • 9. E. Venturino, V. Volpert, Ecoepidemiology: a More Comprehensive View of Population Interactions, Mathematical Modelling of Natural Phenomena, 2016, 11, 1, 49, 10.1051/mmnp/201611104
  • 10. Julia E. Middleton, Joaquín Martínez Martínez, William H. Wilson, Nicholas R. Record, Functional dynamics of Emiliania huxleyi virus-host interactions across multiple spatial scales, Limnology and Oceanography, 2017, 62, 3, 922, 10.1002/lno.10476
  • 11. Joydeb Bhattacharyya, Samares Pal, Yong Hong, Dynamics of asymmetric intraguild predation with time lags in reproduction and maturation, Cogent Mathematics, 2015, 2, 1, 10.1080/23311835.2015.1021604
  • 12. Joydeb Bhattacharyya, Samares Pal, Microbial disease in coral reefs: An ecosystem in transition, Discrete and Continuous Dynamical Systems - Series B, 2015, 21, 2, 373, 10.3934/dcdsb.2016.21.373
  • 13. Joydeb Bhattacharyya, Samares Pal, Macroalgal allelopathy in the emergence of coral diseases, Discrete and Continuous Dynamical Systems - Series B, 2017, 22, 3, 741, 10.3934/dcdsb.2017036
  • 14. C.J. Rhodes, A.P. Martin, The influence of viral infection on a plankton ecosystem undergoing nutrient enrichment, Journal of Theoretical Biology, 2010, 265, 3, 225, 10.1016/j.jtbi.2010.04.022
  • 15. Josep L. Garcia-Domingo, Joan Saldaña, Extinction threshold for spatial forest dynamics with height structure, Journal of Theoretical Biology, 2011, 276, 1, 138, 10.1016/j.jtbi.2011.02.003
  • 16. DAAN J. GERLA, ALENA S. GSELL, BOB W. KOOI, BAS W. IBELINGS, ELLEN VAN DONK, WOLF M. MOOIJ, Alternative states and population crashes in a resource-susceptible-infected model for planktonic parasites and hosts, Freshwater Biology, 2013, 58, 3, 538, 10.1111/fwb.12010
  • 17. Halil I. Egilmez, Andrew Yu. Morozov, Martha R. J. Clokie, Jinyu Shan, Andrey Letarov, Edouard E. Galyov, Temperature-dependent virus lifecycle choices may reveal and predict facets of the biology of opportunistic pathogenic bacteria, Scientific Reports, 2018, 8, 1, 10.1038/s41598-018-27716-3
  • 18. Andrew B. Holder, Marianito R. Rodrigo, An integration-based method for estimating parameters in a system of differential equations, Applied Mathematics and Computation, 2013, 219, 18, 9700, 10.1016/j.amc.2013.03.052

Reader Comments

your name: *   your email: *  

Copyright Info: 2008, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved