# American Institute of Mathematical Sciences

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

## An extension of the Beretta-Kuang model of viral diseases

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

Received  December 2007 Revised  February 2008 Published  June 2008

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.
Citation: Ivo Siekmann, Horst Malchow, Ezio Venturino. An extension of the Beretta-Kuang model of viral diseases. Mathematical Biosciences & Engineering, 2008, 5 (3) : 549-565. doi: 10.3934/mbe.2008.5.549
 [1] Xiulan Lai, Xingfu Zou. Dynamics of evolutionary competition between budding and lytic viral release strategies. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1091-1113. doi: 10.3934/mbe.2014.11.1091 [2] Don A. Jones, Hal L. Smith, Horst R. Thieme. Spread of viral infection of immobilized bacteria. Networks and Heterogeneous Media, 2013, 8 (1) : 327-342. doi: 10.3934/nhm.2013.8.327 [3] Hongying Shu, Lin Wang. Global stability and backward bifurcation of a general viral infection model with virus-driven proliferation of target cells. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1749-1768. doi: 10.3934/dcdsb.2014.19.1749 [4] Sukhitha W. Vidurupola, Linda J. S. Allen. Basic stochastic models for viral infection within a host. Mathematical Biosciences & Engineering, 2012, 9 (4) : 915-935. doi: 10.3934/mbe.2012.9.915 [5] Shaoli Wang, Huixia Li, Fei Xu. Monotonic and nonmonotonic immune responses in viral infection systems. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 141-165. doi: 10.3934/dcdsb.2021035 [6] Jaouad Danane. Optimal control of viral infection model with saturated infection rate. Numerical Algebra, Control and Optimization, 2021, 11 (3) : 363-375. doi: 10.3934/naco.2020031 [7] 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 [8] Stephen Pankavich, Deborah Shutt. An in-host model of HIV incorporating latent infection and viral mutation. Conference Publications, 2015, 2015 (special) : 913-922. doi: 10.3934/proc.2015.0913 [9] Wei Wang, Wanbiao Ma, Xiulan Lai. Sufficient conditions for global dynamics of a viral infection model with nonlinear diffusion. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3989-4011. doi: 10.3934/dcdsb.2020271 [10] Yu Ji. Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences & Engineering, 2015, 12 (3) : 525-536. doi: 10.3934/mbe.2015.12.525 [11] Zhixing Hu, Weijuan Pang, Fucheng Liao, Wanbiao Ma. Analysis of a CD4$^+$ T cell viral infection model with a class of saturated infection rate. Discrete and Continuous Dynamical Systems - B, 2014, 19 (3) : 735-745. doi: 10.3934/dcdsb.2014.19.735 [12] Alexander Rezounenko. Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1547-1563. doi: 10.3934/dcdsb.2017074 [13] Jinliang Wang, Jiying Lang, Xianning Liu. Global dynamics for viral infection model with Beddington-DeAngelis functional response and an eclipse stage of infected cells. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3215-3233. doi: 10.3934/dcdsb.2015.20.3215 [14] Zhikun She, Xin Jiang. Threshold dynamics of a general delayed within-host viral infection model with humoral immunity and two modes of virus transmission. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3835-3861. doi: 10.3934/dcdsb.2020259 [15] Alexander Rezounenko. Viral infection model with diffusion and state-dependent delay: Stability of classical solutions. Discrete and Continuous Dynamical Systems - B, 2018, 23 (3) : 1091-1105. doi: 10.3934/dcdsb.2018143 [16] Yu Ji, Lan Liu. Global stability of a delayed viral infection model with nonlinear immune response and general incidence rate. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 133-149. doi: 10.3934/dcdsb.2016.21.133 [17] Simona Viale, Elisa Caudera, Sandro Bertolino, Ezio Venturino. A viral transmission model for foxes-cottontails-hares interaction: Infection through predation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5965-5997. doi: 10.3934/dcdsb.2021158 [18] Hui Miao, Zhidong Teng, Chengjun Kang. Stability and Hopf bifurcation of an HIV infection model with saturation incidence and two delays. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2365-2387. doi: 10.3934/dcdsb.2017121 [19] Stephen Pankavich, Nathan Neri, Deborah Shutt. Bistable dynamics and Hopf bifurcation in a refined model of early stage HIV infection. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 2867-2893. doi: 10.3934/dcdsb.2020044 [20] Hossein Mohebbi, Azim Aminataei, Cameron J. Browne, Mohammad Reza Razvan. Hopf bifurcation of an age-structured virus infection model. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 861-885. doi: 10.3934/dcdsb.2018046

2018 Impact Factor: 1.313

## Metrics

• PDF downloads (31)
• HTML views (0)
• Cited by (20)

## Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]