Ecological Modelling 151 (2002) 15 – 28 Viral infection on phytoplankton – zooplankton system — a mathematical model J. Chattopadhyay a, *, S. Pal b a Embryology Research Unit, Indian Statistical Institute, 203, B.T. Road, Calcutta 700 035, India b Ramakrishna Mission Viekananda Centenary College, Rahara, 24 Parganas (N), India Received 7 November 2000; received in revised form 6 July 2001; accepted 30 July 2001 Abstract The present paper deals with the problem of a phytoplankton–zooplankton system in which some of the phytoplankton cells are infected by some viral infection and forming an infected group. The proposed model is similar to the model of Beltrami and Carroll (J. Math. Biol. 32 (1994) 857) and the model of Venturino (Math. Popul. Dyn. Anal. Heterogeneity 1 (1995) 381). The conditions for the coexistence of the populations are presented. The essential mathematical features are analyzed with the help of local stability, global stability and numerical analysis to compare the findings of Beltrami – Carroll and Venturino. Our conclusion is that the role of viral infection in plankton community is very much unpredictable and model dependent. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Susceptible and infected phytoplankton; Grazer; Non-existence of periodic solutions; Persistence www.elsevier.com/locate/ecolmodel 1. Introduction Plankton are the basis of all aquatic food chain. Phytoplanktons are very small, usually single celled organisms, chiefly diatoms, that photosyn- thesize just like plants do and occupy the first trophic level in food chain. Phytoplankton pro- vides oxygen for human life and food for marine life. The dynamics of rapid increase or decrease of plankton populations is an important subject for marine plankton ecology. Several authors argued that there has been global increase in harmful phytoplankton blooms in recent decades (see Hal- legraeff, 1993). The role of virus in the termina- tion of algal blooms (Emiliania huxleyi, Micromonas pusilla and Noctiluca scintillans ) was modelled by Beltrami and Carroll (1994). The predicted dynamics of an infected monospecific phytoplankton bloom shown in the model resem- bles that observed in natural blooms. Viral infec- tions are responsible for cell lysis and for the collapse for E. huxleyi blooms in mesocosms (Bratbak et al., 1995). Viruses are sometimes strain specific and hence increase genetic diversity (Nagasaki and Yamaguchi, 1997). Pathogens (virus, bacteria and parasite) are considered to be important for the termination of phytoplankton * Corresponding author. Tel.: +91-33-55-68049; fax: +91- 33-57-76680. E-mail address: joydev@isical.ac.in (J. Chattopadhyay). 0304-3800/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII:S0304-3800(01)00415-X