Mathematical Models in Biology
Mathematical Models in Biology
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In this study, a four-compartment non-linear mathematical model is proposed to understand plankton dynamics in brackish water bodies. Local stability criteria are derived which are also used to estimate the range of values of model parameters. Numerical experiments and sensitivity tests with different parameters show that of all the seventeen parameters in the model the critical parameters affecting the stability of the solution are the growth rate of the phytoplankton which depends on light and nutrients. As a case study, the model is then applied to Chilika Lagoon (19028'N-19054'N and 85006'E-85036'E), the largest brackish water lagoon with estuarine character on the east coast of India. A distinct salinity gradient exists along the lagoon due to the mixing of freshwater and saline water from the adjoining sea. This salinity gradient has a pronounced effect on the seasonal variability of the freshwater and marine phytoplankton species in the lagoon. The model is tested for different sectors of the lagoon which have distinct characteristics in terms of depth, light penetration, nutrients, salinity and hence planktonic growth. A fine tuning of the model parameters was done in order to validate the model results with the available data of the lagoon. Even in its simplest form, the model is able to reproduce most of the significant characteristics of the planktonic distribution in the lagoon-the bimodal oscillations, major plankton peaks etc.