Coagulation and cell division are both processes that are important in controlling the fate of phytoplankton cells through sedimentation. In this paper, we examine some basic mathematical issues associated with the development of a numerical simulation of an algal aggregation model. The numerical algorithm is then used to examine the basic model behavior.

We study an SIR epidemic model with a variable host population size. We prove that if the model parameters satisfy certain inequalities then competition between n pathogens for a single host leads to exclusion of all pathogens except the one with the largest basic reproduction number. It is shown that a knowledge of the basic reproduction numbers is necessary but not sufficient for determining competitive exclusion. Numerical results illustrate that these inequalities are sufficient but not necessary for competitive exclusion to occur. In addition, an example is given which shows that if such inequalities are not satisfied then coexistence may occur.

In this paper we discuss the asymptotic behavior of a logistic model with distributed growth and mortality rates. In particular, we prove that the entire population becomes concentrated within the subpopulation with highest growth to mortality ratio, and converges to the equilibrium defined by this ratio. Finally, we present a numerical example illustrating the theoretical results.

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Coagulation of phytoplankton is a fundamental mechanism for vertical ux of carbon in the ocean. This process is dependent on parameters that are not available from experimental data, such as the encounter rate of particles, the contact e ciency of unlike particles and the probability of sticking upon contact. Fragmentation, the breakup of large particles into two smaller ones has been observed in the ocean, but very little modeling e ort for incorporating this process in the dynamics of phytoplankton has been attempted. In this paper we incorporate fragmentation process into a nonlinear hyperbolic equation that describes the evolution of a size structured algal population with the aggregation model. We examine through numerical simulation the e ect of fragmentation on the dynamics of phytoplankton. We present convergence theory for estimating parameters in this model using nonlinear least squares t. The least square method is then tested numerically in ideal cases where the data is the model output with some added noise.