Algicidal effect of Bacillus cereus on Microcystis aeruginosa: An ODE perspective

Harmful algal blooms in eutrophic waters motivate the development of effective and environmentally compatible control strategies. Algicidal bacteria can inhibit algae through direct contact (enzyme-mediated cell-wall disruption) and indirect action via secreted extracellular algicidal compounds. Guided by experimental observations, we develop a mechanistic ordinary differential equation model that integrates both pathways and explicitly represents three lysis modes: bacterial suspension, bacterial cells, and cell-free filtrate. The model reproduces observed time courses of algal density and bacterial abundance across treatments through parameter estimation, and it reveals a rich dynamical structure including forward and backward bifurcations, transcritical and saddle-node bifurcations, and Hopf bifurcations, implying threshold responses, potential bistability, and oscillatory regimes under plausible conditions. When the initial algal density is 10⁵ cells/ml, the predicted algicidal rates by day 6 are 99.99%, 99.99%, and 84.2% for bacterial suspension, bacterial cells, and filtrate, respectively; for 10⁶ cells/ml the corresponding rates decrease to 82.5%, 69.38%, and 45.1%. Analysis indicates that direct lysis is dominant, while indirect lysis provides auxiliary suppression and can act synergistically with direct effects to reduce algal biomass. The model further predicts delayed and weakened control when initial algal density exceeds a critical level associated with severe blooms ( ∼ 10⁶ cells/ml), and we provide forecasts for an initial density of 10⁷ cells/ml.