This study develops and analyzes a nonlinear eco-epidemiological model describing the interaction between susceptible phytoplankton, infection-induced vulnerable phytoplankton, and zooplankton predators. The model incorporates viral infection in the prey population, toxin-mediated defense by phytoplankton, and differential predation on susceptible and infected hosts. The system exhibits a transcritical bifurcation around the infection-predator-free equilibrium when the infection rate crosses the critical threshold <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\alpha =\delta /K\)</EquationSource></InlineEquation>, and a supercritical Hopf-bifurcation at the positive interior equilibrium, demonstrating that increasing the infection rate can destabilize the system and induce sustained oscillations. To characterize disease persistence, the basic reproduction number <InlineEquation ID="IEq2"><EquationSource Format="TEX">\({\mathcal {R}}_0\)</EquationSource></InlineEquation> is derived, and its threshold form reveals that infection can be suppressed if the equilibrium host density remains below <InlineEquation ID="IEq3"><EquationSource Format="TEX">\(x_3^{*TH}\)</EquationSource></InlineEquation>. Since this threshold increases with zooplankton density, enhanced predation acts as a natural biological control mechanism against disease invasion. Numerical simulations validate the analytical predictions, confirming the presence of bifurcations and oscillatory dynamics consistent with natural plankton cycles. A Partial Rank Correlation Coefficient (PRCC) analysis identifies key parameters governing system behavior: phytoplankton dynamics are most sensitive to K, <InlineEquation ID="IEq4"><EquationSource Format="TEX">\(\alpha\)</EquationSource></InlineEquation>, and <InlineEquation ID="IEq5"><EquationSource Format="TEX">\(\delta\)</EquationSource></InlineEquation>, while infected prey and zooplankton are strongly influenced by k, <InlineEquation ID="IEq6"><EquationSource Format="TEX">\(p_1\)</EquationSource></InlineEquation>, and m. To complement the theoretical analysis, a Physics-Informed Neural Network (PINN) is employed to approximate system trajectories and estimate model parameters. PINN demonstrates superior performance over the least squares method, achieving lower loss values and yielding ecologically meaningful parameter estimates. Overall, this study integrates dynamical systems theory, sensitivity analysis, and machine-learning-based inference to advance understanding of infection-mediated plankton interactions and their ecological implications.

A physics-informed neural network approach to eco-epidemiological dynamics in planktonic food webs

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2026年8月5日

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Anuraj Singh,
Trishla Dhruw,
Deepak Tripathi

摘要

This study develops and analyzes a nonlinear eco-epidemiological model describing the interaction between susceptible phytoplankton, infection-induced vulnerable phytoplankton, and zooplankton predators. The model incorporates viral infection in the prey population, toxin-mediated defense by phytoplankton, and differential predation on susceptible and infected hosts. The system exhibits a transcritical bifurcation around the infection-predator-free equilibrium when the infection rate crosses the critical threshold \(\alpha =\delta /K\), and a supercritical Hopf-bifurcation at the positive interior equilibrium, demonstrating that increasing the infection rate can destabilize the system and induce sustained oscillations. To characterize disease persistence, the basic reproduction number \({\mathcal {R}}_0\) is derived, and its threshold form reveals that infection can be suppressed if the equilibrium host density remains below \(x_3^{*TH}\). Since this threshold increases with zooplankton density, enhanced predation acts as a natural biological control mechanism against disease invasion. Numerical simulations validate the analytical predictions, confirming the presence of bifurcations and oscillatory dynamics consistent with natural plankton cycles. A Partial Rank Correlation Coefficient (PRCC) analysis identifies key parameters governing system behavior: phytoplankton dynamics are most sensitive to K, \(\alpha\), and \(\delta\), while infected prey and zooplankton are strongly influenced by k, \(p_1\), and m. To complement the theoretical analysis, a Physics-Informed Neural Network (PINN) is employed to approximate system trajectories and estimate model parameters. PINN demonstrates superior performance over the least squares method, achieving lower loss values and yielding ecologically meaningful parameter estimates. Overall, this study integrates dynamical systems theory, sensitivity analysis, and machine-learning-based inference to advance understanding of infection-mediated plankton interactions and their ecological implications.