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Mathematical Modelling of Parasite Dynamics: A Stochastic Simulation-Based Approach and Parameter Estimation via

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A new mathematical model enhances understanding of infectious disease dynamics in gyrodactylid-fish systems. This stochastic simulation model incorporates crucial biological details, improving ecological and epidemiological research.

Keywords:
GyrodactylusApproximate Bayesian computationHost-parasite modellingIndividual-based modelTau-leaping simulation

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Area of Science:

  • Ecology
  • Epidemiology
  • Mathematical Biology

Background:

  • Host-parasite systems, like gyrodactylids and fish, are vital for studying infectious diseases.
  • Existing models lack detail on Gyrodactylus strains and fish microhabitat preferences.
  • Global events highlight the need for advanced infectious disease modeling.

Purpose of the Study:

  • To develop a novel individual-based stochastic simulation model for the gyrodactylid-fish system.
  • To incorporate species-specific biological data and microhabitat preferences into the model.
  • To compare infection dynamics of different Gyrodactylus strains across host populations.

Main Methods:

  • A hybrid $\tau$-leaping algorithm was employed for stochastic simulation.
  • A modified sequential approximate Bayesian computation (ABC) method was developed.
  • Penalised local-linear regression (L1 and L2 regularisation) was used for model fitting.

Main Results:

  • The new model successfully incorporates detailed biological data for enhanced simulation.
  • Infection dynamics of three gyrodactylid strains across three host populations were compared.
  • The model was fitted to empirical data, addressing key biological questions.

Conclusions:

  • The developed model offers a more comprehensive understanding of the gyrodactylid-fish system.
  • The mathematical model is adaptable to other host-parasite systems.
  • The modified ABC methodologies offer efficient calibration for complex multi-parameter models.