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Antonio Di Crescenzo1, Paola Paraggio1, Patricia Román-Román2,3

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This study introduces a novel lognormal diffusion model for multi-stage population growth, offering two statistical inference methods for parameter estimation. The model is validated with simulations and applied to epidemiological data.

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Area of Science:

  • Mathematical Biology
  • Statistical Modeling
  • Population Dynamics

Background:

  • Population growth often exhibits complex, multi-stage dynamics.
  • Accurate modeling of these stages is crucial for understanding population evolution.
  • Existing models may not fully capture the nuances of prolonged growth phases.

Purpose of the Study:

  • To introduce a lognormal diffusion process with a multisigmoidal logistic mean for modeling multi-stage population growth.
  • To develop and compare statistical inference procedures for estimating model parameters.
  • To analyze the first-passage-time problem for this diffusion process.

Main Methods:

  • Utilized a lognormal diffusion process with a multisigmoidal logistic mean.
  • Developed two maximum likelihood estimation procedures: critical points resolution and simulated annealing.
  • Conducted simulation studies for validation and applied the model to epidemiological data.

Main Results:

  • Successfully modeled population growth reaching maximum levels after multiple stages.
  • Demonstrated the efficacy of both critical points resolution and simulated annealing for parameter estimation.
  • Validated the model and estimation strategies through simulations and a real-world epidemiological case study.

Conclusions:

  • The proposed lognormal diffusion model effectively captures complex, multi-stage population growth.
  • The presented statistical inference methods provide reliable parameter estimation.
  • The model shows potential for applications in epidemiology and other fields studying staged growth phenomena.