Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal...

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.