Birth/birth-death processes and their computable transition probabilities with biological applications

Area of Science:

• Mathematical Biology
• Computational Statistics
• Population Dynamics

Background:

• Traditional birth-death processes model single populations, limiting analysis of interacting biological systems.
• Existing methods for bivariate processes are computationally intensive, hindering statistical inference.
• Lack of efficient bivariate transition probability calculations restricts modeling of complex ecological and epidemiological systems.

Observation:

• Many biological systems involve interactions between multiple populations.
• Evaluating finite-time transition probabilities for bivariate processes is computationally challenging.
• Current inference methods for bivariate models are often indirect or limited to small systems.

Findings:

• Introduced a tractable bivariate birth/birth-death process with nonlinear rates.
• Developed an efficient algorithm using continued fraction representation for transition probabilities.
• Demonstrated applicability to molecular epidemiology, macro-parasite evolution, and infectious disease modeling, including the susceptible-infectious-removed (SIR) model.

Implications:

• Enables direct statistical inference for previously intractable bivariate population models.
• Facilitates more accurate parameter estimation in complex systems like the SIR model.
• Provides a computationally efficient alternative to existing methods for analyzing interacting populations.