A fast numerical integration scheme for clonal expansion processes on graphs

Area of Science:

• Mathematical Biology
• Computational Oncology
• Stochastic Processes

Background:

• Compound birth-death processes are standard for modeling cancer age-incidence curves.
• Current methods are limited to linear models, lacking generalizability to complex biological networks.
• Existing approaches like simulations or mean-field approximations have accuracy limitations.

Purpose of the Study:

• To develop a numerical integration scheme for birth-death processes on arbitrary directed graphs.
• To overcome the limitations of existing methods for modeling cancer progression on complex structures.
• To enable accurate computation of survival probabilities without full stochastic simulations.

Main Methods:

• Developed a novel numerical integration scheme for first-order birth-death processes.
• Applied the scheme to models represented by arbitrary directed graphs.
• Validated the method by inferring parameters from simulated data.

Main Results:

• The new scheme accurately computes survival probabilities for birth-death processes on directed graphs.
• It bypasses the need for computationally expensive stochastic simulations.
• Demonstrated successful parameter inference for a graphical model.

Conclusions:

• The presented numerical method offers an efficient and accurate alternative for modeling cancer progression on complex graphs.
• This advancement extends the applicability of birth-death processes to more realistic biological network structures.
• The method facilitates more precise parameter estimation in cancer modeling studies.