First detection of threshold crossing events under intermittent sensing.

Area of Science:

• Stochastic Processes
• Probability Theory
• Applied Mathematics

Background:

• First passage time is crucial in science and engineering, assuming continuous monitoring.
• Realistic sensors often operate intermittently, necessitating a different metric: first detection time.
• Existing models typically assume continuous sensor activity, limiting applicability.

Purpose of the Study:

• To analyze the first detection time for a birth-death process with an intermittent sensor.
• To establish the relationship between first detection time and first passage time.
• To demonstrate the framework's utility in various applications and infer first passage time from first detection time.

Main Methods:

• Developed analytical methods to derive the first detection time distribution for birth-death processes.
• Utilized simulations to validate the analytical results.
• Applied the framework to compartmental models (SIS, logistic) and birth-death processes with resetting.

Main Results:

• Obtained the first detection time distribution for the studied stochastic process.
• Demonstrated that first detection time is derivable from first passage time.
• Showed excellent agreement between analytical predictions and simulation data.
• Successfully applied the framework to diverse models and addressed the inverse problem.

Conclusions:

• The first detection time is a relevant metric for intermittently monitored stochastic processes.
• The derived relationship between first detection and first passage times offers practical insights.
• The developed framework is versatile and applicable to various scientific and engineering problems.