A pressing challenge in ensuring the safety of buildings and structures is the development of reliable and efficient fire alarm systems. Despite the widespread use of various automatic fire alarm systems, many sensors exhibit high sensitivity to non-target factors such as dust, humidity, and lighting, leading to false alarms. Contemporary research often employs generalized approaches to smoke detection but typically does not account for the dynamic features of smoke propagation and the influence of external interferences. As a result, the quantitative relationship between smoke concentration, false factors, and automatic fire alarm systems response time remains unresolved. The aim of this study is to develop a mathematical model describing this relationship and an algorithm that enhances the accuracy and reliability of sensor activation. A mathematical model has been developed to describe convection and diffusion processes of smoke in an enclosed space, as well as the influence of external factors on the sensor signal. Equations are provided for calculating aerosol concentration, and a mathematical signal model is presented that incorporates the impact of false factors and smoke concentration. A smoke detection algorithm was developed to predict sensor activation time and estimate the probability of false alarms. The proposed mathematical model of the sensor signal, which accounts for smoke concentration and false factors, along with the smoke detection algorithm, can be used to calibrate the sensitivity of fire detectors, improve the accuracy of smoke detection, and reduce the number of false alarms.