Transmission Dynamics Model Incorporating Risk Perception and Behavioral Fatigue

The classical SIR model provides a foundational framework for studying transmission dynamics, but its standard form often assumes a fixed transmission rate and therefore cannot directly represent adaptive changes in human behavior. In real transmission processes, individuals may reduce contact when perceived risk rises, while prolonged protection may also generate behavioral fatigue and weaken adherence. To describe this coupled mechanism, this paper extends the classical SIR model by introducing two bounded behavioral variables: risk perception and behavioral fatigue. The effective transmission rate is specified as an exponential function of these variables, which guarantees positivity and captures two opposite effects: risk perception suppresses transmission, whereas fatigue amplifies transmission. Ideal numerical simulations are conducted to compare the classical SIR model, a risk-perception-only model, and a full risk-perception-fatigue model. The results show that risk perception substantially lowers the infection peak and final epidemic size, while behavioral fatigue partially offsets the protective effect and delays the infection peak. Sensitivity analysis further indicates