ON THE STABILITY OF THE “INFECTION-FREE” ALMOST PERIODIC SOLUTION IN AN IMPULSIVE SIR MODEL

Abstract

The paper investigates the stability of an infection-free almost periodic solution of an impulsive SIR model describing the spread of infection in biological systems or vulnerability to malicious software in computer networks. The model accounts for impulsive perturbations interpreted as vaccination or antivirus updates occurring at nonperiodic moments in time. The existence and asymptotic stability of an almost periodic solution are proved under certain conditions imposed on the sequence of impulses and the time intervals between them. The analysis is based on the theory of impulsive differential equations and almost periodic functions, employing Lyapunov stability criteria for the corresponding linearized system. The obtained results generalize known periodic cases and provide a theoretical foundation for constructing robust control strategies in nonlinear impulsive systems arising in epidemiological and cybernetic models.