Analysis of a Filippov-type SIV epidemic model with switching dynamics: Effects of vaccination, media awareness, and treatment interventions

Arjun Kumar, Uma S. Dubey and Balram Dubey

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 247, issue C, 422-452

Abstract: Mass media reporting during epidemics can significantly influence public behavior and shape societal attitudes. In this study, we construct a Filippov system to examine how media coverage, vaccination, and treatment interact to affect disease transmission. The model incorporates a threshold policy in which interventions are triggered when the number of infected individuals exceeds a critical value. At the same time, a constant rate of media awareness is maintained throughout the epidemic. When the basic reproduction number (R2) is below one, these measures may facilitate disease eradication; however, the presence of backward bifurcation cannot prevent guaranteed elimination. Our analysis explores the global stability of the Filippov model for varying infected thresholds (Ic), emphasizing the existence and stability of equilibria and the nature of sliding-mode dynamics. Depending on the chosen threshold, the system may converge to the endemic equilibrium of the continuous subsystem, a pseudo-equilibrium on the switching manifold, or another endemic equilibrium. Appropriate threshold selection can thus constrain infection levels to remain below a critical or predetermined value. By investigating sliding-mode behavior, boundary equilibrium bifurcations, and the system’s global properties, we find that the pseudo-equilibrium can sometimes be globally stable. Alternatively, the system may exhibit bistability, involving combinations of pseudo-equilibrium, endemic, and disease-free equilibrium (DFE). The resulting long-term infection levels depend on whether parameter choices and initial conditions determine a zero value, a fixed intermediate value, or a higher endemic value. Global sensitivity analysis using the PRCC method identifies the key parameters that influence both the threshold values and the overall both system. These results highlight the potential of threshold-based intervention strategies and reveal the inherent difficulties in controlling infectious diseases, even under ideal conditions with highly effective vaccines, sustained media engagement, and adequate treatment capacity.

Keywords: Global dynamics; Filippov; Stability; Bifurcation; Threshold; Sensitivity (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:247:y:2026:i:c:p:422-452

DOI: 10.1016/j.matcom.2026.03.023

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