Global dynamics of a non-smooth SIV system with uncertain effective vaccine protection rate

• Published in: Nonlinear dynamics Vol. 112; no. 10; pp. 8739 - 8760
• Main Authors: Wang, Dongshu, Luo, Shifan, Li, Wenxiu
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.05.2024; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Control; Differential equations; Disease control; Dynamical Systems; Effectiveness; Engineering; Fields (mathematics); Immunization; Mathematical analysis; Mathematical models; Mechanical Engineering; Original Paper; Qualitative analysis; Thresholds; Vaccines; Vibration; Vaccine protection rate; Stability; Filippov system; Global dynamics; Threshold
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-024-09499-7

This study focuses on a specific class of SIV systems and investigates the impact of vaccine efficacy and control measures on disease control. We utilize piecewise smooth functions to describe the efficacy of the vaccine, which consists of three segments. To accurately simulate complex factors in real-life scenarios, such as the number of infected individuals and the ratio of infected to vaccinated individuals, we consider their influence on vaccine efficacy. Therefore, the incorporation of piecewise smooth functions for modeling aligns with reality, offering improved accuracy and interpretability. Based on the qualitative theory of discontinuous differential equations, Filippov convex analysis, vector field analysis and some analysis techniques, we systematically examine the global dynamical behavior of discontinuous SIV systems. These theoretical findings carry significant importance in shaping vaccination strategies and guiding practical efforts. It is vital to highlight that we establish two distinct thresholds based on the number of infected individuals and the ratio of infected to vaccinated individuals. Unlike previous studies that have employed threshold strategies, our approach encompasses a more comprehensive and detailed selection of thresholds. Additionally, our threshold selection results in the system exhibiting three sliding-mode domains and two pseudo-equilibrium points, thereby showcasing highly complex bistable or tristable global dynamical behavior. Finally, through numerical simulations, we validate the chosen thresholds and two quantitative values related to vaccine efficacy while exploring optimal vaccine effectiveness. These research findings offer valuable academic insights, contributing to a deeper comprehension of the impact of vaccination and its role in disease control.