arXiv subjects

Xinxin Tian

Publications and source records attributed to Xinxin Tian.

3 recordsLinked to original sources

arXiv2026

Stability and Hopf Bifurcation of a Delayed SVIRS Epidemic Model with Media Coverage

This paper formulates and analyzes a delayed SVIRS epidemic model incorporating media coverage effects, vaccination, waning immunity, temporary post-recovery immunity, saturated treatment, and delayed behavioral responses induced by media coverage. The positivity and uniform boundedness of solutions are established, the basic reproduction number is derived, and the local and global asymptotic stability of the disease-free and endemic equilibria is investigated. Taking the media-induced behavioral delay as the Hopf bifurcation parameter, a critical delay threshold is obtained, beyond which the endemic equilibrium loses stability and periodic oscillations emerge. Center manifold and normal form theories are applied to determine the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions, while a global Hopf bifurcation theorem is used to establish the unbounded continuation of the periodic solution branch. Numerical simulations confirm the theoretical results and indicate that stronger media intervention can suppress epidemic oscillations and enhance system stability. These findings reveal the coupled effects of multiple epidemiological mechanisms and delayed media responses, providing theoretical support for the design of effective infectious disease control strategies.

math.DS↗

arXiv2025

Stability and Hopf bifurcation analysis of an age-structured SVIRS epidemic model with temporary immunity

In this paper, we investigate an SVIRS epidemic model that incorporates both temporary immunity and an age-structured recovery process. By reformulating the system as a non-densely defined abstract Cauchy problem, we establish the existence and uniqueness of solutions and derive the basic reproduction number $ \mathcal{R}_0 $. The stability of the equilibria is analyzed through the associated characteristic equations, and the occurrence of Hopf bifurcation near the endemic equilibrium is rigorously demonstrated. Our theoretical results reveal that temporary immunity plays a crucial role in shaping the stability of the endemic state. Finally, numerical simulations are carried out to verify and illustrate the analytical findings.

math.DS↗

arXiv2025

Stability and Hopf bifurcation analysis of an HIV infection model with latent reservoir, immune impairment and delayed CTL immune response

In this paper, we develop a dynamic model of HIV infection that incorporates latent hosts, cytotoxic T lymphocyte (CTL) immunity, saturated incidence rates, and two transmission mechanisms: virus-to-cell and cell-to-cell transmission. The model has three kinds of delays: intracellular delay, replication of viruses delay, immune response delay. Initially, the model's solutions are confirmed to be both nonnegative and bounded for nonnegative initial values. Subsequently, two biologically critical parameters were identified: the virus reproduction number $\mathcal{R}_0$ and the immune reproduction number $\mathcal{R}_1$. Thereafter, by invoking LaSalle's principle of invariance alongside Lyapunov functionals, we establish stability criteria for each equilibrium. The results indicate that the stability of the endemic equilibrium may be altered by a positive immune delay, whereas intracellular and viral replication delays do not affect the equilibria. By considering the delay in the immune response as a bifurcation-inducing threshold, we derive the exact conditions necessary for these stability transitions. Further analysis shows that increasing the immune delay destabilizes the endemic equilibrium, inducing a Hopf bifurcation. Additionally, using the center manifold theorem and normal form theory, we explored the direction and stability of Hopf bifurcations in detail. To corroborate these theoretical results, numerical simulations are systematically conducted.

math.DS↗