Analyzing dengue fever with constrained medical resources: A dynamical systems approach.

Dengue fever, a major mosquito-borne viral disease, poses a significant public health threat, particularly in high-incidence countries like Brazil, where rising cases strain limited medical resources. We analyze the impact of constrained medical resources, specifically hospital bed capacity, on dengue transmission dynamics. A novel compartmental model is developed where the availability of hospital beds (B) is a key parameter governing treatment access. Employing classical linearization theory, we conduct a comprehensive stability analysis of the system equilibrium points. Systematic bifurcation analysis, utilizing center manifold theory and normal form theory, reveals complex dynamical behaviors: backward bifurcation (indicating disease persistence for basic reproduction numbers R0<1), Saddle-node bifurcation, Hopf bifurcation (giving rise to periodic solutions), and a codimension-2 Bogdanov-Takens bifurcation. Model validation is performed using incidence data from the São Paulo, Brazil dengue outbreak, enabling parameter estimation and calculation of R0. Sensitivity analysis identifies key parameters for disease control. Crucially, hospital bed capacity B exhibits a threshold regulatory effect: below a critical value, backward bifurcation occurs, sustaining endemicity even when R0<1; above the critical value, increasing beds initially reduces infection prevalence, but can subsequently induce periodic oscillations via Hopf bifurcation before further reducing disease burden. This demonstrates that medical resource constraints fundamentally alter epidemic outcomes through nonlinear dynamical mechanisms.