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