Modeling the synergistic effects of resource-constrained testing and vaccination on emerging epidemics dynamics

We develop a novel compartmental model integrating a piecewise-saturated vaccination rate and a saturated testing function to investigate how constrained medical resources impact the control of emerging infectious diseases. Theoretical analysis characterizes the basic reproduction number R₀ and identifies critical thresholds linked to complex bifurcation phenomena, including backward and Hopf bifurcations. Numerical simulations further reveal that increasing daily testing capacity effectively reduces infection prevalence and simplifies epidemic dynamics. Our study highlights the synergistic effects of vaccination and testing under resource constraints: while enhancing vaccination coverage improves outbreak control at moderate to high testing levels, it may paradoxically worsen infections when testing capacity is severely limited, especially for highly transmissible pathogens. These findings offer important theoretical insights and practical guidance for optimizing intervention strategies amid limited resources.