A multiobjective optimal control problem for the dynamics of an infectious disease with limited healthcare facilities...

Infectious diseases remain a significant threat to global public health, often causing substantial economic burdens. Effective disease management requires an integrated approach involving healthcare facilities, particularly hospital bed capacity, and vaccination campaigns. A four-dimensional mathematical model is investigated to study the dynamics of an emerging infectious disease, considering both vaccination efforts and the limitations of healthcare resources. The model undergoes a series of local bifurcations, including transcritical (both forward and backward), saddle-node, Hopf (supercritical, subcritical, and Bautin), and Bogdanov-Takens bifurcations, revealing the complex dynamics that govern disease transmission and control. To derive optimal control strategies, we apply a multiobjective optimal control approach, transforming the problem into a multiobjective optimization problem and solving it using the $ϵ$ -constraint method. The analysis of Pareto optimal fronts provides valuable insights into the relative effectiveness of varying vaccination and hospitalization strategies under different transmission rates. The numerical results validate the analytical findings and provide comprehensive insight into the best strategies to minimize the infected individuals and associated cost. One such result reveals that the use of saturation-type cost functions offers a cost-efficient approach for managing intervention resources, while more comprehensive cost models may incur higher implementation costs.