<abstract><p>One of the key factors to control the spread of any infectious disease is the health care facilities, especially the number of hospital beds. To assess the impact of number of hospital beds and control of an emerged infectious disease, we have formulated a mathematical model by considering population (susceptible, infected, hospitalized) and newly created hospital beds as dynamic variables. In formulating the model, we have assumed that the number of hospital beds increases proportionally to the number of infected individuals. It is shown that on a slight change in parameter values, the model enters to different kinds of bifurcations, e.g., saddle-node, transcritical (backward and forward), and Hopf bifurcation. Also, the explicit conditions for these bifurcations are obtained. We have also shown the occurrence of Bogdanov-Takens (BT) bifurcation using the Normal form. To set up a new hospital bed takes time, and so we have also analyzed our proposed model by incorporating time delay in the increment of newly created hospital beds. It is observed that the incorporation of time delay destabilizes the system, and multiple stability switches arise through Hopf-bifurcation. To validate the results of the analytical analysis, we have carried out some numerical simulations.</p></abstract>

To explore the impact of available and temporarily arranged hospital beds on the prevention and control of an infectious disease, an epidemic model is proposed and investigated. The stability analysis of the associated equilibria is carried out, and a threshold quantity basic reproduction number (R0) that governs the disease dynamics is derived and observed whether it depends both on available and temporarily arranged hospital beds. We have used the center manifold theory to derive the normal form and have shown that the proposed model undergoes different types of bifurcations including transcritical (backward and forward), Bogdanov–Takens, and Hopf-bifurcation. Bautin bifurcation is obtained at which the first Lyapunov coefficient vanishes. We have taken advantage of Sotomayor’s theorem to establish the saddle-node bifurcation. Numerical simulations are performed to support the theoretical findings.

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This paper deals with a three-dimensional nonlinear mathematical model to analyze an epidemic’s future course when the public healthcare facilities, specifically the number of hospital beds, are limited. The feasibility and stability of the obtained equilibria are analyzed, and the basic reproduction number ([Formula: see text]) is obtained. We show that the system exhibits transcritical bifurcation. To show the existence of Bogdanov–Takens bifurcation, we have derived the normal form. We have also discussed a generalized Hopf (or Bautin) bifurcation at which the first Lyapunov coefficient evanescences. To show the existence of saddle-node bifurcation, we used Sotomayor’s theorem. Furthermore, we have identified an optimal layout of hospital beds in order to control the disease with minimum possible expenditure. An optimal control setting is studied analytically using optimal control theory, and numerical simulations of the optimal regimen are presented as well.