This paper is concerned to a mathematical model for the management of hospital beds when a new infection emerges in the population with the existing infections. The study of this joint dynamics presents formidable mathematical challenges due to a limited number of hospital beds. We have derived the invasion reproduction number, which investigates the potential of a newly emerged infectious disease to persist when some infectious diseases are already invaded the host population. We have shown that the proposed system exhibits transcritical, saddle-node, Hopf, and Bogdanov–Takens bifurcations under certain conditions. We have also shown that the total number of infected individuals may increase if the fraction of the total number of hospital beds is not properly allotted to the existing and a newly emerged infectious disease. The analytically obtained results are verified with the help of numerical simulations.
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2023
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