Modeling the effect of time delay in the increment of number of hospital beds to control an infectious disease

A. K. Misra; Jyoti Maurya; Mohammad Sajid; A. K. Misra; Jyoti Maurya; Mohammad Sajid

doi:10.3934/mbe.2022541

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 11628-11656. doi: 10.3934/mbe.2022541

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Research article

Modeling the effect of time delay in the increment of number of hospital beds to control an infectious disease

1.
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
2.
Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia

Academic Editor: Vladimir Mityushev

Received: 29 June 2022 Revised: 30 July 2022 Accepted: 07 August 2022 Published: 15 August 2022

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.
- hospital beds,
- saddle-node bifurcation,
- backward bifurcation,
- Hopf-bifurcation,
- BT-bifurcation,
- time delay
Citation: A. K. Misra, Jyoti Maurya, Mohammad Sajid. Modeling the effect of time delay in the increment of number of hospital beds to control an infectious disease[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11628-11656. doi: 10.3934/mbe.2022541

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Abstract

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.

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