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Bifurcation analysis and optimal control of an epidemic model with limited number of hospital beds

International Journal of Biomathematics 2023年第4期16卷 229-253页

作者： A.K.Misra Jyoti Maurya Department of Mathematics Institute of Science Banaras Hindu UniversityVaranasi 221005India

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(Ro)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.

关键词： hospital beds Hopf-bifurcation saddle-node bifurcation transcritical bifurcation Bogdanov-Takens bifurcation optimal control

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SEIHCRD Model for COVID-19 Spread Scenarios,Disease Predictions and Estimates the Basic Reproduction Number,Case Fatality Rate,hospital,and ICU beds Requirement

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Computer Modeling in Engineering & Sciences 2020年第12期125卷 991-1031页

作者： Avaneesh Singh Manish Kumar Bajpai PDPM Indian Institute of Information Technology Design and ManufacturingJabalpur482005India

We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.

关键词： COVID-19 coronavirus SIER model SEIHCRD model parameter estimation mathematical model India Brazil United Kingdom United States Spain Italy hospital beds ICU beds basic reproduction number case fatality rate

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